Development of Solar Cells: Theory and Experiment 3030694445, 9783030694449

Table of contents :
Preface
Contents
Contributors
Recent Progress in Perovskite Solar Cell: Fabrication, Efficiency, and Stability
1 Introduction
1.1 The Structure and Properties of PSC
1.2 Preparation Techniques for PSC
2 The Efficiency Improvement of PSC
2.1 Materials and Microstructure
2.2 Advanced Fabrication Methods and Techniques
3 PSC Stability
3.1 Moisture Stability
3.2 UV Light Stability
3.3 Thermal Stability
4 Other Issues
5 Conclusions and Perspectives
References
State-of-the-Art of Solution-Processed Crystalline Silicon/Organic Heterojunction Solar Cells: Challenges and Future
1 Introduction
2 PEDOT:PSS and PEDOT:PSS/c-Si Heterojunction Solar Cells
2.1 Electronic Structure of PEDOT:PSS/c-Si Heterojunction Solar Cells
2.2 Fabrication Procedure of PEDOT:PSS/n-Si Heterojunction Solar Cells
3 Carrier Transport in PEDOT:PSS/n-Si Heterojunction: Schottky or p+n Junction?
3.1 Modeling of PEDOT:PSS/n-Si Junction
3.2 Analysis of PEDOT:PSS/n-Si Junction
3.3 Junction Type of PEDOT:PSS/n-Si
3.4 Evolution of the PEDOT:PSS/c-Si Heterojunction Solar Cells
4 Challenges of PEDOT:PSS/c-Si Heterojunction Solar Cells
4.1 Light Soaking Stability
4.2 Air Storage Stability
5 Future Directions to PEDOT:PSS/n-Si Heterojunction Solar Cells
5.1 Use of BSF Layer for Higher Open-Circuit Voltage
5.2 Efficient Light Management: ARC Design for PEDO:PSS/n-Si Heterojunction Solar Cells
6 Conclusions
References
Structure, Electronic, and Charge Transfer Properties of Organic Photovoltaics from Density Functional Theory Methods
1 Introduction
2 The P3HT/PCBM OPV
3 Structure of the P3HT/PCBM Interface
3.1 The Model System
3.2 Computational Details
3.3 The PES of the P3HT/PCBM Dimer
4 QTAIM Properties
5 Optical Properties
6 Charge Separation Rates
7 Conclusions
References
Dye-Sensitized Solar Cells: A Brief Historical Perspective and Uses in Multijunction Devices
1 A Brief Historical Perspective
2 Multijunction System Performances and Analysis
3 DSC/DSC Multijunction Systems
4 DSC/OPV Multijunction Systems
5 DSC/PSC Multijunction Systems
6 DSC/CIGS Multijunction Systems
7 DSC/Silicon Multijunction Systems
8 Conclusions
References
Delving Charge-Transfer Excitations in Hybrid Organic–Inorganic Hetero Junction of Dye-Sensitized Solar Cell: Assessment of Excitonic Optical Properties Using the GW and Bethe–Salpeter Green’s Function Formalisms
1 Introduction
2 Theoretical Framework
2.1 GW Formalism
2.2 Bethe–Salpeter Equation
3 Applications
3.1 Estimation of Electronic Band Gap and Optical Spectra of DSSC Photoanode Material (TiO2)
3.2 Calculations of Low-Lying Charge-Transfer Excitation Energies of Coumarin-based DSSC Photosensitizers
3.3 Estimation of Quasi-Particle Energy Levels in Organic Chromophores and Dye/Semiconductor Interfaces and Simulation of Photoelectron Spectroscopy of Organic–Inorganic Hybrid
3.4 Determination of Rate of Interfacial Electron Injection and Open-Circuit Voltage in DSSC
3.5 Large-Scale GW-BSE Formulation for Evaluating Excitonic Energies and Optical Absorption Spectra of Dye/Semiconductor Systems in DSSC
4 Summary and Outlook
References
Promising DSSCs Involving Organic D–π–A and Similar Structures for n- and p-type Semiconductors—A Theoretical Approach
1 Introduction
1.1 Requirement of Energy
1.2 Sources of Energy
2 Why Solar Energy?
2.1 What Are Photovoltaic/Solar Cells?
2.2 Different Kinds of Solar Cells
3 Why DSSCs Are Important
4 Development of New Dye Sensitizers
4.1 Studies on Metal-Centered Dyes
4.2 Studies on Organic Dyes
5 My Contributions
5.1 Theoretical Calculation Strategy
6 Conclusion
References
Application of QSPR Modeling in Designing and Prediction of Power Conversion-Efficient Solar Cell
1 Introduction
2 QSPR Modeling and Its Importance in Solar Cell
3 How QSPR Works for Solar Cell Modeling
4 Successful QSPR Models in Solar Cell
4.1 Modeling Study on DSSC
4.2 Modeling Study on PSCs
4.3 QSPR Modeling of Absorption Maxima
5 Designing of Solar Cells, Employing QSPR and Machine Learning Models
6 Databases of Solar Cells for Modeling
7 Future Avenues
7.1 Webserver for %PCE Prediction of Solar Cell
7.2 Global Models
8 Conclusion
References
Computational Screening of Organic Dye-Sensitizers for Dye-Sensitized Solar Cells: DFT/TDDFT Approach
1 Introduction
2 Working Principle of DSSCs
3 Essential Criteria of an Efficient Sensitizer
4 Factors Affecting the PCE of DSSCs
4.1 Short-Circuit Current Density (JSC)
4.2 Open-Circuit Voltage (Voc)
4.3 Interfacial Properties
4.4 Planar Electrostatic Average Protentional
4.5 Photostability in the Excited State of the Dyes
4.6 TDDFT Nonadiabatic Molecular Dynamics (NAMD) Simulation
5 Conclusions
References
Chemometric Modeling of Absorption Maxima of Carbazole Dyes Used in Dye-Sensitized Solar Cells
1 Introduction
1.1 Mechanism of DSSCs
1.2 Ideal Characteristics of the Dye Used in DSSCs
2 Materials and Methods
2.1 Dataset Preparation
2.2 Structure Representation
2.3 Descriptor Calculation and Dataset Division
2.4 Model Development and Validation
2.5 Applicability Domain Assessment
3 Results and Discussion
4 Conclusion
References
Index

Citation preview

Challenges and Advances in Computational Chemistry and Physics 32 Series Editor: Jerzy Leszczynski

Juganta K. Roy Supratik Kar Jerzy Leszczynski   Editors

Development of Solar Cells Theory and Experiment

Challenges and Advances in Computational Chemistry and Physics Volume 32

Series Editor Jerzy Leszczynski, Department of Chemistry and Biochemistry, Jackson State University, Jackson, MS, USA

This book series provides reviews on the most recent developments in computational chemistry and physics. It covers both the method developments and their applications. Each volume consists of chapters devoted to the one research area. The series highlights the most notable advances in applications of the computational methods. The volumes include nanotechnology, material sciences, molecular biology, structures and bonding in molecular complexes, and atmospheric chemistry. The authors are recruited from among the most prominent researchers in their research areas. As computational chemistry and physics is one of the most rapidly advancing scientific areas such timely overviews are desired by chemists, physicists, molecular biologists and material scientists. The books are intended for graduate students and researchers. All contributions to edited volumes should undergo standard peer review to ensure high scientific quality, while monographs should be reviewed by at least two experts in the field. Submitted manuscripts will be reviewed and decided by the series editor, Prof. Jerzy Leszczynski.

More information about this series at http://www.springer.com/series/6918

Juganta K. Roy · Supratik Kar · Jerzy Leszczynski Editors

Development of Solar Cells Theory and Experiment

Editors Juganta K. Roy Department of Chemistry, Physics and Atmospheric Sciences, Jackson State University, Interdisciplinary Center for Nanotoxicity Jackson, MS, USA

Supratik Kar Department of Chemistry, Physics and Atmospheric Sciences, Jackson State University, Interdisciplinary Center for Nanotoxicity Jackson, MS, USA

Jerzy Leszczynski Deparment of Chemistry, Physics and Atmospheric Sciences, Jackson State University, Interdisciplinary Center for Nanotoxicity Jackson, MS, USA

ISSN 2542-4491 ISSN 2542-4483 (electronic) Challenges and Advances in Computational Chemistry and Physics ISBN 978-3-030-69444-9 ISBN 978-3-030-69445-6 (eBook) https://doi.org/10.1007/978-3-030-69445-6 © Springer Nature Switzerland AG 2021 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

For Magdalena, Alina, Jazlyn, Rituja, Shubhika

Preface

To provide fossil fuel alternatives, novel approaches are necessary. Photovoltaic technologies have emerged as a compelling solution for sustainable electricity generation by harvesting solar energy. Different photovoltaic technologies from highefficiency crystalline to rapidly growing Organic Photovoltaics (OPV) materialized since discovering the photoelectric effect by Edmond Becquerel in 1839 [1]. Firstgeneration solar cells are based on silicon wafers. Second-generation solar cells are a combination of amorphous silicon (a-Si) and thin films. The third-generation includes a polymer, dye-sensitized, along with perovskite solar cells. The latter also can be categorized as emerging photovoltaics [2, 3]. Dye-sensitized solar cells (DSSCs) represent one of the diverse OPV, which has a comprehensive spectrum for molecular engineered sensitizers combined with nanostructured TiO2 semiconductors to improve thePphotoconversion Efficiency (PCE) [4]. But the commercialization of DSSCs is very challenging due to their low PCE and stability. It has been proposed that the maximum theoretical efficiency can be achieved by up to 32% by harvesting UV to near IR photons [5]. Currently, DSSCs reached an efficiency of 13.6% using organic triazatruxene dye sensitizers, and there are ample scopes for further improvements of DSSCs [6]. DSSCs and organic Polymer Solar Cells (PSCs) are the most promising, environmentally friendly, and cost-effective solar cells. PSCs are a member of excitonic photovoltaics due to strongly bound electron-hole pairs generated after light excitation. As this type of solar cell acts as a bilayer, it is often called a Bulk-Heterojunction cell (BHJ). One suitable example of BHJ cell is P3HT/PCBM where poly(3- hexylthiophene) (P3HT) and the fullerene derivative [6,6]-phenyl-C61-butyric acid methyl ester (PCBM) used as donor and acceptor, respectively. The conventional PSC based on the pi-conjugated donor polymer and fullerene acceptor reached the PCE value of 10%, to date [7, 8]. Intrinsic limitations like using only a narrow part of the spectral region, modulation of energy levels, and morphology impede the further improvement of polymer/fullerene solar cells [9]. To overcome the limitations, non-fullerene acceptors like small-molecule organic polymer and polymeric acceptors were explored by the scientific community and allow to reach the PCE of 16.5% [10].

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Organic-inorganic-based solar cells like perovskite a metal halide device, change optoelectronic landscapes by achieving PCE values > 25% [11]. Unlike conventional inorganic semiconductors such as Si and GaAs, the perovskite solar cell possesses pronounced dynamic disorder in their crystal structure, enabling the coupling between electronic excitations and lattice vibrations. The electron-phonon coupling has been revealed to restrain the charge-carrier mobilities and develop emission linewidth broadening in hybrid lead halide perovskites [12]. Besides the perovskite matrix, the research also evolves to make the organic Hole Transport Materials (HTMs) more effective as the efficiency losses via interfacial carrier recombination (non-radiative) processes [13, 14]. Those metal halide devices have led to remarkably rapid development in the renewable energy research community. However, intrinsic instability of the perovskite layers and the charge transport layer when coming into contact with moisture makes this type of solar cell vulnerable. Another class of photovoltaics is dopant-free silicon (Si)/organic Heterojunction Solar Cells (HSCs), very much promising due to the availability of raw materials and the nearly optimum bandgap of Si to harvest more sunlight [15, 16]. Different hole-transporting layers like tungsten oxide, vanadium oxide, and poly(3,4-ethylene dioxythiophene):polystyrene (PEDOT:PSS) have been used to ease the band offsets and ultimately increase an efficiency of HSCs. Recently, the HTCs reached the efficiency of over 26% with the use of a combination of c-Si solar cells with an Interdigitated Back Contact (IBC) technology and c-Si/a-Si heterojunction (HJ) technology [17]. The advancement of quantum chemical methodology and availability of efficient computational resources enable studying the different microkinetic of the electron/charge transfer mechanism at the interface or in intramolecular species [14, 18, 19, 20]. Density Functional Theory (DFT) and Time-Dependent DFT (TDDFT) are powerful tools to predict or explore the mechanism of different essential processes in the PVs. Intramolecular charge transfer to intermolecular charge transfer, radiative and nonradiative lifetime can be computed with acceptable accuracy. Hybrid functional like HSE06 is very efficient to predict the band offset of semiconductor or hybrid matrix for perovskite solar cells [21]. Besides, Green;s function (G0 W0 ) approach is based on many-body perturbation theory, Bethe–Salpeter Equation (BSE) methods, excited state dynamics being used to predict the different lifetime constant of the photophysical systems [20]. It is viable to obtain the new atomistic, photophysical properties, and the photophysics of energetic materials precisely through theoretical and computational modeling. Knowledge of most of the quantum chemical properties and the chemical 1D to 3D properties of major structural components of specific solar cells may help design further power-efficient solar cells than the existing ones employing strategies like Quantitative Structure-Property Relationships (QSPRs), machine learning (ML), and artificial intelligence. The QSPR analysis [22] can isolate relatively more efficient materials to start with, followed by the computation of electrochemical and photophysical parameters through quantum chemical studies to establish the best feasible materials for future solar cells.

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The book comprises nine chapters covering fundamental aspects of numerous solar cells that require further research in upcoming days for major commercialization and making of a more durable and efficient solar cell. Chapter “Recent Progress in Perovskite Solar Cell: Fabrication, Efficiency, and Stability” by Zhang et al. discussed the latest progress and fundamentals of Perovskite Solar Cells and provided some useful insights related to Fabrication, Efficiency, and Stability for future study. Chapter “State-of-the-Art of Solution-Processed Crystalline Silicon/Organic Heterojunction Solar Cells: Challenges and Future” prepared by Hossain et al. analyzed the present state-of-the-art solution-processed PEDOT:PSS/n-Si heterojunction solar cells in detail. Additionally, the authors discussed the advent, principle of operation, fabrication process, carrier transport properties, and evolution of the efficiency of the PEDOT:PSS/n-Si heterojunction solar cells followed by the challenges of the solar cells and proposed selected design guidelines for further improvement in the efficiency of the solar cells. Chapter “Structure, Electronic, and Charge Transfer Properties of Organic Photovoltaics from Density Functional Theory Methods” by Rodríguez and Götz reviewed how DFT methods can be employed to characterize interfacial properties, UV-Vis absorption spectra, and photoinduced charge separation in BHJ-OPV donor-acceptor complexes based on semiconducting polymers as donor and fullerene derivatives as acceptor. Chapter “Dye-Sensitized Solar Cells: A Brief Historical Perspective and Uses in Multijunction Devices” by Daniel and Delcamp reported a brief history of the development of solar-to-electric devices for the classically researched solar cell technologies, including Si, CIGS, CdTe, GaAs, OPV, DSC, and PSC devices. These technologies’ relative strengths and weaknesses are also presented along with the importance of multijunction system research toward higher efficiency solar-to-electric systems. Chapter “Delving Charge-Transfer Excitations in Hybrid Organic-Inorganic Heterojunction of Dye-Sensitized Solar Cell: Assessment of Excitonic Optical Properties Using the GW and Bethe–Salpeter Green’s Function Formalisms” by Samanta and Leszczynski highlighted crucial ideas of practical implementation of BetheSalpeter Equation (BSE) involving the computations of single-particle states, quasiparticle energy levels, and the screened Coulomb interaction with the aid of Gaussian atomic basis sets and resolution-of-identity techniques. Additionally, the authors reported the most recent advancements in theoretical methods that employ the Maximally Localized Wannier’s Function (MLWF) and curtail BSE calculations’ overall scaling. The viable applications are subsequently illustrated critically with selected examples. Chapter “Promising DSSCs Involving Organic D–π–A and Similar Structures for n- and p-type Semiconductors—A Theoretical Approach” by Sen illustrated promising DSSCs involving organic D-pi-A and similar structures for n- and p-type semiconductors. Chapter “Application of QSPR Modeling in Designing and Prediction of Power Conversion-Efficient Solar Cell” prepared by Kar et al. discussed the implication

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of QSPR models to explore multiple chemical classes in search of the best possible efficient materials for solar cells with higher %PCE values than those currently on the market. Major QSPR models developed for Dye-Sensitized Solar Cells (DSSCs) and Polymer Solar Cells (PSCs) are thoroughly interpreted. The authors also reported how QSPR models could be implemented in solar cell designing as well as the virtual screening of materials databases. Additionally, solar cell databases and preparation of webserver for future prediction of %PCE are also offered to provide an easy start for beginners. Chapter “Computational Screening of Organic Dye-Sensitizers for Dye-Sensitized Solar Cells: DFT/TDDFT Approach” by Roy et al. highlights DFT and TDDFT frameworks’ importance to design organic dye-sensitizers for DSSCs to predict different photophysical properties. This chapter also includes a basic introduction to the mechanism of DSSCs, based on the energetics of the various constituents of the heterogeneous device. Chapter “Chemometric Modeling of Absorption Maxima of Carbazole Dyes Used in Dye-Sensitized Solar Cells” by Krishna et al. demonstrates the application of QSPR analysis to model absorption maxima of carbazole dyes used in DSSCs employing Partial Least Squares (PLS) based chemometric tool. The statistical results suggested that the model was statistically significant. Most of the model’s descriptors are easily interpretable 2D atom pair descriptors that may be employed to design and develop new carbazole dyes and to predict λmax values before they are synthesized. The Editors express their gratitude to all the authors for their knowledge enlightening contributions in the middle of pandemic COVID-19. Moreover, we thank the reviewers for their time, expertise, and comments to improve the manuscripts’ quality. We believe that this book will help the budding researcher in solar energy and experts in this specific field. Jackson, MS, USA

Juganta K. Roy Supratik Kar Jerzy Leszczynski

References 1. 2. 3. 4. 5. 6.

Bequerel E (1839) Recherches sur les effets de la radiation chimique de la lumière solaire, au moyen des courants électriques. CR Acad Sci 9:145–149. Ostroverkhova O (2016) Organic Optoelectronic Materials: Mechanisms and Applications. Chemical Reviews 116:13279–13412. Rahn Kim M, Ma D (2014) Quantum-Dot-Based Solar Cells: Recent Advances, Strategies, and Challenges. The Journal of Physical Chemistry Letters 6:85–99. O’Regan B, Grätzel M (1991) A low-cost, high-efficiency solar cell based on dye-sensitized colloidal TiO2 films. Nature 353:737–740. Snaith HJ (2010) Estimating the Maximum Attainable Efficiency in Dye-Sensitized Solar Cells. Advanced Functional Materials 20:13–19. Zhang L, Yang X, Wang W, G. Gurzadyan G, Li J, Li X, An J, Yu Z, Wang H, Cai B, Hagfeldt A, Sun L (2019) 13.6% Efficient Organic Dye-Sensitized Solar Cells by Minimizing Energy Losses of the Excited State. ACS Energy Letters 4:943–951.

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Thompson BC, Fréchet JMJ (2008) Polymer-fullerene composite solar cells. Angewandte Chemie (International ed in English) 47:58–77. Gutiérrez-González I, Molina-Brito B, Götz AW, Castillo-Alvarado FL, Rodríguez JI (2014) Structural and electronic properties of the P3HT–PCBM dimer: A theoretical Study. Chemical Physics Letters 612:234–239. Lee C, Lee S, Kim GU, Lee W, Kim BJ (2019) Recent Advances, Design Guidelines, and Prospects of All-Polymer Solar Cells. Chemical Reviews 119:8028–8086. Cui Y, Yao H, Zhang J, Zhang T, Wang Y, Hong L, Xian K, Xu B, Zhang S, Peng J, Wei Z, Gao F, Hou J (2019) Over 16% efficiency organic photovoltaic cells enabled by a chlorinated acceptor with increased open-circuit voltages. Nature Communications 10:2515. National Renewable Energy Laboratory (2019). https://www.nrel.gov/pv/cell-efficiency. html. Accessed on November 1, 2020. Wright AD, Verdi C, Milot RL, Eperon GE, Pérez-Osorio MA, Snaith HJ, Giustino F, Johnston MB, Herz LM (2016) Electron-phonon coupling in hybrid lead halide perovskites. Nature communications 7. Kim H-S, Mora-Sero I, Gonzalez-Pedro V, Fabregat-Santiago F, Juarez-Perez EJ, Park N-G, Bisquert J (2013) Mechanism of carrier accumulation in perovskite thin-absorber solar cells. Nature Communications 4:2242. López-Estrada O, G. Laguna H, Barrueta-Flores C, Amador-Bedolla C (2018) Reassessment of the Four-Point Approach to the Electron-Transfer Marcus–Hush Theory. ACS Omega 3:2130–2140. He J, Wan Y, Gao P, Tang J, Ye J (2018) Over 16.7% Efficiency Organic-Silicon Heterojunction Solar Cells with Solution-Processed Dopant-Free Contacts for Both Polarities. Advanced Functional Materials 28:1802192. He J, Gao P, Ling Z, Ding L, Yang Z, Ye J, Cui Y (2016) High-Efficiency Silicon/Organic Heterojunction Solar Cells with Improved Junction Quality and Interface Passivation. ACS Nano 10:11525–11531. Yoshikawa K, Kawasaki H, Yoshida W, Irie T, Konishi K, Nakano K, Uto T, Adachi D, Kanematsu M, Uzu H, Yamamoto K (2017) Silicon heterojunction solar cell with interdigitated back contacts for a photoconversion efficiency over 26%. Nature Energy 2:17032. Shee J, Head-Gordon M (2020) Predicting Excitation Energies of Twisted Intramolecular Charge-Transfer States with the Time-Dependent Density Functional Theory: Comparison with Experimental Measurements in the Gas Phase and Solvents Ranging from Hexanes to Acetonitrile. J. Chem. Theory Comput. 16:6244–6255. Azpiroz JM, Infante I, Angelis FD (2015) First-Principles Modeling of Core/Shell Quantum Dot Sensitized Solar Cells. J. Phys. Chem. C.119:12739−12748. Snir N, Toroker MC (2020) The Operando Optical Spectrum of Hematite during Water Splitting through a GW–BSE Calculation. J. Chem. Theory Comput. 16:4857–4864. Heyd J, Scuseria GE, Ernzerhof M (2003) Hybrid functionals based on a screened Coulomb potential. J. Chem. Phys. 118:8207 Roy K, Kar S, Das RN (2015) Understanding the basics of QSAR for applications in pharmaceutical sciences and risk assessment. Academic Press, Amsterdam

Contents

Recent Progress in Perovskite Solar Cell: Fabrication, Efficiency, and Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Lin Zhang, Yao Zhao, and Qilin Dai State-of-the-Art of Solution-Processed Crystalline Silicon/Organic Heterojunction Solar Cells: Challenges and Future . . . . . . . . . . . . . . . . . . . Jaker Hossain, A. T. M. Saiful Islam, Koji Kasahara, Ryo Ishikawa, Keiji Ueno, and Hajime Shirai

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Structure, Electronic, and Charge Transfer Properties of Organic Photovoltaics from Density Functional Theory Methods . . . . . . . . . . . . . . . Juan I. Rodríguez and Andreas W. Götz

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Dye-Sensitized Solar Cells: A Brief Historical Perspective and Uses in Multijunction Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Andrew Daniel and Jared H. Delcamp

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Delving Charge-Transfer Excitations in Hybrid Organic– Inorganic Hetero Junction of Dye-Sensitized Solar Cell: Assessment of Excitonic Optical Properties Using the GW and Bethe–Salpeter Green’s Function Formalisms . . . . . . . . . . . . . . . . . . . . Pabitra Narayan Samanta and Jerzy Leszczynski

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Promising DSSCs Involving Organic D–π–A and Similar Structures for n- and p-type Semiconductors—A Theoretical Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 Anik Sen Application of QSPR Modeling in Designing and Prediction of Power Conversion-Efficient Solar Cell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 Supratik Kar, Juganta K. Roy, and Jerzy Leszczynski Computational Screening of Organic Dye-Sensitizers for Dye-Sensitized Solar Cells: DFT/TDDFT Approach . . . . . . . . . . . . . . . 187 Juganta K. Roy, Supratik Kar, and Jerzy Leszczynski xiii

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Chemometric Modeling of Absorption Maxima of Carbazole Dyes Used in Dye-Sensitized Solar Cells . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207 Jillella Gopala Krishna, Probir Kumar Ojha, and Kunal Roy Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233

Contributors

Qilin Dai Department of Chemistry, Physics, and Atmospheric Sciences, Jackson State University, Jackson, MS, USA Andrew Daniel Department of Chemistry and Biochemistry, University of Mississippi, University, MS, USA Jared H. Delcamp Department of Chemistry and Biochemistry, University of Mississippi, University, MS, USA Jillella Gopala Krishna Department of Pharmacoinformatics, National Institute of Pharmaceutical Educational and Research (NIPER), Chunilal Bhawan, Kolkata, India Andreas W. Götz San Diego Supercomputer Center, University of California San Diego, La Jolla, CA, USA Jaker Hossain Solar Energy Laboratory, Department of Electrical and Electronic Engineering, University of Rajshahi, Rajshahi, Bangladesh Ryo Ishikawa Graduate School of Science and Engineering, Saitama University, Saitama, Japan Supratik Kar Interdisciplinary Center for Nanotoxicity, Department of Chemistry, Physics and Atmospheric Sciences, Jackson State University, Jackson, MS, USA Koji Kasahara Graduate School of Science and Engineering, Saitama University, Saitama, Japan Jerzy Leszczynski Interdisciplinary Center for Nanotoxicity, Department of Chemistry, Physics and Atmospheric Sciences, Jackson State University, Jackson, MS, USA Probir Kumar Ojha Drug Theoretics and Cheminformatics Laboratory, Department of Pharmaceutical Technology, Jadavpur University, Kolkata, India Juan I. Rodríguez Escuela Superior de Física y Matemáticas, Instituto Politécnico Nacional, Ciudad de México, Mexico xv

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Juganta K. Roy Interdisciplinary Center for Nanotoxicity, Department of Chemistry, Physics and Atmospheric Sciences, Jackson State University, Jackson, MS, USA Kunal Roy Drug Theoretics and Cheminformatics Laboratory, Department of Pharmaceutical Technology, Jadavpur University, Kolkata, India A. T. M. Saiful Islam Department of Electronics and Telecommunication Engineering, Bangabandhu Sheikh Mujibur Rahman Science & Technology University, Gopalganj, Bangladesh Pabitra Narayan Samanta Interdisciplinary Center for Nanotoxicity, Department of Chemistry, Physics and Atmospheric Sciences, Jackson State University, Jackson, MS, USA Anik Sen Department of Chemistry, GITAM Institute of Science, GITAM (Deemed To Be University), Visakhapatnam, Andhra Pradesh, India Hajime Shirai Graduate School of Science and Engineering, Saitama University, Saitama, Japan Keiji Ueno Graduate School of Science and Engineering, Saitama University, Saitama, Japan Lin Zhang Department of Chemistry, Physics, and Atmospheric Sciences, Jackson State University, Jackson, MS, USA; Department of Mechanical Engineering, Villanova University, Villanova, PA, USA Yao Zhao Department of Mechanical Engineering, Temple University, Philadelphia, PA, USA

Recent Progress in Perovskite Solar Cell: Fabrication, Efficiency, and Stability Lin Zhang, Yao Zhao, and Qilin Dai

Abstract The perovskite solar cells (PSC) are believed to have great potential in solar cell industries, since the dramatic power conversion efficiency (PCE) improvement in such short time (i.e., from 3.8% in 2009 to 25% up to date). Organolead halide perovskite materials are commonly used in the PSC, such as CH3 NH3 PbI3 . In order to improve the PCE, many methods have been taken, such as doping ions in perovskite materials, charge transporting layer modification, microstructure modification, and utilizing advanced fabrication techniques. Besides PCE, stability is also an important issue in PSC, because the perovskite can be easily decomposed with moisture, UV light, and overheating, which is a big challenge for the commercialization of PSCs. This chapter summarizes the latest progress of PSCs and provides some useful insights for future study.

1 Introduction Fossil fuels have been playing an important role in the science and technology development for centuries. They brought so many benefits and convenience to human beings in industries and our daily life. However, they may fade away in the future with the rising of the alternative and renewable energy, because the traditional fossil fuels can lead to some environmental problems, such as air pollution and greenhouse effect. One of the most promising substitutes is the solar energy, which is believed to be the cleanest energy source. Solar cell is a kind of device which can directly convert the light energy into electric energy with photovoltaic effect. The photovoltaic effect L. Zhang · Q. Dai (B) Department of Chemistry, Physics, and Atmospheric Sciences, Jackson State University, Jackson, MS 39217, USA e-mail: [email protected] L. Zhang Department of Mechanical Engineering, Villanova University, Villanova, PA 19085, USA Y. Zhao Department of Mechanical Engineering, Temple University, Philadelphia, PA 19122, USA © Springer Nature Switzerland AG 2021 J. K. Roy et al. (eds.), Development of Solar Cells, Challenges and Advances in Computational Chemistry and Physics 32, https://doi.org/10.1007/978-3-030-69445-6_1

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was firstly discovered by French physicist Edmond Becquerel in 1839, and the first solar cell was made by American inventor Charles Fritts around 1886 with about 1% efficiency [1]. During the last several decades, with the development of materials science and fabrication technologies, quite a few kinds of solar cells have been made, such as amorphous silicon solar cell, crystalline silicon solar cell, dye-sensitized solar cell, thin-film solar cell, perovskite solar cell, and so on. Perovskite Solar Cell (PSC) has exhibited great potential since the unveiling of the perovskite solar cell in year of 2009 [2], because of the extraordinary growth in power conversion efficiency (PCE) (> 20% up to date).

1.1 The Structure and Properties of PSC Figure 1 illustrates the perovskite crystal structure, which was named after Russian mineralogist L. A. Perovski. The structure is also known as ABX3 structure, where A and B are two kinds of cations while X is an anion. The size of A is normally larger than B. As shown in Fig. 1, generally a cubo-octahedral site is occupied by the large A cation and 12 X anions, while an octahedral site is occupied by the small B cation and 6 anions [3]. Take CH3 NH3 PbI3 (aka MAPI3 , a commonly used material in PSC) as an example, the cation CH3 NH3 + occupies the position A, the cation Pb2+ occupies the position B, while the anion I− is on position X. Recently, compared to the conventional perovskite oxides, organometallic lead halide perovskites have attracted much more attention due to their superb performance such as low fabrication cost and high power conversion efficiency (PCE) [4]. Besides Pbbased halide perovskite materials (CH3 NH3 PbX3 , X=Cl, Br, or I), some other kinds of perovskite materials have also been investigated, such as Sn-based halide perovskite materials (CH3 NH3 SnX3 ) and mixed halides (CH3 NH3 SnBrx I3-x, x=0-3) [4, 5].

Fig. 1 Perovskite crystal structure (ABX3 )

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It is well known that two important factors can be used to predict the structure and stability of perovskite materials: one is the octahedral factor μ and another is the tolerance factor t. They are defined as follows: [6]  t = (R A + Rx )/ 2(R B + Rx )

(1)

μ = R B /Rx

(2)

Here, RA is the ionic radius of A cation, RB is the ionic radius of B cation, and Rx is the ionic radius of anion X. Generally, as for halide perovskite materials, the t is in the range between 0.81 and 1.11 and μ is in the range 0.44–0.90, while a lower (t < 0.8) or higher value (t > 1) will result in the structure distortion or the formation of alterative structures [7]. Figure 2a shows calculated values of t and µ for commonly used hybrid perovskite components [8]. As shown in Fig. 2b, Sun et al. also developed a new factor (μ + t)η (η is the atomic packing fraction) to accurately describe the relative stability among any two perovskites for photovoltaic applications [9]. The PSC architectures significantly affect their overall performance of devices and can be broadly divided into six types, namely, the mesoscopic n-i-p configuration, the planar n-i-p configuration, the mesoscopic p-i-n configuration, the planar p-in configuration, the electron transporting layer (ETL)-free configuration, and the (hole transporting layer) HTL-free configuration. Four typical PSC architectures are shown in Fig. 3 [10]. Furthermore, as shown in Fig. 4, many efforts have been made to develop advanced structures of PSC for applications in photolysis, power source, and photodetectors [11], such as flexible cells [12], carbon-electrode-based cells [13], semitransparent cells [14], tandem cells [15], integrated cells [16], switchable cells [17], and single crystal cells [18]. The as-prepared PSC devices are supposed to possess high power efficiency, high stability, and large-scale applicability. However,

Fig. 2 a Calculated octahedral factors for various combinations of commonly used organic and inorganic hybrid perovskite materials [8]. Reused with permission from Ref. [8]. Copyright 2015, Elsevier Ltd. b Map of (t, µ) for 138 perovskite compounds [9]. Adapted with permission from Ref. [9]. Copyright 2017, American Chemical Society

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Fig. 3 Schematic illustration for four typical types of PSC architectures [10]. Reproduced with permission from Ref. [10]. Copyright 2016, Society of Photo-Optical Instrumentation Engineers

Fig. 4 a Photograph of a flexible PSC [12]. Adapted with permission from Ref. [12]. Copyright 2018, Korean Ceramic Society. b Device architecture and photographic image of colorful PCS [23]. Adapted with permission from Ref. [23]. Copyright 2016, American Chemical Society. c Schematic configuration and operating mechanism of an integrated PSC [16]. Printed with permission from Ref. [16]. Copyright 2018, The Royal Society of Chemistry. d Photographic images of obtained single crystals [24]. Printed with permission from Ref. [24]. Copyright 2015, The Royal Society of Chemistry

there are still several issues in practical operations of PSC, such as the long-term instability due to the perovskite degradation [19, 20], the toxicity of most commonly used compounds [21], and the current-voltage hysteresis in devices [22]. Therefore, several techniques have been developed to fabricate large-scale PSC for enhancing stability, improving PCE, and relieving toxicity issue.

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1.2 Preparation Techniques for PSC The performance of PSC is significantly affected by the morphology, the crystallinity structure, and the optoelectronic property of perovskite films. The quality of perovskite films greatly depends on their construction methods including intrinsic properties of initial materials, the depositing substrate, the conditions for film growth, and the subsequent thermal annealing [8]. Depending on the structure, interface, and morphology of perovskite materials, there are two general methods to fabricate perovskite films by either wet chemistry processing method or vapor-assisted processing method as shown in Fig. 5 [25].

1.2.1

Wet Chemistry Processing Methods

One-Step Coating Deposition The one-step coating (one method of solution processes) has been considered as the most preferable method to generate PSC due to its simplicity and low cost. Generally, for the one-step method, a solution is firstly prepared by mixing organic and inorganic halides (e.g., CH3 NH3 I and PbI2 ). Then the mixed solution is spinning coated on a substrate followed by drying and thermal annealing [26]. Figure 6a shows a solution-saving one-step dip-coating method developed by Huang et al. Compared to the conventional one-step spinning coating method, this facile and waste-free one-step dip-coating method enables the PSC not only to possess a similar PCE around 12%, but also to show negligible hysteresis [27]. Based on Zhang’s method, the spin-coating precursor solution (e.g., HI +PbI2 ) can be directly deposited by CH3 NH2 in its atmosphere to generate high-performance perovskite. The composition of precursors can be well controlled by this one-step gaseous reaction (see Fig. 6b) [28]. Fig. 5 PSC manufacturing techniques based on the literature [25]

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Fig. 6 a One-step dip-coating method for perovskite formation [27]. Reused with permission from Ref. [27]. Copyright 2017, Elsevier Ltd. b A non-CH3 NH3 X (X = I, Br) one-step deposition of CH3 NH3 PbX3 for PSC [28]. Printed with permission from Ref. [28]. Copyright 2016, The Royal Society of Chemistry

Two-Step Deposition The two-step sequential coating method for PSC fabrication is originally developed by Mitzi et al. [29]. Compared to one-step coating processing, the PSC fabricated by the two-step deposition method shows a higher performance because the morphology and interface of perovskite films can be better controlled via this sequential two-step coating. In a typical two-step spin-coating process, the PbI2 solution was first spin coated on a substrate to form PbI2 film and then the CH3 NH3 I solution was spin coated on the top of the dried PbI2 film [26]. As shown in Fig. 7a, Li et al. reported a new method to control the morphology of PbI2 by antisolvent treatment in twostep deposition method. The as-prepared PSC shows a high PCE improvement from 12% to 16.1%, a less hysteresis, and a high air stability [30]. A modified two-step method for CH3 NH3 PbI3 PSC was adopted by Bi et al. Unlike the general procedure, there was a dichloromethane (DCM) treatment for the as-prepared CH3 NH3 PbI2 film before drying step and this improved method showed a DCM-induced quality enhancement [31]. Figure 7b shows a two-step deposition method-mediator extraction treatment (MET) to generate large-scale perovskite. In this MET method, a predeposited PbI2 -DMSO film went through twice bathing with 2-propanol (IPA) and CH3 NH3 I solution, respectively. This proposed MET method including successive

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Fig. 7 a A modified two-step deposition method including antisolvent treatment [30]. Adapted with permission from Ref. [30]. Copyright 2017, American Chemical Society. b A fast two-step deposition of perovskite by mediator extraction treatment [32]. Printed with permission from Ref. [32]. Copyright 2018, The Royal Society of Chemistry

slot-die coating and bathing provides an important insight into fabricating large-scale and high-quality perovskite films within a short processing time [32].

1.2.2

Vapor-Assisted Processing Methods

Vapor-Assisted Solution Process Compared to conventional solution methods, the vapor-assisted solution (VASP) approach takes advantage of easy sublimation of organic species and efficient reaction of organic-inorganic components, and further controls the growth of perovskite films, such as the grain structure, the morphology, and the crystal size [33]. Typically, there are two key steps in the VASP method: one is the inorganic film deposition and another is the reaction between inorganic film and organic species in the vapor phase. Figure 8a shows a low-pressure vapor-assisted solution approach (LP-VASP). In this study, the PbI2 films were firstly generated by spin-coating technique. Then the PbI2 films around amine salts were sealed in a petri dish and heated in a vacuum oven. The performance of as-prepared CH3 NH3 PbX3-y Iy (X=Cl, Br)

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Fig. 8 a Schematic illustration of perovskite film preparation based on low-pressure vapor-assisted solution process (LP-VASP) [34]. Reused with permission from Ref. [34]. Copyright 2017, Elsevier, Ltd. b Perovskite film preparation based on low-temperature vapor-assisted solution process (LWVASP) [35]. Adapted with permission from Ref. [35]. Copyright 2014, American Chemical Society. c Perovskite film preparation based on a modified VASP [36]. Adapted with permission from Ref. [36]. Copyright 2015, American Chemical Society

films could be adjusted via tuning the reaction parameters. The PSC based on the optimum perovskite film exhibited a high PCE at 17.3% and a good stability over 3600 h [34]. Chen et al. developed a low-temperature vapor-assisted solution method to fabricate planar heterojunction PSC [35]. As shown in Fig. 8b, compared to the co-deposition of PbI2 and CH3 NH3 I in the conventional vacuum deposition method, this novel simple approach enabled the in situ reaction of pre-deposited inorganic film and organic vapor based on the kinetic and thermodynamic properties of the synthetic reaction. The as-synthesized perovskite film with this method possessed full surface coverage with small roughness and uniform grain structure. The PCE is up to 12.1% and this method provides important insight into generating perovskite films and devices in high reproducibility [35]. Liu et al. also developed a modified VASP to construct uniform and high-quality perovskite thin film as shown in Fig. 8c [36]. The amine salt was evaporated bottom-up and reacted with the pre-prepared PbI2 films facing down to vapor. The as-fabricated PSC shows a PCE at 10.2% and a slight hysteresis effect. This method paves the way to explore the stability of PSC.

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Fig. 9 a Organometal halide-based perovskites synthesis [39]. Printed with permission from Ref. [39]. Copyright 2014, The Royal Society of Chemistry. b Formamidinium iodide (FAI)-based perovskite synthesis by Leyden et al. [40]. Printed with permission from Ref. [40]. Copyright 2015, The Royal Society of Chemistry. c Synthesis PSC with low defect density and high efficiency by Ng et al. [41]. Adapted with permission from Ref. [41]. Copyright 2016, American Chemical Society. d Synthesis PSC with a simple in situ tubular VCD (ITVCD) method by Luo et al. [42]. Printed with permission from Ref. [42]. Copyright 2015, The Royal Society of Chemistry

Chemical Vapor Deposition Compared to other vapor-assisted processing methods, chemical vapor deposition (CVD) technique with high production yield and scalability has been considered as one of the most desirable techniques to produce high-quality perovskite films in a large scale [2, 37, 38]. Leyden et al. reported a hybrid chemical vapor deposition (HCVD) to synthesize perovskite [39]. As shown in Fig. 9a, the amine salt was placed in the high temperature zone and the pre-deposited PbI2 substrates were in the low-temperature zone. The MAI would land on, diffuse to, and react with the PbI2 film. This method can tune the reaction parameters (e.g., gas flow rate, temperature, and pressures) enabling the PSC with a PCE as high as 11.8% and an ability to be scaled up to the industry level [39]. The method was also firstly applied to fabricate formamidinium iodide (FAI)based perovskite as shown in Fig. 9b [40]. The obtained FAI-based PSC could have a 14.2% PCE and keep stability for 155 days. Ng et al. also synthesized CH3 NH3 PbI3 perovskite based on HCVD method as shown in Fig. 9c [41]. In this process, the

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Fig. 10 a Single-source physical vapor deposition (SSPVD) for perovskite film preparation [43]. Reused with permission from Ref. [43]. Copyright 2016, Springer Nature. b Schematic illustration of perovskite film fabrication by microwave irradiation annealing [46]. Adapted with permission from Ref. [46]. Copyright 2016, American Chemical Society

sublimated MAI was transported to the pre-deposited PbI2 substrate by the gas of N2 /O2 , and the growth parameters including the temperature, the carrying gas ratio (N2 /O2 ), and the postdeposition cooling rate were systematically investigated. It is found that under the optimal conditions, a PCE of as-fabricated PSC as high as 17.6% can be obtained. Luo et al. presented an in situ tubular CVD (ITCVD) technique to fabricate uniform perovskite films in large scale and low cost [42]. Figure 9d shows the schematic diagram for the PSC preparation, in which the pre-deposited PbI2 substrate faced down to the amine salt and reacted to the CH3 NH3 I gas once heated. Based on this ITCVD method, the PSC with planar structure is possessing a high PCE efficiency of 12.2%, a high crystallinity, and excellent optical properties can also be achieved [42].

Thermal Vapor Deposition Generally, the thermal vapor deposition covers single-source and dual-source evaporation systems. A single-source physical vapor deposition (SSPVD) was proposed by Fan et al. [43]. As shown in Fig. 10a, the MAPbI3 powder was firstly placed into a crucible and then the powder sublimated efficiently when the temperature was raised to a certain point. Finally, the gas phase of MAPbI3 was deposited on the substrate and the PSC showed a PCE around 10.90% [43]. Liu et al. reported the dual-source thermal vapor deposition (TVD) for perovskite synthesis [44]. The inorganic and organic species were deposited on the pre-deposited substrate layer. In this study, the as-prepared PSC exhibited a PCE as high as 15.4%. Additionally, Hwang et al. produced a CH3 NH3 PbI3 -based memory cells by a sequential vapor deposition [45].

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This method provides a potential to explore the organic-inorganic perovskites for application in data storage.

Microwave Irradiation Method The microwave irradiation deposition (MIP) was firstly employed to produce perovskite films by Cao et al. [46]. Figure 10b shows a simple schematic for preparation of perovskite films assisted by MIP. The as-prepared perovskite films were loaded on a Teflon shelf and subsequently placed into the microwave oven for microwave annealing. Compared to the conventional thermal annealing, this method contributed to producing perovskite films with higher crystallinity and lower defect density [46].

2 The Efficiency Improvement of PSC The power conversion efficiency (PCE) of organic-inorganic lead halide perovskite solar cell is one of the key factors of the solar cell [47]. Since the debut of the PSC in 2009, the PCE has been improving rapidly [48, 49]: the PCE of the first PSC reported by Kojima et al. was only 3.8% [50]. In 2011, Im et al. [51] achieved 6.5% in PCE; in 2012, Kim et al. [52] reported a PCE exceeding 9%. To our best knowledge, over 22% PCE has been confirmed in 2016 [53]. All of the exciting results and findings in such short time show the great potential of PSC. Many methods and techniques have been utilized to enhance the PCE, which can be divided into three main aspects: materials selection and optimization, better device fabrication methods and techniques, and microstructure designing and engineering.

2.1 Materials and Microstructure The material selection includes perovskite materials, charge transferring materials, and electrode materials. In terms of the perovskite materials, many crystals and compounds which have similar structure with CH3 NH3 PbX3 (X=I, Br, Cl) have been researched. It is believed that larger grain sizes, lower defects and pinholes, and stronger bonding can lead to higher PCE [19, 25, 54]. Instead of using pure CH3 NH3 PbI3 , Jin et al. [55] partially substituted the PbI2 with ZnCl2 to obtain CH3 NH3 I(PbI2 )1-x (ZnCl2 )x thin film. The CH3 NH3 I, PbI2 , and ZnCl2 powders were mixed together with different molar ratios. The ZnCl2 -doped thin film exhibited larger but uniform grains than the undoped CH3 NH3 PbI3 . Consequently, the CH3 NH3 I(PbI2 )1-x (ZnCl2 )x thin-film solar cell shows 18.2% in efficiency with 3 mol% ZnCl2 doped as shown in Fig. 11a [55]. Boopathi et al. studied the effect of the addition of alkali salts (e.g., KCl, NaCl, and LiCl) into the perovskite precursor on the PSC performance [56]. It is found that the addition of a small amount of KCl

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Fig. 11 a Efficiency enhancement of PSC based on adding zinc chloride [55]. Adapted with permission from Ref. [55]. Copyright 2017, American Chemical Society. b Efficiency enhancement of PSC based on incorporating salt additives [56]. Printed with permission from Ref. [56]. Copyright 2016, The Royal Society of Chemistry

can improve the crystallinity and morphology of the perovskite film and the PCE of the as-prepared device can be increased to 15.08% due to the enhancement of absorption and excitation ability as shown in Fig. 11b. Moreover, the device based on KCl addition exhibited a high long-term stability, showing a small degradation ~16% in dark after 50 days [56]. In order to obtain large grain size of perovskite crystals, Seo et al. adopted the methylammonium formate ionic liquid (IL) to hinder the perovskite growth [57]. It is concluded that the addition of specific IL into precursor will result in the formation of large crystalline domain that is beneficial for collecting charges and improving performance of PSC. The as-obtained planar PSE based on IL-driven mechanism can reach 19.5% [57]. Li et al. developed a three-dimensional (3D) metal-organic assembly [In2 (phen)3 Cl6 ]·CH3 CN·2H2 O (In2) and firstly introduced it into the perovskite precursor PbI2 [58]. The perovskite thin film was obtained based on a two-step sequential deposition method. It is discovered that introduction of In2 can improve the crystallization and modify the morphology of both the

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precursor PbI2 and the perovskite film. Consequently, the performance of the device was largely enhanced with an efficiency as high as 17.15% due to the high quality of the as-synthesized perovskite film [58]. Aeineh et al. employed the inorganic NPs (Au@SiO2 ) to modify the interface between compact TiO2 and mesoporous TiO2 substrate as shown in Fig. 12a [59]. The SiO2 shell of the inorganic NPs can avoid the reaction between Au and CH3 NH3 PbI3 perovskite film. The surface modification of PSC enabled the increasing of PCE to 17.55% due to the photocurrent and photovoltage enhancement [59]. Cao et al. also modified the interface between TiO2 and perovskite film by introducing thiol leads as shown in Fig. 12b [60]. The TiO2 film was firstly treated with HOOC-R-SH and then was deposited by perovskite layer. The perovskite film was also modified by thiols to become hydrophobic. On the one hand, this surface modification can enhance the electron transport between TiO2 layer and perovskite payer. On the other hand, the morphology of the perovskite crystals can be optimized. As a result, the performance of the PSC was significantly enhanced with a high efficiency of 14.1% [60]. Jung et al. reported that the PCE of the flexible PSC can be enhanced by optimizing the thickness of the ZnO electron transport layer, the precursor PbI2 phase, and the crystal growth of the perovskite layer [61]. Figure 12c shows the schematic illustration of fabrication process, and the thickness of the ZnO layer was

Fig. 12 a Efficiency enhancement of PSC based on interface modification by Au/SiO2 NPs [59]. Adapted with permission from Ref. [59]. Copyright 2017, American Chemical Society. b Efficiency enhancement of PSC based on interface modification by thiols [60]. Printed with permission from Ref. [60]. Copyright 2015, The Royal Society of Chemistry. c Efficiency enhancement of PSC based on interface modification by controlling ZnO layer thickness, PbI2 phase, and perovskite morphology [61]. Reused with permission from Ref. [61]. Copyright 2016, Elsevier Ltd. d Efficiency enhancement of PSC based on interface modification by constructing brookite-based TiO2 heterophase junction [62]. Adapted with permission from Ref. [62]. Copyright 2019, American Chemical Society

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adjusted by varying the cycles of spin coating. The morphology/size of the perovskite was optimized by controlling the precursor MAI volume with a fixed concentration. In this case, the PbI2 phase can be tuned to block the recombination. Furthermore, both the grain size and thickness of the crystals increased after spin coating. As a result, the flexible PSC based on this modified two-step coating method shows a best PCE around 12.34% due to the enhanced absorbance and reduced recombination [61]. Recently, Shahiduzzaman et al. tried to modify the TiO2 electron transport to enhance the PSC efficiency [62]. Experimentally, they hydrothermally synthesized the brookite TiO2 nanoparticles (NPs) with high purity for the first time. Then the brookite-based TiO2 heterophase NPs were deposited on the fluorine-doped tin oxide (FTO)-patterned substrate. It is found that the resultant PSC based on this technique showed an efficiency up to 16.82% due to well controlling of the electron transfer and the electron-hole density (Fig. 12d) [62]. Zhao et al. developed a facile method to modify the perovskite film by depositing a cesium acetate film [63]. The introduced cesium acetate can react with the perovskite and retard the migration of MA+ , so that the organic transport layer can be well protected by avoiding the ionic penetration. Figure 13a shows the cross-sectional SEM image of the Spiro-OMeTAD-modified perovskite film and it can be seen the optimized PSC exhibits a 20.9% PCE [63]. In the study of Hu et al., a selfassembled poly (3,4-ethylenedioxythiphene):poly(styrenesulfonate) (PEDOT:PSS) monolayer was generated on the surface of PEDOT:PSS film (Fig. 13b) [64]. In this case, an oriented electric field was constructed due to the structural arrangement of the PEDOT:PSS layer. This structural alignment contributes to accelerating the hole Fig. 13 a Efficiency enhancement of PSC based on interface modification by cesium acetate [63]. Adapted with permission from Ref. [63]. Copyright 2018, American Chemical Society. b Efficiency enhancement of PSC based on fabricating the PEDOT:PSS monolayer [64]. Printed with permission from Ref. [64]. Copyright 2018, The Royal Society of Chemistry

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Fig. 14 Efficiency enhancement of PSC based on CsPbBr3 NPs additive [67]. Reused with permission from Ref. [67] Copyright 2019, Elsevier Ltd

extraction and hence enhance the PCE to 18% [64]. Moreover, Seo et al. used mesoporous TiO2 beads modified with CsBr as the electron-specific contact [65]. In this strategy, the light absorption is enhanced and the interfacial interaction is strengthened. Consequently, the efficiency of PSC prepared based on the Rb/Cs/FA0.95 MA0.05 perovskite can reach as high as 21% [65]. Chen et al. [66] found that adding 1.5% Bi3+ in (FA0.83 MA0.17 Pb(I0.83 Br0.17 )3 ) (FA: formamidinium) can effectively increase the perovskite thin-film grain size into roughly 1.4 µm without pinhole formation. The well-controlled microstructure with less grain boundaries and enhanced crystallization led to a PCE of 19.4%. Simultaneously, the long-term thermal stability was also improved. Similarly, Gao et al. [67] reported that the perovskite thin film exhibited better crystallinity and larger grains by adding 2% CsPbBr3 nanoparticles in MAPI3 film, which resulted in high efficiency of 20.46% (Fig. 14). Tong el al. [68] added guanidinium thiocyanate (CuaSCN) into (FASnI3 )0.6 (MAPbI3 )0.4 thin film and found that the 7% doped perovskite not only had enhanced grain sizes, and less pinholes and pinholes, but also had larger carrier lifetime (>1 µs) with 2.5 µm in diffusion lengths. Moreover, the morphology changed with GuaSCN addition. With this method, they achieved 25% efficiency for four-terminal and 23.1% for two-terminal thin-film tandem PSC, which is the highest reported efficiency up to date to our best knowledge.

2.2 Advanced Fabrication Methods and Techniques Advanced solar cell fabrication methods and techniques can help to enhance the efficiency by improving the materials properties, and lessen the defects and undesired microstructures. For instance, Gao el al. [69] utilized pulsed laser deposition (PLD)

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method to prepare densified electron transportation layers (ETL). The amorphousZn2 SnO4 ETL thin film illustrated better contact with FTO substrate, while the ETL prepared by conventional spin-coating method possessed a lot of pinholes and defects. The better contact between ETL and FTO decreased the leakage current and enhanced the interfacial charge collection. Consequently, the PCE was improved to 20.04%. Zhou et al. discovered that the defect of the CH3 NH3 PbI3 perovskite thin film prepared by the conventional one-step method can be reduced by introducing methylamine (CH3 NH2 ) gas [70]. After heat treatment, the MAPbI3 film will go through CH3 NH2 treatment for 2–3 s in their gas phase. It is observed that the CH3 NH2 gas had a healing effect on the original perovskite film due to the formation of CH3 NH3 PbI3 ·xCH3 NH2 phase resulting from the interaction between perovskite and gas. After the healing treatment by CH3 NH2 gas, a high-quality, large-scale, and defect-free perovskite film was formed, enabling the efficiency of the PSC up to 15.1% [70]. Lee et al. reported a strategy to fabricate PSC with a large area by an air-knife-assisted D-bar coater [71]. Figure 15 shows the schematic illustration for the coating process. As shown in Fig. 15, the precursor solution (e.g., MAI + PbI2 ) was loaded on the D-bar and the substrate is moved at a certain speed. Then the argon gas was supplied by an air knife to help evaporate the solvent. Finally, the as-prepared substrate was thermal annealed. It is found that, introducing lead acetate (PbAc2 ) into the precursor solution (MAI + PbI2 ) in the solvent of 2-methoxyethanol (2ME) will produce the methylammonium acetate (MAAc) as a by-product during the coating process. The presence of MAAc is beneficial for the formation of perovskite film with high quality. Furthermore, when a small amount of guanidinium iodide (GAI) was added into the PbAc2-containing precursor solution, the hysteresis was reduced and the efficiency was further enhanced. The highest PCE of the as-prepared device can reach 19.44% [71]. In 2016, Li et al. fabricated a large-area PSC using a vacuum flash-assisted solution process (VASP) [72]. Typically, the surface of the TiO2 film Fig. 15 Efficiency enhancement of PSC based on an air-knife-assisted D-bar coater [71]. Adapted with permission from Ref. [71]. Copyright 2019, American Chemical Society

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was firstly spin coated by the precursor FA0.81 MA0.15 PbI2.51 Br0.45 solution including dimethylsulfoxide (DMSO). Then the as-prepared film is put into a vacuum chamber for crystallization. It is found that the vacuum flash plays a significant role in forming perovskite film. This VASP method enabled the formation of perovskite film with high electronic quality in a large area, showing the maximum PCE of 20.5% [72]. Chou et al. used an ultrasonic spray-coating strategy to produce the perovskite film [73]. Figure 16 shows the schematic illustration for the ultrasonic spray-coating technique. Experimentally, the pre-treated indium-doped tin oxide (ITO)/PEDOT:PSS substrate was spray coated with the precursor solution, in which a commercial ultrasonic nozzle was used. Then the substrate coated with precursor solution was thermally treated for the solvent evaporation. The CH3 NH3 PbI2 film with high crystallinity and large area was successfully fabricated based on this facile one-step spray-coating method. The ultrasonic spray-coated PSC exhibited a less hysteresis and a high PCE of 12.3% [73]. Park et al. also reported the megasonic spray-coating method to fabricate large-area PSC [74]. The CH3 NH3 PbI3 solution was deposited on the pre-treated ITO/PEDOT:PSS substrate based on a meagasonic nebulizer spray system and the highest PCE could reach 16.9% [74]. In 2017, an aerosol-jet (AJ)assisted method is introduced for CH3 NH3 PbI3 perovskite growth by Bag et al. [75]. In general, the perovskite film was generated by a two-step sequential deposition method. Firstly, the ITO/PEDOT:PSS substrate was deposited by the PbI2 film. In this step, the microstructures of the PbI2 phase could be well controlled. Then the PbI2 film was coated by the CH3 NH3 I aerosol mist that is generated by the AJ printer. Through this technique, the printed perovskite film can be tuned from the composition, the morphology, and the electronic properties. Furthermore, the PCE of the as-prepared PSC based on the modified precursor ink containing NaI can be up to

Fig. 16 Efficiency enhancement of PSC based on one-step ultrasonic spray-coating method [73]. Adapted with permission from Ref. [73]. Copyright 2018, American Chemical Society

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15.4% [75]. Tang et al. produced the perovskite film using the doctor-blade coating method [76]. In their study, a small amount of cesium (Cs+ ) and bromine ions (Br− ) were added into the precursor solution and the highest PCE of the as-prepared device based on the doctor-bladed MA0.6 FA0.38 Cs0.02 PbI2.975 Br0.025 films can reach 19.3% [76]. The PSC was also fabricated using the slot-die coating method [77]. In the slotdie coating process, the gas quenching contributes to the formation of the PbI2 film without pinholes. Furthermore, the charge transporting layers (e.g., ZnO and P3 HT) were also produced based on this method. Based on the slot-die-coated perovskite film, the best PCE of the as-obtained device was 11.96% [77].

3 PSC Stability Besides efficiency, the stability is also a vital matter for PSC. Unfortunately, several factors can lead to the degradation of the solar cell, such as moisture, UV light, thermal effects, and so on. The limited durability of PSC can potentially hinder the commercialization of PSC. Therefore, longer life span and more stable performance are always pursued by researchers.

3.1 Moisture Stability The mechanism of PSC moisture degradation was proposed by Frost et al. [78] by speculating the XRD phase change before and after moisture exposure. The perovskite may hydrolyze with the following reactions: [79] CH3 NH3 PbI3 (s) ↔ PbI2 (s) + CH3 NH3 I(aq)

(3)

CH3 NH3 I(aq) ↔ CH3 NH2 (aq) + HI(aq)

(4)

4HI(aq) + O2 ↔ 2I2 (s) + 2H2 O(l)

(5)

2HI(aq) ↔ H2 (g) + I2 (s)

(6)

It is believed that water is served as the catalyst for the degradation process [80]. It was also reported that CH3 NH3 PbI3 was more vulnerable than CH3 NH3 PbBr3 [79]. Some researchers tried to improve the moisture resistance of the perovskite crystals by adding extra ions. Smith et al. [81] found that although the PCE of the (PEA)2 (MA)2 [Pb3 I10 ] (PEA:C6 H5 (CH2 )2 NH3 + ; MA:CH3 NH3 + ) was as low as 4.73%, nonetheless, it exhibited better stability under moisture. The crystal stability was studied by XRD profiles. Specifically, both the (PEA)2 (MA)2 [Pb3 I10 ]

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and (MA)[PbI3 ] were conditioned in 52% relative humidity for 46 days, during which the XRD patterns were collected periodically. With water exposure, the (MA)[PbI3 ] showed PbI2 peaks gradually and became the major phase after 40 days, while the (PEA)2 (MA)2 [Pb3 I10 ] barely showed any differences. Furthermore, Xu el al. [82] embedded the CH3 NH3 PbBr3 nanoparticles into hyperbranched polyamidoamine (PAMAM) dendrimers and found that the moisture stability time was 800 h and the halide exchange was also delayed. Cai et al. [83] reported that the addition of Pb(SCN)2 additive may be able to modify the morphology of the FA0.8 Cs0.2 PbI2.68 Br0.32 and enhance the moisture stability of the PSC. The Pb(SCN)2 with different concentrations were directly added into the perovskite solution. It was concluded that with 2% Pb(SCN)2 addition, the PCE was much improved from 13.9 to 17.0, and 85.1% of the PCE remained after the PSCs were kept in 60% relative humidity for 45 days (Fig. 17a). Cai et al. [83] speculated that this improvement could be due to stronger interaction between Pb2+ and SCN− . Apart from adding ions, an alternative method is surface modification which improves the hydrophobicity of the perovskite crystals. To improve the moisture resistance of PSC, Chen et al. [84] utilized zinc phthalocyanine (ZnPc) hydrophobic hole modification layer in the planar hetero-junction structure. The ZnPc layer was deposited on the MAPI3 layer by rotary vacuum thermal evaporation at 320 °C. On top of the hydrophobic layer, a layer of spiro-OMeTAD was spun coated. Exposed to 30% relative humidity at 25 °C, the PCS with ZnPc layer still possessed 85% efficiency on average after 100 days, while the efficiency of the PSC without the hydrophobic layer decayed to almost 0 after 800 h exposure (Fig. 17b). Hangoma [85] et al. created a hydrophobic layer with the surface treatment of the electron transport layer [6]-phenyl-C61-butyric acid methyl ester (PCBM). Ethylenediamine was spin coated on the PCBM thin film, followed by hydrophobic stearic acid dipped on it. The ethylenediamine could help to form better bonding between the stearic acid and PCBM and lead to higher hydrophobicity of the film. To test the water and moisture resistivity, the sample with and without surface treatment was immersed into water for a certain amount of time. Comparing to the treated sample, the non-treated sample displayed lighter color (a) and clearer PbI2 peaks in the XRD profiles (b) after 50 s water immersion, which illustrated the better stability of the PSC with surface treatment. Im el al. [86] utilized a kind of Ti-doped MoO− 2 as the hole transporting material. In order to synthesize Ti-doped MoO2 , MoO3 powders were firstly prepared by ultrasonic spray pyrolysis method. Then the MoO3 particles were dispersed in a DI water and ethylene glycol mixture, followed by the addition of triethanolamine and titanium diisopropoxide bis (acetylacetonate) which was dissolved in methanol. At last, the Ti-doped MoO2 nanoparticles can be harvested after 210 °C heating for 12 h. The moisture stability was studied by the XRD patterns after the materials were immersed in water for several days. The Ti-doped MoO2 barely had any phase changes after 15 days while the pristine MoO2 decomposed very soon. Serving as the hole transporting layer, which is on the top of perovskite layer, the Ti-doped MoO2 was found to be more stable than pristine MoO2 under moisture, and was able to provide protection for the perovskite crystals herein. The possible reason for

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Fig. 17 a Moisture stability enhancement based on lead thiocyanate additive [83]. Reused with permission from Ref. [83]. Copyright 2017, Elsevier B.V. b Moisture stability enhancement based on introducing a hydrophobic hole modification layer [84]. Reused with permission from Ref. [84]. Copyright 2016 Elsevier Ltd. c Moisture stability enhancement based on Ti-doped MoO2 nanoparticle-hole-transporting material [86]. Reused with permission from Ref. [86]. Copyright 2017, Elsevier B.V.

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the robust performance under moisture can be the doped MoO2 which has stronger Mo-O bonding than the undoped MoO2 (Fig. 17c).

3.2 UV Light Stability Researchers found that the UV light can also degrade the perovskite crystals. A degradation mechanism for the CH3 NH3 PbI3 PSCs with TiO2 as the photoanode was proposed by Ito et al. [87] with the following reactions: 2I− ↔ I2 + 2e− [at the interface between TiO2 and CH3 NH3 PbI3 ]

(7)

3CH3 NH3+ ↔ 3CH3 NH2 (g) + 3H+

(8)

I− + I2 + 3H+ + 2e− ↔ 3HI(g)

(9)

They believed that the TiO2 can extract electrons from the I− of CH3 NH3 PbI3 at the interfacial areas. The dissipations of gaseous products can also lead to further CH3 NH3 PbI3 irreversible degradations. By exposing the perovskite materials in UV light and subsequently analyzing the XRD profiles of them, Ouafi et al. [88] found that CH3 NH3 PbBr3 had better UV stability than CH3 NH3 PbI3 . The reason could be that the CH3 NH3 PbBr3 is denser than CH3 NH3 PbI3 , and Br can form stronger bonding with Pb and hydrogen bond with the ammonium cation. They also found that with 20% Br doping, the PSC can have effective UV stability improvement. The most intuitive way to improve the UV stability probably is by adding UV filter material to block UV light. Sun et al. [89] added an extra UV absorber layer on the top of the FTO glass to filter the UV light with 275–400 nm in wavelength. Although the current density of the PSC was a little comprised (2.2% decreased), the UV resistance was much improved: the modified PSC decreased 13.67% in PCE after exposed to UV for 25 h while the control device almost lost all the PCE. As shown in Fig. 18a, the control device (a) decomposed into PbI2 which corresponded to the yellowish color of the solar cell, while the perovskite film of the modified solar cell (b) still stayed intact. Inspired by Mother Nature, Cao et al. [90] introduced sinapoyl malate (SM) to mimic the sunscreen effect which can provide protection to plants from UV light. After TiO2 surface modification with SM (one efficient sunscreening agent), on one hand, the PSC UV stability was improved; on the other hand, it also benefited the PCE because the SM enhanced the interfacial bonding between TiO2 and perovskite materials. Another idea to elongate the lifetime from UV degradation is to convert the UV into other wavelength light. Jin el al. [91] added carbon dots (CD) in the mesoporous TiO2 layers by dip-coating method, considering the CDs outstanding UV absorption, wavelength-dependent emissions, and stable photochemical property (Fig. 18b). The CDs were prepared by mixing and dissolving citric acid and ethylenendiamine in DI

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Fig. 18 a UV light stability enhancement based on interface modification and a UV absorption layer [89]. Printed with permission from Ref. [89]. Copyright 2017, The Royal Society of Chemistry. b UV light stability enhancement based on introduction of fluorescent carbon dots [91]. Adapted with permission from Ref. [91]. Copyright 2017, American Chemical Society. c UV light stability enhancement based on incorporating YVO4 :Eu3+ , Bi3+ nanophosphor into the mesoporous TiO2 layer [92]. Adapted with permission from Ref. [92]. Copyright 2018, American Chemical Society

water, and then heated to 200 °C for 5 h in a Teflon-lined autoclave. The luminance test results showed that the addition of the CDs could convert the UV light into blue light. The PSC with CDs can remain more than 70% of the initial PCE after 12 h of UV exposure, while the control sample only had 20% remaining. Additionally, the PCE of the PSC with CDs was also improved from 14.6% to 16.4%. With similar mechanism, Jin et al. [92] introduced luminescent semiconductors YVO4 :Eu3+ , Bi3+ into the mesoporous TiO2 layer. The YVO4 :Eu3+ , Bi3+ was able to convert the UV light into red light, which was also called “luminescent downshifting (LDS).” Specifically, the high-energy UV light was downshifted into low-energy visible light. The YVO4 :Eu3+ , Bi3+ in this work was prepared by hydrothermal method; firstly, Y(NO3 )3 •6H2 O,

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Eu(NO3 )3 •6H2 O, and Bi(NO3 )3 •5H2 O were added in nitric acid solution; secondly, NH4 VO3 water solution was added in the previous solution; and then the solution was mixed and stirred, and heated at 180 °C for 24 h. The luminescent semiconductor was mixed into the TiO2 paste, which was diluted with ethanol and directly spin coated on compact TiO2 layer. After 60 h UV light irradiation, the doped PSC had about 70% of initial PCE retained, while the control sample only had 20% remaining (Fig. 18c). In terms of fabrication method, Chen et al. [93] utilized pulsed laser deposition method to obtain the downshifting semiconductor SrAl2 O4 :Eu2+ , Dy3+ (SAED) layer. The SAED is a kind of long-lasting and non-radioactive downshifting phosphor material which can convert the UV light into green light region. The SAED target which was prepared by powder cold pressing and annealing was irritated by laser with 6 Hz frequency. More interestingly, this PSC possesses a solar energy storage effect. Because the SAED had long-lasting luminescence, even if the light illumination was turned off, the PSC was able to generate power for some time. This method may provide a new insight on how to store solar energy in solar cells. Separating the CH3 NH3 PbI3 layer and TiO2 layer from directly contacting may be another alternative method to improve the PSC UV light stability. Chen et al. [94] introduced an extra CsPbBr3 layer in between the CH3 NH3 PbI3 and Cp-TiO2 layers. After 100 h UV irradiation, the modified PSC remained 82% of the initial PCE, which is much larger than 55% of the control device. According to their speculation, the advantages of the extra CsPbBr3 layer can be threefold: 1. The CsPbBr3 layer can improve the charge transfer between the CH3 NH3 PbI3 and Cp-TiO2 layers. 2. The CsPbBr3 can downshift the UV light into visible light. 3. The CsPbBr3 can also serve as a UV filter.

3.3 Thermal Stability Dualeh et al. [95] proposed a possible mechanism for the perovskite materials’ thermal degradation, with the following equation: CH3 NH3 PbI3 ↔ PbI2 + CH3 NH2 (g) + HI(g)

(10)

And the temperature, and presence of water and air can also influence the reaction rate [80]. The CH3 NH3 PbI3 was found to be stable until 300 °C at which the PbI2 starts to form [95]. Nonetheless, Philippe et al. [96] discovered that the CH3 NH3 PbI3 started to decompose from 100 °C when the thermal stability test was performed in ultrahigh vacuum. Chen et al. [66] systematically researched the influence of the Bi3+ doping. They found that the Bi3+ may be able to help enhance the grain sizes and lower the pinholes and defects. Additionally, the Bi3+ – doped PSC exhibited higher thermal stability. The Bi3+ doped solar cell remained 81% of the initial PCE and the control device decreased to almost zero after kept at 80 °C for 22 days. They speculated the possible reason was that the Bi3+ could shorten the lattice spacing and

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hence stronger the bonding. Shao el al. [97] found that adding dimethyl ammonium (DMA+ ) may be helpful to increase the symmetry of CH3 NH3 PbI3 . Single crystals of MA1-x DMAx PbI3 (x:0-0.25) were prepared by dissolving PbI2 , MAI, and DMAI into butyrolactone (GBL) solution. By analyzing the XRD peaks of the samples, they discovered that with the doping amount of DMA+ increasing, the symmetry of the perovskite increased. Namely, the crystal structure tended to convert from tetragonal into cubic structure. They believed that the more symmetric structure can benefit the thermal stability of the PSC. After kept at 85 °C for 168 h, the PCE of the modified solar cell gradually decreased from 18.0% to 13.4% while the control device only had 35% of the initial PCE retained. Zou et al. [98] found that the thermal stability can be improved by adding guanidine thiocyanate (GITC) (Fig. 19a). The perovskite thin film was prepared with typical two-step method through adding GITC into lead precursor solution. To study the thermal stability of the solar cell, the devices were annealed at 120 °C in air, and the corresponding XRD patterns were measured and compared. For the pristine device, the CH3 NH3 PbI3 decomposed into PbI2 significantly after 35 min, while the doped device only had minor phase change. To further understand the role of the doped ions, Pb(SCN)2 were added into the perovskite layer and the same test was performed. With only SCN− doped, the thermal stability was

Fig. 19 a Thermal stability enhancement based on an efficient guanidinium isothiocyanate additive [98]. Reused with permission from Ref. [98]. Copyright 2018, Elsevier Ltd. b Thermal stability enhancement based on poly(9-vinylcarbazole)-modified perovskite/PCBM interface [99]. Reused with permission from Ref. [99]. Copyright 2019, Elsevier Ltd

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quite comparable with the control device, which indicated that the guanidinium ions resulted in the stability improvement. Zhang el al. [99] tried to engineer the interfacial area between perovskite and PCBM layers. Poly(9-vinylcarbazole) (PVK), which was considered to be able to improve the bonding and crystallization of the perovskite layer, was utilized to form a quasi-continuous sheet for this purpose. It was reported that both the humidity and thermal stabilities of the solar cell were improved with the PVK modification (Fig. 19b). The explanation could be that the PVK layer can decrease the perovskite grain boundary exposed and make the Perovskite surface much smoother. Park et al. [100] tried to improve the thermal stability by introducing phenyl-C61 -butyric acid methyl ester (PCBM) in the perovskite layer, which was found to be located at the grain boundary areas. They also found that with the concentration of the PCBM increasing, the thermal stability of the PSC increased accordingly. Furthermore, Park et al. also researched the influence of perovskite grain sizes on the thermal stability. Several different grain size (10–150 µm) perovskite films were fabricated through hot-casting method, and the grain sizes were controlled by the substrate temperature. The results indicated that the larger grain size, the more stable the PSC was. They supposed that the chemical binding of the grain boundaries was smaller than the inside of the crystals. With the grain size growing larger, the grain boundary area decreased, which improved the stability. In terms of sealed solar cells, Baranwal el al. [101] reported that the sealing technique can also influence the thermal performance. A kind of UV-curing glue was utilized to seal the porous carbon counterelectrode PSCs. Two different sealing designs were studied in this work, which were over sealing and side sealing. Surprisingly, on one hand, the over sealing device showed even worse thermal stability when tested at 100 °C. On the other hand, the side sealing device had very robust behavior, with no apparent change in PCE even after 1500 h testing. The reason for this phenomenon is still waiting to be found. However, this finding can provide an important reference to the solar cell industry for the commercialization of the PSC.

4 Other Issues With the advent of the PSCs recently, issues other than efficiency and stability should also be focused, such as toxicity. Pb is a major element in PSCs as well as a toxic element. After intake, the Pb compounds can be transported to the entire body through blood transportation, which might be harmful to many organs, such as liver, kidney, and nerve system [21]. For better environmental sustainability and toxicity removal, Singh et al. [102] substituted Pb with Mn to fabricate MAPbx Mn1-x I1+2x Cl2-2x (x:0.11.0) PSCs. The PSC can provide 1.19 V in Voc and 87.9% in fill factor as shown in Fig. 20a. Johansson et al. [103] utilized a lead-free and low-toxic CsBi3 I10 as the perovskite material. They found that the CsBi3 I10 can absorb broader spectrum, and it could be an important alternative material in solar energy harvesting with low toxicity (Fig. 20b).

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Fig. 20 a A lead-free manganese-based PSC [102]. Printed with permission from Ref. [102]. Copyright 2016, The Royal Society of Chemistry. b A lead-free and low-toxic CsBi3 I10 -based PSC [103]. Adapted with permission from Ref. [103]. Copyright 2016, American Chemical Society. c Efficient colorful PSC based on a transparent conductive polymer as the top electrode [23]. Adapted with permission from Ref. [23]. Copyright 2016, American Chemical Society

Besides, aesthetics of the PSCs was also an interesting topic, which may meet the requirement of architecture design. Jiang et al. [23] found that the perovskite was commonly in dark-brown color due to the large absorption coefficient. To get colorful PSCs, they utilized a transparent conductive polymer poly(3,4ethylenedioxythiophene):poly(styrenesulfonate) (PEDOT:PSS) as the top electrode, which was a selective antireflection coating simultaneously. The PEDOT:PSS layers were deposited by spin-coating or transfer-printing technique (denoted as PEDOT:PSST ). The colorful PSCs can be obtained by compromising part of the PCE, as shown in Fig. 20c.

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5 Conclusions and Perspectives Since the debut of the perovskite solar cell (PSC) in 2009, a lot of researches have been done with respect to different aspects. The PSCs are believed to have great potential in solar cell industries, since the dramatic power conversion efficiency (PCE) improvement in such short time (i.e., from 3.8% in 2009 to 25% up to date). Organolead halide perovskite materials are commonly used in the PSC, such as CH3 NH3 PhI3 . In order to improve the PCE, many methods have been taken. In terms of the materials, some ions and molecules were doped in the perovskite layer, charge transporting layers, and/or even the electrode layers. Some of the doped ions and molecules can help to improve the intrinsic PCE, and some of them can help modify the microstructure. It is also believed that increasing the crystal sizes, decreasing the defects and pinholes, and strengthening the chemical bonding can lead to PCE improvement. Moreover, advanced processing and fabricating methods such as interface modification, spray-coating, doctor-blading coating, slot-die coating, and aerogel-jet-assisted printing can also improve the PCE of the PSC. Besides PCE, stability is also an important issue in PSC, because the perovskite can be easily decomposed with moisture, UV light, and overheating, which is a big challenge for the commercialization of PSCs. Many ions were introduced into the perovskite to improve the intrinsic stability. Many engineering methods have been taken to improve a particular stability. For example, to improve the moisture stability, hydrophobic layers were added to protect the perovskite layers from wetting by the working environment. In order to improve the UV stability, not only a UV blocking layer can be added, which can filter the UV light, but also some “downshifting materials” can be doped, which is a kind of luminescence semiconductor and able to convert the UV light into visible region. Last but not least, some issue, such as toxicity and aesthetics, are also considered. The researches in this topic will make the PSCs more comprehensive and complete in terms of the functionality. All in all, more studies should be conducted, respect to all the aspects. Hopefully, PSCs with high efficiency and stability, low cost and toxicity PSCs can be commercialized within a short time.

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State-of-the-Art of Solution-Processed Crystalline Silicon/Organic Heterojunction Solar Cells: Challenges and Future Jaker Hossain, A. T. M. Saiful Islam, Koji Kasahara, Ryo Ishikawa, Keiji Ueno, and Hajime Shirai Abstract In this chapter, we delineate the present state-of-the-art of solutionprocessed PEDOT:PSS/n-Si heterojunction solar cells in detail. Here, we discuss the emergence, principle of operation, fabrication process, carrier transport properties, and evolution of the efficiency of the PEDOT:PSS/n-Si heterojunction solar cells. We also discuss with the challenges of the solar cells and propose few design guidelines to further improve the efficiency of the solar cells in future. The SCAPS1D simulation reveals that the use of n+ CdS or In3 Se4 BSF layer which can be deposited by simple solution process enhances the efficiency of the PEDOT:PSS/nSi heterojunction solar cells to 30.94–35.05% with a higher VOC of 0.89 V. The short-circuit current of the solar cells can be further increased by the use of proper ARC layer on the top of the PEDOT:PSS/n-Si heterojunction solar cells.

1 Introduction The study of photovoltaics as a promising renewable clean energy technology has become indispensable due to the global energy challenges as well as the greenhouse effects. In the last few decades, crystalline silicon (c-Si) solar cells have covered over 90% share of the market in the field of photovoltaic technology despite its very high temperature of ~1400 °C and high vacuum fabrication process [1, 2]. Nowadays, the efficiency of this solar cell using back contact structure has been demonstrated to 26.33% with a practical module size of 180 cm2 [3]. J. Hossain (B) Solar Energy Laboratory, Department of Electrical and Electronic Engineering, University of Rajshahi, Rajshahi 6205, Bangladesh e-mail: [email protected] A. T. M. Saiful Islam Department of Electronics and Telecommunication Engineering, Bangabandhu Sheikh Mujibur Rahman Science & Technology University, Gopalganj 8100, Bangladesh K. Kasahara · R. Ishikawa · K. Ueno · H. Shirai Graduate School of Science and Engineering, Saitama University, Saitama 338-8570, Japan © Springer Nature Switzerland AG 2021 J. K. Roy et al. (eds.), Development of Solar Cells, Challenges and Advances in Computational Chemistry and Physics 32, https://doi.org/10.1007/978-3-030-69445-6_2

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Almost a decade ago, a research group of Princeton University introduced a new type of heterojunction solar cell based on the n-type crystalline silicon and a conductive polymer poly(3,4-ethylenedioxythiphene):poly (styrene sulfonate) (PEDOT:PSS), i.e., PEDOT:PSS/n-Si structure [4]. These types of solar cells combine the high efficiency of silicon solar cells and the advantages of low-cost solution processed organic polymers being simple to process on silicon substrate and thus reducing high technological demands [4–8]. Thin films of the PEDOT:PSS polymer are mechanically flexible and highly transparent in the visible spectrum [9–11]. The electrical conductivity of this polymer has been modified to 1000–1500 S/cm by incorporating different types of polar solvents, e.g., methanol (MeOH) or ethylene glycol (EG) solvent alone, MeOH/EG cosolvents, DMSO, and graphene oxide (GO) to enhance the efficiency of the solar cells [12–16]. And also, the uniformity of spin-coated PEDOT:PSS film on hydrophobic H-terminated crystalline Si has been improved by the addition of surfactants like Zonyl and Triton X100 [5, 17]. The efficiency of solution-processed organic/n-Si heterojunction solar cells has already increased to 13–20% by adjusting a type of solvents, the PEDOT:PSS film thickness, and the resistivity of silicon wafers without an extra light-harvesting technique [8, 18–24]. Day by day, the PEDOT:PSS/n-Si heterojunction solar cells are becoming compatible with the well-established c-Si PV technology. Most recently, the modules of PEDOT:PSS/n-Si solar cells have also been reported with ten units of series-connected 2 × 2 cm2 (4 inch)-sized cells showing an output power of 0.37 W (7.3 W) having an efficiency of 13–14% (11–12%) fabricating by all solution process [25]. In this chapter, we discuss the present state of the art of PEDOT:PSS/n-Si heterojunction solar cells along with challenges associated with the fabrication process and provide some guidelines to further improve the efficiency of the solar cells in future.

2 PEDOT:PSS and PEDOT:PSS/c-Si Heterojunction Solar Cells The chemical structure of the PEDOT:PSS polymer is depicted in Fig. 1a. The chemical structures of PEDOT:PSS consist of two ionomers. One ionomer is the conjugated hydrophobic and conductive polymer, PEDOT which transports the positive charges. Another ionomer is the hydrophilic and insulating PSS chain which transports negative charge. However, spectroscopic ellipsometry (SE) study reveals that the average carrier concentration of the modified PEDOT:PSS is about 1020 –1021 cm−3 [26]. Thus, the PEDOT:PSS polymer has metal-like properties. The Schottky junction is frequently observed at the metal/semiconductor junction and there are many studies which consider n-Si/PEDOT:PSS interface as Schottky-like junction [27–31]. In addition, PEDOT:PSS shows optical anisotropic behavior, uniaxial with the optic axis parallel to the surface normal [32] and large HOMO and LUMO energy different (~5.05 eV) [33].

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(a)

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(b)

(c)

Fig. 1 a The chemical structure of PEDOT:PSS polymer, b the schematic structure of the PEDOT:PSS/n-Si HOT solar cell, and c the schematic band diagram of PEDOT:PSS/n-Si heterojunction HOT solar cells

Because of having high transparency, preferred work function and enhanced hole mobility PEDOT:PSS became the most extensively studied polymer [34–36]. A number of solution process techniques such as spin coating, electrospray, chemical mist deposition, screen printing, and ink jet can be used to fabricate silicon-polymer (PEDOT:PSS) heterojunction, which allows a wide range of parameter controls to optimize the junction [5, 37–39]. Figure 1b depicted the schematic structure of the c-Si/PEDOT:PSS heterojunction with organic thin-layer (HOT) solar cell, in which c-Si is responsible for adequate amount of light absorption; on the other hand, PEDOT:PSS serves as both the anti-reflection and carrier transporting layer [40–42].

2.1 Electronic Structure of PEDOT:PSS/c-Si Heterojunction Solar Cells The device operation of PEDOT:PSS/c-Si heterojunction solar cell is based on charge-selective n-type Si and the synthetic hole-conducting p-type metal PEDOT:PSS as schematically shown in Fig. 1c. The photogenerated holes at the silicon pass through the junction and are collected by the anode and photogenerated

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electrons are blocked by the PEDOT:PSS layer due to higher LUMO and collected by the cathode. Despite the immense success of this device concept, the working principle has not been entirely resolved. There are few studies which consider PEDOT:PSS/n-Si interface as “Schottky-like” junction ascribing the high opencircuit voltage (VOC ) to an un-pinning of Fermi level at the junction [27–31]. In a Schottky junction, carrier transport is mainly dominated by thermionic emission of majority carriers over the potential barrier formed at the interface [43]. There are some other reports which consider this junction as a conventional abrupt p+ n heterojunction [36, 44, 45]. In a conventional abrupt p+ n heterojunction, carrier transport is dominated by the diffusion of minority carriers in the bulk silicon [36].

2.2 Fabrication Procedure of PEDOT:PSS/n-Si Heterojunction Solar Cells Most of the PEDOT:PSS/n-Si heterojunction solar cells discussed in this chapter were produced by spin-coating method. Here, we, therefore, discuss the recipe of the spin-coated PEDOT:PSS/n-Si solar cells. The highly conductive PEDOT:PSS (CleviosR PH1000) purchased from Heraeus was used in this study which contains 0.37 wt.% of PEDOT and 0.93 wt.% of PSS. Before use, the solution was filtered out with a syringe filter of 0.45 μm pore size to remove the coagulated parts and other contaminants. The PEDOT:PSS solution was further modified by adding ethylene glycol (EG) and capstone fluorosurfactant in the ratio of 93:7:0.16 wt.% to increase conductivity and to improve the wettability of the solution for uniform deposition over the hydrophobic silicon surface. As a first step, 250-μm-thick oriented plain n-Si substrates were cleaned by standard RCA cleaning. RCA cleaning was done in two steps. First, the samples were immersed in RCA1 solution of DI water, 37% ammonium hydroxide (NH4 OH), and 30% hydrogen peroxide (H2 O2 ) in the weight ratio of 5:1:1 for 15 min, followed by rinsing in DI water. Secondly, these RCA1 cleaned samples were immersed in RCA2 solution of DI water, 37% hydrochloric acid (HCl), and 30% H2 O2 in the weight ratio of 6:1:1 for 10 min, followed by rinsing in DI water. Then, the native oxide was removed by hydrofluoric acid treatment and blow-dried with N2 . In the next stage, the PEDOT:PSS was spin coated at 2000 rpm for 30 s, (thickness: ~80 nm) then the films were annealed at 140 °C for 30 min to dispel the residual solvent. The Ag paste was screen printed onto the PEDOT:PSS as anode and screen-printed Ag together with evaporated Al at the backside worked as a cathode.

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3 Carrier Transport in PEDOT:PSS/n-Si Heterojunction: Schottky or p+ n Junction? To understand the junction properties, C–V, J–V in dark and under the illumination of 1.5AM simulated light, EQE of PEDOT:PSS/n-Si solar cells with different N d of n-Si substrate, together with two-diode model analysis of the experimental dark J–V characteristics are studied in detail. Then, these data are compared assuming Schottky and p–n junction models.

3.1 Modeling of PEDOT:PSS/n-Si Junction As mentioned in Sect. 2.1, there may form two possible junctions at the PEDOT:PSS/n-Si interface, namely, Schottky junction and p+ -n junction. In both cases, the J–V characteristics under illumination can be described by an ideal diode equation (Eq. 1) [46].     qV − 1 − Jsc J (V ) = J0 exp kT

(1)

From the definition of open-circuit voltage (Voc ), by setting J = 0, Eq. 1 can be rewritten as follows:   Jsc kT (2) ln Voc ≈ q J0 The Voc is dominated by J 0 and J sc . Usually, the J sc varies in small scale, whereas J 0 varies in order, so the Voc is mostly dependent on J 0 . However, it is well known that the J 0 of a Schottky junction is described by the thermionic emission of the majority carriers. On the other hand, the diffusion of the minority carrier dominates the p–n junction [46]. Therefore, the J 0 for both the Schottky and p–n junctions can be written as follows:   q∅ B (3) J0 = A∗∗ T 2 exp − kT J0 =

n i2 μ p kT L p Nd

(4)

respectively, where A∗∗ is Richardson constants and J. M. Andrews et al. reported its value ~110 A/(cm K)2 for majority carrier by considering tunneling and scattering at phonon together with a small contribution of majority carrier diffusion for moderately doped silicon [47]. From Eq. 3, at a constant junction temperature (T) the J0 of Schottky junction is varied with Schottky barrier height (∅ B ), and the ∅ B varies

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slightly at very high N d [46]. In Eq. 4, n i represent the intrinsic carrier concentration of the Si substrate (~1010 cm−3 at 300 °K [48, 49]), μ p and L p are the minority carrier mobility and diffusion length, respectively. So, the J0 of the p–n junction is greatly influenced by minority carrier density at the bulk. However, J–V characteristic (Eq. 1) of single diode model is only considering the bulk recombination, but in practice, junction parasitic resistance (series Rs and shunt Rsh ) with recombination and generation of the carrier at space-charge region are also the dominating factors [50]. In that case, the J–V characteristics of an abrupt p–n junction are described by two-diode model [46]:         V − Rs J q(V − Rs J ) q(V − Rs J ) − 1 + J02 exp −1 + J = J01 exp − Jsc n 1 kT n 2 kT Rsh

(5)

where J01 is associated with bulk diffusion contribution and the J02 from the trapassociated generation and recombination at the space-charge region.

3.2 Analysis of PEDOT:PSS/n-Si Junction 3.2.1

Inversion at Heterojunction Interface

It is well known that, when a p-type material meets with n-Si, an inversion layer is formed at the interface. Figure 2 shows a typical band diagram of an inversion interface. Depending on the value of surface potential (ψs ) the inversion layer is classified as weak and strong. In case of the Schottky junction, the Fermi level pinning is frequently observed at the surface defects, and the threshold V bi is determined by the difference between the intrinsic energy of c-Si and the Fermi energy [46].   q Vbi(weak) ≈  E f − E i  Fig. 2 Energy band structure of an organic/n-Si heterojunction

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  = (E c − E i ) − (E c −E f ) Eg kT Nc = − ln 2 q Nd

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(6)

On the other hand, the band bending in the intrinsic energy level of Si crosses the Fermi level when the surface of the silicon is passivated sufficiently, which induces a strong inversion at the surface. In that case, the V bi is determined by   q Vbi(Str ong) ≈ 2 E f − E i    = 2(E c − E i ) − (E c −E f ) = Eg −

2kT Nc ln q Nd

(7)

3.3 Junction Type of PEDOT:PSS/n-Si The built-in potential at PEDOT:PSS/n-Si junction for different Nd (ranging from 1016 to 1018 cm−3 ) of Si substrates was extracted from 1/C2 -V characterization at a measurement frequency of 100 kHz [33]. It was observed that built-in potential (V bi ) was increased with increasing doping density of the n-Si. The V bi together with weak inversion (Eq. 7) and strong inversion (Eq. 8) as a function of N d is illustrated in Fig. 3. All the experimental V bi are at the strong inversion zone, suggesting that n-type Si is fully inverted to a p-type at the interface without additional doping. Figure 4 depicts J–V and normalized EQE under 1.5AM simulated solar light of solar cell devices with the corresponding donor-doped Si substrates. The V oc Fig. 3 V bi of PEDOT:PSS/n-Si junction with respect to strong and weak inversion for different N d of Si substrates

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Fig. 4 a Light J–V characteristics and b EQE of PEDOT:PSS/n-Si solar cells for different N d of Si substrate

increased from 563 to 623 mV with increasing N d of the Si substrate because of rising the V bi , and highly conductive nature of the PEDOT:PSS, which lead toward higher (>70%) FF for all the fabricated devices, higher FF also indicating good passivation of the Si surface by PEDOT:PSS. However, J sc is slightly reduced for higher Nd of solar cells. A reason is, with increasing N d the carrier diffusion length decreases, and the recombination center increases, and as a result, the EQE at longer wavelength (above 600 nm) region decreases with increasing N d . On the other hand, due to the enhancement of V bi with N d , the carrier collection near the junction will also increase with N d . Thus, higher EQE is observed for high N d solar cells at the short wavelength ( 4 × 1012 s−1 ). It is worth mentioning that Liu and Troisi reported that kCS depends strongly on the structure of the P3HT-PCBM dimer. In order to consider more realistic dimer structures for the CS (CR) calculations, Troisi and coworkers performed molecular dynamics (MD) simulations on a system formed by 160 molecules of PCBM interacting with a 4-layer crystal domain of 20-unit P3HT oligomers [32]. In these simulations, each layer was formed by eight P3HT oligomers. They considered snapshots of P3HT/PCBM dimers from the MD trajectories to obtain geometries to be used in the DFT calculations. Troisi and coworkers concluded that kCS and kCR can vary orders of magnitude depending on the dimer structure (7.7 × 109 s−1 < kCS < 1.8 × 1012 s−1 ) [32]. There is strong experimental evidence, and it is also clear from a theoretical perspective, that dispersion forces are an important component in intermolecular interactions. In particular for weakly interacting systems including aromatic molecules or fullerenes, a proper inclusion of van der Waals (vdW) interactions in the Hamiltonian is indispensable for an accurate description of interaction energies, intermolecular forces, and hence structures of supramolecular systems [33–37]. Surprisingly almost

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none of the DFT/TDDFT studies that report CS and CR rates for the P3HT/PCBM OPV included vdW interactions to obtain the structure of the P3HT/PCBM interface. An exception is our recent work in which we report that dispersion forces can have drastic effects on structural, and in consequence electronic, optical and CS properties in OPVs [15–18]. In particular the charge separation rate constant kCS that was computed in our work reached, to the best of our knowledge for the first time, the experimental range as a result of properly taking into account vdW interactions in the theoretical model. It is worth mentioning that other recent DFT based studies also started to consider vdW interactions [38]. In the following sections our computational approach and results are described in more detail.

3 Structure of the P3HT/PCBM Interface 3.1 The Model System Similar to previous works, we decided to model the P3HT-PCBM interface considering a single dimer composed of one PCBM acceptor molecule and an 8-unit oligomer of P3HT as donor (see Fig. 4). The length of the oligomer had already been discussed in a previous work by Liu and Troisi, who concluded that a six-unit oligomer was sufficiently long to describe CT reactions between P3HT and PCBM [39]. Different oligomer sizes have been considered in the literature [31, 38–40]. The conjugation length of polythiophene was experimentally evaluated between 6 and 12 thiophene rings [39, 41]. In our studies, a P3HT oligomer with 8 units was chosen as the largest oligomer to model the P3HT chains, which is sufficiently large to converge electronic properties and sufficiently small to keep calculations of P3HT-PCBM dimers computationally feasible within the DFT framework [15–18].

Fig. 4 Dimer formed by a PCBM molecule and an 8-unit oligomer of P3HT. This dimer is a simplified model system for the P3HT/PCBM active layer interface

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3.2 Computational Details All our results presented in this chapter were performed with the Amsterdam Density Functional (ADF) package [42–44]. Different versions of ADF have been used since the results presented here were obtained over the course of several years. The specific version and a detailed list of ADF settings used to compute a specific property can be found below and in the corresponding original work that is cited throughout this chapter. All geometry optimizations were carried out using the Perdew-Burke-Ernzerhof (PBE) GGA xc functional [30] along with an all-electron uncontracted set of Slatertype orbitals (STOs) of triple-ζ quality (TZP) containing one set of polarization and diffuse functions [45]. The ADF integration parameter was set to 6 in order to ensure good numerical accuracy for the numerical quadrature. Unless otherwise explicitly stated, ADF default settings were used for the SCF procedure, geometry optimizations and property calculations. The Grimme dispersion correction scheme DFT-D3 was employed in order to take vdW interactions into account. In this approach, the C6 dispersion coefficient is parameterized for each pair of atom types (elements) for the hydrates of each element based on ab-initio reference calculations using the Casimir-Polder formula. The C8 coefficients are obtained recursively from C6 , while cutoff radii and damping function parameters are obtained empirically for each xc potential [46]. The geometries were fully optimized at the all-electron PBE-D3/TZP level of theory considering a convergence threshold for the energy gradients with respect to the nuclear coordinates equal to 10−4 Hartree/Angstrom. The TDDFT calculations were carried out with the PBE GGA xc functional, the B3LYP [47, 48] global hybrid xc functional, and two different range-separated hybrid xc functionals, CAMY-B3LYP [49, 50] and ωB97X [51]. It is well known that GGA xc functionals in particular but also global hybrid xc functionals fail to correctly describe excitations with charge-transfer character. Range-separated xc functionals overcome this problem and benchmarks have shown that in particular ωB97X performs very well for different types of excitations with or without charge-transfer character [52, 53]. Because of the high computational cost for range-separated xc functionals, the simplified TDDFT approach by Grimme [54] (sTDDFT) was used with the ωB97X functional, after carefully checking that sTDDFT gives effectively the same spectra as a full TDDFT calculation. The B3LYP and ωB97X calculations were performed with a Becke integration grid [55] of ADF quality setting “good” in order to guarantee numerically accurate solutions of the TDDFT equations. The libxc library [56] was employed with ADF for TDDFT calculations with range-separated hybrid functionals. The convergence of spectra computed with TDDFT was carefully checked with respect to the number of allowed singlet-singlet transitions that were computed. To plot the absorption spectra, the absorption peaks were broadened using Gaussian functions with a half-width of 0.2 eV. All QTAIM calculations were performed by using our high performance method as implemented in ADF, which allows one to apply QTAIM to large systems containing hundreds of atoms [57–60].

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3.3 The PES of the P3HT/PCBM Dimer An exhaustive exploration of the Born-Oppenheimer potential energy surface (PES) of the P3HT/PCBM dimer at the DFT level of theory is out of reach with current computational resources. A valid approach would be to use less computationally demanding but more approximate methods to explore the dimer PES, for instance through the application of classical force fields, which would enable sampling via MD simulations. Instead of resorting to empirical potentials we decided, as a first approximation, to partially explore the PES by performing DFT based geometry optimizations starting from a family of over 10 different initial nuclear geometries of the P3HT/PCBM dimer [15]. The optimized structures of the isolated molecules (8-unit P3HT oligomer and PCBM) were used to construct the starting geometries for the dimer optimizations while changing the relative position of P3HT and PCBM but restraining the closest intermolecular distance in the range of 3–5 Å. Two distinct P3HT/PCBM starting structures are shown in Figure 5a along with the resulting stable local isomers that were obtained from geometry optimizations, see Fig. 5b, c. A relevant structural feature of the stable P3HT/PCBM dimers is that, driven by dispersion forces, the P3HT oligomer embraces the PCBM bucky ball, thus adopting a bent (U-shape) conformation as can be seen in Fig. 5b, c. In addition to the curvature along the backbone, adjacent thiophene rings are also rotated with respect to each other, with S-C-C-S dihedral angles of approximately 15◦ . Figure 6 contains a visualization of the dihedral angles between adjacent thiophene rings for the optimized dimers P3HT-I1 and P3HT-I2. The relative rotations of the thophene rings follow an alternating clockwise and anticlockwise pattern. The reason for this deformation is

Fig. 5 Two stable isomers for the P3HT/PCBM dimer formed by an 8-unit P3HT oligomer and one PCBM molecule. First row refers to the lowest-energy isomer (I1); second row to the next higher energy isomer (I2). a Initial geometries used in the geometry optimization procedure; b optimized geometries; c optimized geometries without P3HT alkyl side chains and hydrogen atoms. The energy difference between the two isomers is 3.126 eV. Reproduced from Ref. [15], Copyright (2014), with permission from Elsevier

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Fig. 6 P3HT chain in a isomer I1 and b isomer I2. The dihedral angles (Di ) between adjacent thiophene rings are explicitly shown. Reproduced from Ref. [16], Copyright (2016), with permission from Elsevier

that it minimizes the distance between the P3HT and the bucky ball thus maximizing the interaction energy that is dominated by dispersion forces. The adjacent thiophene rings of the P3HT oligomer backbone are in general in trans-position with respect to the C–C bond that connects two thiophene rings. However, this symmetry can be easily broken by complete rotation around the connecting bond. This is the case for dimer P3HT-I2, where thiophene ring R7 is in a cis position with respect to thiophene ring R6. This is in contrast to oligomer P3HT-I1 where all thiophene rings are in the more favorable trans configuration [15]. The minimum distance between the P3HT and PCBM in the stable isomers I1 (the lowest-energy isomer) and I2 is equal to 2.08 Å and 2.27 Å, respectively [15]. This is in the range of typical π–π interactions. Another interesting feature of these isomers is that the P3HT alkyl side chains are also wrapped around the PCBM. In fact, it has been reported that these alkyl chains help to “anchor” the P3HT onto the PCBM. Of course there are no covalent bonds formed between P3HT and PCBM but rather weak dispersion forces, which, however, in sum lead to a considerable interaction energy. These facts are corroborated by an analysis with Bader’s quantum theory of atoms in molecules (QTAIM), which is introduced in the next section of this chapter. In order to demonstrate the impact of the vdW interactions on the structure of the P3HT/PCBM isomers, complementary geometry optimizations were performed without considering the vdW Grimme correction (using PBE instead of PBE-D3 approximation) [15]. Geometry optimizations with PBE did not lead to bound dimers, and depending on the initial starting geometry, interactions can actually be repulsive without addition of dispersion corrections. Thus, we can conclude that the distortion of both the P3HT backbone and the alkyl side chains towards PCBM are a result of

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dispersion forces, which, in turn, lead to stable P3HT/PCBM dimers in the first place [15, 16]. Other computational studies report stable P3HT/PCBM dimers obtained with the B3LYP xc functional without dispersion correction. However, in this case the P3HT chain remains completely unperturbed and planar also in the P3HT/PCBM dimers [39], indicating that the minima are very shallow, underestimating the interaction between P3HT and PCBM. In the following sections of this chapter, we will show that these structural distortions of P3HT due to dispersion forces between P3HT and PCBM in the P3HT/PCBM dimer are the source for the experimentally observed changes in optical properties. They also form the basis for a computational prediction of charge separation properties that closely match the experimental data.

4 QTAIM Properties The quantum theory of atoms in molecules (QTAIM) provides a topological description of a molecule by using the electron density to define atoms in real space [61–63]. Atoms are partitioned by the so-called zero-flux surfaces and atomic properties can be computed by integrating a property density over the atomic volumes enclosed by the zero-flux surfaces. Using this approach, it is possible to uniquely determine partial charges of individual atoms or molecular fragments. The total charge (in a.u.) of the P3HT and PCBM molecules within the two most stable dimer isomers I1 and I2 take on the following values according to the P3HT PCBM = 0.094 and qI1 = −0.098; and distribution of QTAIM atomic charges: qI1 P3HT PCBM = −0.008. These values do not exactly add up to zero qI2 = 0.010 and qI2 due to the numerical method employed. In any case, they clearly indicate a charge transfer between P3HT and PCBM, particularly in Isomer 1, which is in agreement with the reported experimental non-photoinduced charge transfer [15, 16]. As shown in the last section, the dispersion interactions are responsible for stabilizing the dimers. Are there alternative ways to quantify these interactions? In addition to atomic properties, Bader’s QTAIM method allows one to explore the nature of the chemical bond and quantitatively analyze how many chemical bonds, of any type, exist in the system. According to QTAIM, a chemical bond in a molecule is predicted by the existence of a bond critical point (BCP) between two atoms and, as a complementary information, its corresponding bond path (BP). Figure 7 shows the so-called molecular graph for the dimer isomer I1, which was obtained from a QTAIM calculation at the optimized geometry. It displays all 385 chemical bonds in the dimer I1 predicted by the electron density BCPs (green dots). Out of these 385 bonds, 37 are intermolecular bonds, that is, bonds formed by one atom in P3HT and the other in PCBM [16]. The remaining 348 bonds correspond to covalent bonds formed in each monomer (P3HT or PCBM), which are well classified in the literature as typical covalent bonds in organic molecules [61, 63]. Thus we here focus only on the 37 intermolecular bonds whose bond information is listed in Tables 1 and 2.

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Fig. 7 Molecular graph of the P3HT/PCBM isomer. Red, green, light blue and light gray dots are bond (BCP), ring (RCP), cage (CCP) and nuclear critical points (NCP) of the electron density. Bond paths are colored according to the density value: from dark-blue/high to yellow/low Table 1 Minimum, maximum and mean values (in a.u.) of the electron density (ρ) and its Laplacian (∇ 2 ρ) at each type of intermolecular BCP. Bond length values (d, in Å) are also shown. The last row shows the global value of each quantity over the total BCPs of each type. Reproduced from Ref. [16], Copyright (2016), with permission from Elsevier Bond type ρ L d Min Max Mean Min Max Mean Min Max Mean Isomer I1 H· · · X H· · · H Stacking Total global Isomer I2 H· · · X H· · · H Stacking Total global

0.0035 0.0024 0.0076 0.0024

0.0107 0.01 0.0117 0.0117

0.0065 0.0069 0.009 0.0074

0.011 0.007 0.023 0.007

0.032 0.037 0.033 0.037

0.02 0.023 0.027 0.024

2.5 2.09 3.01 2.09

3.21 2.75 3.47 3.47

2.81 2.3 3.24 2.79

0.0025 0.0028 0.0035 0.0025

0.0103 0.0063 0.0075 0.0103

0.0046 0.0041 0.0054 0.0047

0.008 0.01 0.013 0.008

0.039 0.021 0.022 0.039

0.015 0.013 0.016 0.015

2.36 2.27 3.47 2.27

3.34 2.72 3.8 3.8

3.01 2.5 3.6 3.03

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Table 2 Number of different types of intermolecular BCPs between atoms of different chemical groups: P3HT-C6 H13 side chains (SC), the P3HT backbone (BB), the C60 in PCBM (C60 ), and the functional group C12 H14 O2 in PCBM (FG). The last row shows the percentage contribution of each intermolecular group interaction. The last column shows the percentage contribution of each type of intermolecular BCPs. Reproduced from Ref. [16], Copyright (2016), with permission from Elsevier Bond type SC-C60 SC-FG BB-C60 BB-FG P3HTPercentage PCBM (%) Isomer 1(I1) H· · · X H· · · H Stacking Total Percentage (%) Isomer 2(I2) H· · · X H· · · H Stacking Total Percentage (%)

20 0 0 20 54.1

1 10 0 11 29.7

0 0 3 3 8.1

3 0 0 3 8.1

24 10 3 37 100.0

64.8 27.0 8.1 100.0

18 0 0 18 45.0

5 7 0 12 30.0

1 0 4 5 12.5

3 0 2 5 12.5

27 7 6 40 100.00

67.5 17.5 15.0 100.0

The QTAIM gives precise information of each bond formed in the system, which is an interesting and useful feature that has been exploited in many research areas [63]. For instance, the 37 intermolecular bonds can be grouped according to the chemical group they belong to. Following our previous work, it is useful to break down the intermolecular BCP (interBCP) bond information into contributions from (i) the P3HT side chains (SC) = C6 H13 , (ii) the P3HT backbone (BB), (iii) the C60 in PCBM (C60 ), and (iv) the PCBM functional group C12 H12 O2 (FG) [16]. In addition, the intermolecular bonds can be classified into three types: a BCP between two hydrogen bonds (H· · · H); a BCP between a hydrogen and another atom (H· · · X; X=C, O, S); and stacking BCP (C· · · C, and S· · · Y; Y=C, O) as defined previously [16, 64, 65]. It is important to keep in mind that the weak intermolecular bonds that involve a hydrogen atom (H· · · H and H· · · X) in this work were not further subclassified according to the conventional definition of hydrogen or dihydrogen bonds. Here we only refer to “a bond where a hydrogen atom is involved” in an intermolecular bond. According to QTAIM, all these 37 intermolecular bonds can be classified as weak bonds because the value of the Laplacian of the electron density at position of the → → r BCP ) > 0) and have a small corresponding BCP (− r BCP ) is greater than zero (∇ 2 ρ(− − → value of the electron density (ρ( r BCP ) < 0.01 a.u.) with an internuclear distance that is generally significantly longer than the sum of the van der Waals radii of the

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atoms sharing a given bond path (see Table 1) [16, 63, 66, 67]. From Table 1, we can see that the corresponding BP of each of these weak intermolecular bonds is longer (>2 Å) than the other “covalent” BPs (≈2 Å). This is indicated by an increasingly red color in Fig. 7 as the electron density decreases on these longer intermolecular BPs. The number of interBCPs belonging to each chemical group is listed in Table 2 for both stable P3HT/PCBM isomers I1 and I2. We can see that noncovalent interactions involving hydrogen atoms (as H· · · X and H· · · H bonds) account for 92% and 85% of the total number of intermolecular bonds for I1 and I2, while the stacking bonding accounts only for 8% and 15% for I1 and I2, respectively. The H· · · X bonds represent 64.9% and 67.5% of the noncovalent interactions for I1 and I2, respectively; the H· · · H bonds represent 27.0% and 17.5%, for I1 and I2, respectively. Notice that the C6 H13 side chains of P3HT participate in 83.8% and 75.0% of the total number of noncovalent bonds for I1 and I2, respectively; the C12 H14 O2 functional group of PCBM participates in 37.8% and 42.5% of the bonds [16]. From these values we can conclude that interactions between the P3HT side chains and the PCBM are mainly responsible for anchoring the P3HT into PCBM. On the other hand, intermolecular bonds that involve hydrogen atoms are the most common type of interBCPs.

5 Optical Properties In order to better quantify the effect of structural deformations due to dispersion forces on the optical properties, three idealized P3HT/PCBM dimers are considered in this section (see Fig. 8). In these dimers (I3, I4, I5) the P3HT chains are planar, similar to the dimers obtained elsewhere [39] from geometry optimization with the B3LYP xc functional without Grimme dispersion correction. As stated in Sect. 3, geometry optimizations did not converge for the P3HT/PCBM dimers using PBE without the Grimme dispersion correction. We therefore manually constructed the idealized dimers I3 to I5 by changing the shortest intermolecular π–π stacking distance between PCBM and P3HT. Single point TDDFT calculations were performed on the optimized P3HT/PCBM dimer isomers I1 and I2 and the P3HT/PCBM dimers I3 to I5 that are shown in Fig. 8. For all five dimers, the TDDFT calculations were performed with different xc functionals, PBE and B3LYP , and also including the ωB97X [51] range-separated hybrid functional to verify that the conclusions drawn are not an artifact of the chosen xc functional. It is well known that the range-separated functionals perform very well for different types of excitations including those with charge-transfer character which are found in P3HT/PCBM dimers (see below). Because the hybrid xc functional B3LYP and in particular the range-separated xc functional ωB97X are computationally more demanding than the PBE generalized gradient approximation xc functional, fewer excitations were computed for B3LYP and Grimme’s simplified TDDFT method was used in conjunction with ωB97X, carefully checking that the number of included excitations is sufficient to cover the desired range in the UV/Vis spectra.

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Fig. 8 Structure of the P3HT-PCBM dimer with different intermolecular π–π stacking distances D between an idealized, planar P3HT oligomer and PCBM. D(I3) = 3.5 Å, D(I4) = 4.5 Å, and D(I5) = 5.5 Å for dimers I3, I4, and I5. Reproduced from Ref. [18], Copyright (2019), with permission from Wiley

Figure 9 shows the absorption spectra of isolated P3HT, isolated PCBM, and the stable P3HT/PCBM dimers I1 ans I2 obtained at the TDDFT-PBE/TZP level of theory. From this figure, it can be seen that our computational results for the dimers succesfully reproduce the experimentally observed reduction of intensity in the red part and a blue-shift of the maximum absorption intensity peaks with respect to the spectrum of the isolated P3HT oligomer (see Fig. 3). As discussed above in Sect. 3, the translational trans symmetry of the P3HT chain is partially broken in isomer I2 but not in isomer I1 (see Fig. 6). Thus it could be argued that the the structural perturbation of the P3HT chain in I2 is more drastic than in I1. Coincidentally the reduction of intensity in the red part and the blue-shift of the maximum absorption intensity peaks in I2 are also more drastic. Interestingly, these two effects have been exprimentally attributed to the deformation of the P3HT chains in the presence of PCBM and, to a lesser extent, a non-pothoinduced charge tranfer between P3HT and PCBM in the OPV active layer [26]. Both effects are confirmed by our calculations. Figure 10 shows that these trends are also reproduced using the hybrid B3LYP and the range-separated ωB97X xc functionals. All three xc functionals PBE (Fig. 9), B3LYP (Fig. 10a) and ωB97X (Fig. 10b) reproduce the reduction of intensity in the red part and a blue-shift of the maximum absorption intensity peaks in the dimer spectrum with respect to the spectrum of the isolated P3HT oligomer. Figure 10 gives, however, additional interesting information. As reported in our recent article [18], all computed spectra of P3HT/PCBM dimers I3–I5 remain quite similar to the spectrum of pure (planar) P3HT. Actually, if the spectrum of I5, in which the intermolecular distance D is equal to 5.5 Å, is superposed with the spectrum

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Fig. 9 Calculated absorption spectra for isolated P3HT (red), isolated PCBM (black), P3HT-PCBM dimer isomer I1 (green) and isomer I2 (blue). The calculated absorption spectrum of isolated PCBM is also shown in the inset. The spectra were obtained via TDDFT-PBE/TZP calculations at the DFT-PBE-D3/TZP optimized geometries. The lowest 250 and 200 singlet-singlet allowed transitions were computed for isolated PCBM and P3HT, respectively; 150 allowed transitions were computed for both dimer isomers. Reproduced from Ref. [15], Copyright (2014), with permission from Elsevier

of isolated P3HT, there is not any perceptible difference (see Ref. [18] for details). A small amount of quenching can be observed in the region of the main absorption peak of dimer I3 (D = 3.5 Å). In other words, when intermolecular distances are larger than 3.5 Å, then there is practically no interaction between P3HT and PCBM and the dimer absorption spectrum reduces entirely to the sum of the spectra of the isolated constituent molecules P3HT and PCBM. In the region between 400 and 700 nm this is effectively the spectrum of isolated P3HT. The distance between P3HT and PCBM has to be as low as 3.5 Å for any perceptible change in the dimer optical properties to occur due to intermolecular interaction. However, as we have discussed above, a planar P3HT is an unrealistic model system. The attractive intermolecular dispersion forces with PCBM lead to deformation of the P3HT oligomer as has been shown above for the stable dimer isomers I1 and I2 (see Fig. 5b, c) [15]. The result of this structural deformation of P3HT is a significant change in the optical spectra for the stable dimer isomers I1 and I2 as compared to the spectra in which P3HT is artifically kept planar. The result is a strongly quenched absorption in combination with a blue-shift of the absorption maximum (see Figs. 9 and 10). We conclude that the main role that PCBM plays in affecting the optical absorption is an indirect one. PCBM induces deformation of the geometry of the P3HT chain through vdW interactions, which in turn changes

Structure, Electronic, and Charge Transfer Properties … Fig. 10 Calculated absoprtion spectrum obtained with the lowest 50 excitations using a TD-B3LYP/TZP and b sTD-ωB97X/TZP, for the optimized dimer isomers I1 (green), I2 (blue), and for the non-optimized structures (see Fig. 8) with planar P3HT, dimers I3 (pink), I4 (red), and I5 (maroon)

73

a)

b)

the absoroption spectrum, while direct electronic interactions between PCBM and P3HT barely reduce the absorption intensity. A small charge transfer from P3HT to PCBM as predicted by the QTAIM calculations above is responsible for the latter. The observed changes in the UV-Vis spectrum that result from interaction between P3HT and PCBM are thus almost entirely due to the structural deformation of P3HT. Similar structural deformations of P3HT have been found in experiments in which regiorandom P3HT was added to pure P3HT and are quite likely to also occur for other acceptor molecules in active layer blends of OPV devices. A more detailed discussion of the role of P3HT on the P3HT/PCBM dimer spectra can be found in our previous work [18].

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6 Charge Separation Rates As mentioned is Sect. 2, the charge separation (CS) rate constant kCS is directly proportional to the OPV efficiency (see Eq. 1). Computing kCS theoretically is thus important to predict, with the aid of a computer, if a certain material will produce a high-performance OPV or not. DFT along with TDDFT methods have been succesfully used to compute kCS within the Marcus’ theory framework. The classical Marcus formula is: [68]  kCS =

 2  2 π V  exp − (G CS + λ) , 2 λkB T i j 4λkB T

(2)

where λ is the total reorganization energy, G CS and Vi j are the CS Gibbs energy and the electronic coupling, respectively; T is the temperature, kB and  are the Boltzmann and reduced Planck constants. The Marcus formula 2 gives kCS corresponding to the nonadiabatic electron transfer reaction, P3HT/PCBM + hν −→ P3HT∗ /PCBM P3HT∗ /PCBM −→ P3HT+ /PCBM−

(3) (4)

wherein a molecular exciton localized at the P3HT fragment is initially formed by photon absorption (Eq. 3), followed by CS after the dissociation of such a Frenkel exciton (Eq. 4). We recently applied DFT/TTDFT methods within Marcus theory to compute kCS for the five P3HT/PCBM dimers I1–I5 introduced in this chapter [17]. A summary of our results is shown in Table 3. The TDDFT calculations were performed using the range-separated xc functional CAMY-B3LYP [49, 50] as implemented in ADF2016. The electronic coupling was calculated via the orbital approximation within the energy splitting in dimer (ESID) method [69–71]. From Table 3 we can see that

Table 3 Electronic couplings, Vi j ; excitation energies, E exc ; main HOMO (H) to LUMO (L) orbital contributions; oscillator strength values f ; and Gibbs energy for charge separation, G CS , for each P3HT/PCBM dimer under study. All energy terms in eV. The rate constant kCS (in 1/s) was calculated considering λint = 0.245 eV. Reproduced with permission from Ref. [17]. Copyright (2017) American Chemical Society Isomer I1

Vi j 0.0427

P3HT∗ /PCBM

P3HT+ /PCBM−

E exc

Transition

f

3.020

H→L+4

1.48

E exc

Transition

G CS

kCS

f

2.745

H→L

0.05

−0.274

5.97 × 1013

2.926

H→L+1

0.01

−0.094

2.48 × 1013 3.02 × 1011

I2

0.0031

3.271

H→L+5

0.75

3.062

H→L

0.00

−0.209

I3

0.0020

2.846

H→L+5

3.00

2.730

H→L+1

0.00

−0.116

I4

0.0004

2.850

H→L+5

3.13

2.858

H→L+1

0.00

0.008

3.68 × 108

I5

0.0003

2.852

H→L+5

3.17

2.977

H→L

0.00

0.126

1.30 × 107

7.00 × 1010

Structure, Electronic, and Charge Transfer Properties …

75

the fastest CS reaction is predicted for the lowest-energy P3HT/PCBM isomer I1. I1 = 8.46 × 1013 s−1 ) is the only one that matches Besides, this value of kCS for I1 (kCS exp the reported experimental value (kCS > 4 × 1012 s−1 ) of the OPV whose active layer I2 is a mix of P3HT and PCBM. The value of kCS for the dimer isomer I2 (kCS = 11 −1 3.02 × 10 s ) is just one order of magnitude below the experimental value. The values of kCS for the other P3HT/PCBM dimers I3–I5, however, are three to six orders of magnitude below the experimental value. Thus, as it was concluded in our original work [17], the CS reaction is predicted to be up to three (six) orders of magnitude faster for the P3HT/PCBM isomers with realistic structures obtained by properly modeling the vdW interactions (I1 and I2) than for P3HT/PCBM dimer structures with intermolecular distances of 3.5 Å (5.55 Å) in which vdW forces are not explicitly accounted for (I3–I5). Therefore, it can be concluded that faster photoinduced CS is attained by states whose geometry and electronic structure are properly predicted, which is the case here for the dimer isomers I1 and I2 with distorted, U-shaped P3HT. These conclusions give quantitative evidence that vdW interactions have to be taken into account for the proper quantum physical modeling of CS reactions and thus computational predictions of the efficiency of BHJ organic solar cells.

7 Conclusions In this chapter we have shown how DFT/TDDFT based methods can be used to properly reproduce experimentally observed OPV properties. First, a partial search of the dimer formed by a P3HT 8-unit oligomer and a PCBM molecule was carried out at the DFT/PBE-D3/TZP level of theory to obtain stable P3HT/PCBM dimers. The structure of such dimers gives an acurate picture of the amorphous P3HT-PCBM interface at the molecular level. It was demostrated that van der Waals forces play an important role in stabilizing the P3HT/PCBM dimers. Hence it is critical to employ an xc functional with dispersion corrections during the geometry optimizations. The stable dimer structures were used to compute the optical properties using TDDFT with different xc functionals. The UV-Vis absorption spectra thus obtained describe the exerimental data qualitatively quite well. While qualitative features of the absorption spectra are reproduced already with GGA xc functionals, rangeseparated hybrid xc functional such as ωB97X should be employed to avoid spurious charge transfer states and improve quantitative agreement with experiment. Performing TDDFT calculations with the range-separated CAMY-B3LYP xc functional, the charge separation rate constant kCS was computed for five P3HT/PCBM dimers (I1– I5). Here, I1 and I2 are low-lying dimer isomers obtained through geometry optimization with dispersion corrected DFT, while I3 through I5 have a geometry with planar P3HT at typical π–π stacking distance between P3HT and PCBM as would be obtained without dispersion correction. While kCS is grossly underestimated by several orders of magnitude for isomers I3 to I5, the value for the lowest-energy I1 = 8.46 × 1013 s−1 ) agrees exceptionally well with the P3HT/PCBM dimer I1 (kCS ex p reported experimental value (kCS > 4 × 1012 s−1 ). To the best of our knowledge,

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no computational value of kCS matching the experimental value had been reported before. We believe that the high quality of the DFT-D3 approximation in predicting realistic dimer structures along with using a range-separated xc functional to compute the excited states are key ingredients to reliably obtain high quality data with predictive power for optical absorption spectra and the charge-separation rate constant in BHJ-OPV materials.

References 1. REN21 (2019) Renewables 2019 global status report. Paris: REN21 Secretariat, ISBN 978-39818911-7-1 2. Sun S, Sariciftci N (eds) (2005) The story of solar cells. In: Organic photovoltaics: mechanisms, materials, and devices. Taylor and Francis Group LLC, Florida 3. Sun SS, Sariciftci NS (eds) (2005) Organic photovoltaics: mechanisms, materials, and devices. Taylor & Francis Group, Boca Raton, Florida 4. Brabec CJ, Dyakonov V, Parisi J, Sariciftci NS (eds) (2003) Organic photovoltaics: concepts and realization. Springer, Berlin 5. Chappell B (2014) http://www.npr.org/blogs/thetwo-way/2014/11/10/363023227/solar-bikepath-opens-this-week-in-the-netherlands. Last accessed on 30 March 2020 6. Wang R, Zhang X, Zhang D (2018) Fluorination with an enlarged dielectric constant prompts charge separation and reduces bimolecular recombination in non-fullerene organic solar cells with a high fill factor and efficiency >13%. Nano Ener 56:494–501 7. Yao H, Zhao W, Li S (2017) Molecular optimization enables over 13% efficiency. J Am Chem Soc 139:7148–7151 8. Xie S, Wang R, Zhang D (2018) High efficiency non-fullerene organic solar cells without electron transporting layers enabled by lewis base anion doping. Nano Ener 51:736–744 9. Hong L, Yu R, Yao H (2018) Design and application of volatilizable solid additives in nonfullerene organic solar cells. Nature Comm 9:4645 10. Brédas JL, Norton JE, Cornil J, Coropceanu V (2009) Molecular understanding of organic solar cells: the challenges. Acc Chem Res 42:1691–1699 11. Scharber MC, Mühlbacher D, Koppe M, Denk P, Waldauf C, Heeger AJ, Brabec CJ (2006) Design rules for donors in bulk-heterojunction solar cells: towards 10% energy-conversion efficiency. Adv Mater 18:789–794 12. Kohn P, Rong Z, Scherer KH, Sepe A, Sommer M, Müller-Buschbaum P, Friend RH, Steiner U, Hüttner S (2013) Crystallization-induced 10-nm structure formation in P3HT/PCBM blends. Macromolecules 46:4002–4013 13. Liu T, Troisi A (2011) Absolute rate of charge separation and recombination in a molecular model of the P3HT/PCBM interface. J Phys Chem C 115:2406–2415 14. Grancini G, Polli D, Fazzi D, Cabanillas-Gonzalez J, Cerullo G, Lanzani G (2011) Transient absorption imaging of P3HT:PCBM photovoltaic blend: evidence for interfacial charge transfer state. J Phys Chem Lett 2:1099–1105 15. Gutiérrez-González I, Rodríguez JI, Molina-Brito B, Götz AW, Castillo-Alvarado FL (2014) Structural and electronic properties of the P3HT-PCBM dimer: a theoretical study. Chem Phys Lett 612:234–239 16. Rodríguez JI, Matta C, Uribe C, Götz AW, Castillo-Alvarado FL, Molina-Brito B (2016) A QTAIM topological analysis of the P3HT-PCBM dimer. Chem Phys Lett 644:157–162 17. Martinez JP, Rodriguez JI, Trujillo-Gonzalez DE, Götz AW, Castillo-Alvarado F (2017) Effects of dispersion forces on structure and photoinduced charge separation in organic photovoltaics. J Phys Chem C 121:20,134–20,140

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Dye-Sensitized Solar Cells: A Brief Historical Perspective and Uses in Multijunction Devices Andrew Daniel and Jared H. Delcamp

Abstract A brief history of the development of solar-to-electric devices is discussed for the classically researched solar cell technologies including Si, CIGS, CdTe, GaAs, OPV, DSC, and PSC devices. Relative strengths and weaknesses of these technologies are presented along with the importance of multijunction system research toward higher efficiency solar-to-electric systems. The combining of DSCs with each technology is discussed along with potential directions for designing next generation multijunction systems.

1 A Brief Historical Perspective Since the initial investigations of Alexandre-Edmond Becquerel in 1839, solar cell technologies have been steadily progressing with remarkable developments in power conversion efficiencies. Historical landmark achievements include the development of a 1% efficient solar cell by Charles Fritts in 1883, the first solar cell patent by Edward Weston in 1888, the Nobel Prize in Physics being awarded to Albert Einstein in 1921 for his work on the photoelectric effect, and Bell Labs’ announcement of the first practical silicon solar cell at about 6% in 1954. From this point, silicon solar cells have continuously improved to nearing the Shockley–Queisser limit for a single-junction device (near 33%) and have dominated multijunction efficiencies at up to >47% certified efficiency today (Fig. 1). Alternatives to silicon solar cells have been attractive due to the harsh processing environments of silicon photovoltaic components which typically require slow crystallization of molten high purity silicon for high efficiencies. Gallium arsenide (GaAs, ~1950s), copper gallium indium diselenide (CIGS, 1932), cadmium telluride (CdTe, 1950s), and amorphous silicon alternatives have emerged since the initial photovoltaic discoveries. Pricing advantages due to both the need for relatively small amounts of materials with thin A. Daniel · J. H. Delcamp (B) Department of Chemistry and Biochemistry, University of Mississippi, 481 Coulter Hall, University, MS 38677, USA e-mail: [email protected] © Springer Nature Switzerland AG 2021 J. K. Roy et al. (eds.), Development of Solar Cells, Challenges and Advances in Computational Chemistry and Physics 32, https://doi.org/10.1007/978-3-030-69445-6_4

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Fig. 1 Shockley–Queisser limit with bandgaps of various solar cell technologies marked. DSCs and OPVs are shown as tunable across a broad range of wavelengths

film processing and more benign processing approaches, among other characteristics, have led to many of these technologies being mass produced. More recently, the processability approach has been the focus of multiple modern advances in dye-sensitized solar cells (DSCs, 1991), organic photovoltaics (OPVs, 2001), and perovskite solar cells (PSCs, ~2009). All of these technologies can be processed via solution-based techniques which dramatically lowers pricing to an estimated less than half that of crystalline silicon solar cells in many cases at a minimum. GaAs, CIGS, or CdTe technologies face some limitations in performance efficiencies under full sun irradiation conditions with practical sized, stable panels relative to crystalline silicon. However, the cost of production of GaAs, CIGS or CdTe largely offsets the performance deficiency for applications where solar irradiation area is not limited. Each of the solution processable technologies have faced unique challenges with OPVs needing better charge domain ordering, DSCs needing functional broader absorption materials, and PSCs initially suffering from substantial instability primarily due to intense sensitivity to moisture. Among these three solution processable technologies, DSCs [1–7] have shown the highest performance under indoor lighting conditions even out competing GaAs [8]. Furthermore, DSCs have shown significantly higher performances under practical outdoor environments than most technologies [9]. A critical point to keep in mind when analyzing the peak efficiencies commonly reported among the solar cell technologies (as described in the first paragraph of this chapter) is that the conditions

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studied for peak performance are set to 1 sun intensity, on a cloudless day, with a perfect 90° incident angle to the solar cell surface. These conditions are effectively only operative for a very short time each day at the earth’s equator year-round. Unfortunately, relatively few studies exist which compare these technologies under practical settings, which is probably due to a lack of a standardization for what practical conditions should be used as the benchmarking method. However, for the studies that do exist, DSCs have shown remarkable total power generation performance throughout a day since they excel in low light intensity environments in the morning and evening. Additionally, DSCs do not require an incident light tracking mechanical system to reposition them throughout the day since incident light angle is not as critical to DSCs as it is for purely inorganic technologies with significant refraction as incident angles narrow. Comparatively to OPVs, DSCs have several clear advantages in that the defining seminal discovery of modern DSCs solved the charge carrier phase separation issue plaguing OPVs by using a combination of solution processable inorganic and organic materials. Conceptually, DSCs rely on single molecule behavior which can be more rationally tuned relative to the bulk biphasic materials used in OPVs that typically employ bulk polymeric materials without discrete predictable energetics, especially in the solid phase. DSCs uniquely operate with a similar diffusion-based mechanism to natural photosynthetic systems which allows for isolated chromophores bound to a surface to undergo photophysical processes in isolation from other chromophores. This unique property of DSCs is exceptional as it allows for materials to be designed with molecular level control of photophysical properties. Even though PSCs have some spectral tunability, DSCs have an incredibly broader set of tunable photophysical properties due to the molecular level being explorable. The most efficient PSCs are all currently lead-based systems using CH3 NH3 PbX3 where X is I, Br, or Cl. These materials are inherently moisture sensitive which requires rigorous dry processing and excellent encapsulation/operational environments to last longer than a few minutes. Despite these challenges, PSCs have shown the highest efficiencies among the OPVs, DSCs, and PSCs technologies, and PSCs are progressing toward widespread commercialization. By comparison, DSCs are often processed in open ambient air conditions for the record setting devices in the field. In fact, DSCs have been shown to operate efficiently with water added to the system with numerous stress test reports showing exceptionally robust results with electricity production under harsh temperature and lighting environments [10, 11]. DSCs have also shown stabilities greatly exceeding the time limits of the 1000 h continuous irradiation stress test at elevated temperatures [11, 12]. Thus, arguably, DSCs may still be one of the most promising solar cell technology when cost and practical consideration are weighed for single cell systems under certain environments. This has led to exceptional displays recently of DSCs in building integrated photovoltaics (BIPVs) in numerous locations world-wide and in consumer electronic areas [2, 9, 13, 14].

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2 Multijunction System Performances and Analysis Notably, the above historical perspective discussion is concerned with single cell systems with the exception of the mention of a >47% silicon-based solar cell system. This landmark achievement for the photovoltaic community was made possible by pursing multijunction systems with silicon solar cells which can exceed the theoretical Shockley–Queisser limit of a single-junction device (~33% PCE). Single junction silicon cells are near 28% PCE presently. With limited room for improvement, multijunction systems are critical to PCE improvements that use photons more efficiently (Fig. 1). Initial multijunction certified efficiencies were reported just below 28%. Notably, in several instances, single-junction GaAs devices reported higher efficiencies than their multijunction device counterparts, and the multijunction system showed only a ~2% power conversion efficiency increase over single-junction silicon devices at the time of the discovery. However, the theoretical potential for multijunction technologies has fueled continuous research efforts which have led to the highest known solar cell performances to date. The key advantage to multijunction systems is that thermal losses are reduced by using materials with varied optical gaps (Fig. 2). In a single-junction system, a solar cell device uses photons across the solar spectrum from high to low energy until the light absorbing material can no longer absorb light because the energy gap of the material becomes too large to facilitate charge separation (Fig. 1). In single-junction systems, charges are separated to the same energetic levels (the photovoltage of the system) regardless of energy input. This means that both low energy photons and high energy photons generate charge separation events of the same voltage or

Fig. 2 Example of how possible solar cell photovoltage outputs change in various spectral regions with example energy level values versus normal hydrogen electrode (NHE) for dyes in DSC devices

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thermodynamic value. This results in the inherent loss of heat from high energy photons as excess energy is provided to generate charge carriers. As an example, a single-junction material absorbing light to 1000 nm (1.2 eV) can theoretically output a maximum of ~1.2 V (see Fig. 2, for example, practical voltage values). If the same 1000 nm absorbing material absorbs a photon at 450 nm, a maximum of ~1.2 V can be output from the device despite the photon providing ~2.8 eV. The remaining 1.6 eV of energy from the photon (over half of the energetic value) is lost as heat. Multijunction systems seek to correct this problem by using multiple light absorbing materials tailored to each spectral region to avoid energetic losses. Two key challenges with this approach are: (1) designing systems that use high energy photons (500 mV) [17]. A donor-π bridge-acceptor (D-πA) type dye (SGT-137) was used as the front absorbing subcell which also shows an IPCE onset of near 800 nm. Chromophores with different spectral region absorptions were not used, so no gain in theoretical PCE is available with this system over the highest preforming subcell as a stand-alone DSC device. Practically, the dyes used in devices seem to be current limited to approximately 19 mA/cm2 for each individual device even though ~28 mA/cm2 is theoretically available in this spectral range (Table 1, entries 1–3) [6]. The subcells were wired in parallel to sum the photocurrent in each device with photovoltage limited by the lowest photovoltage device with a good balance within 4 mV observed (Table 1, entries 4–5). The advantage of this strategy is that each subcell is only required to pass ~14 mA/cm2 if the photons are evenly divided between them which alleviates any potential mass transport issues for these devices which use a relatively bulky cobalt redox shuttle compared to triiodide/iodide. For maximal efficiency, the photovoltages should be balanced between the two subcells, and to aid in this, both subcells use a co-sensitization dye (HCA1 or HC-A4) specifically selected to increase the device photovoltage by limiting recombination of electrons in TiO2 with the electrolyte for each subcell (Table 1, entries 1–2). This allows each subcell to maintain an overall open-circuit voltage (V OC ) of near 880 mV and divide the photocurrent (J SC ) between each subcell. In the parallel device configuration, a total photocurrent of 22 mA/cm2 is obtained which is higher than either subcell alone (Table 1, entries 2, 3, and 6). This strategy of using equal optical gap dyes in tandem is particularly useful for solar cells employing dyes and redox shuttles that have photocurrent limited systems. However, it should be noted that the use of dyes with identical optical gaps in a multijunction system has no theoretical advantage over a single dye system since no additional photocurrent can be added to the system through broader photon absorption, and all of the photons provide the same photovoltage in these systems. More importantly though,

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Table 1 Multijunction devices and measurements of individual subcells in multijunction device configurations Entry

Devicea

1 [16]

SGT-137 (single cell)

0.825

19.4

0.74

11.8

2 [16]

SGT-137 + HC-A1 (single cell)

0.884

18.4

0.77

12.5

3 [18]

SGT-021 (single cell)

0.819

17.9

0.75

11.1

4 [16]

SGT-137 + HC-A1/SGT-021 + HC-A4 (top)

0.877

16.2

0.73

10.4

5 [16]

SGT-137 + HC-A1/SGT-021 + HC-A4 (bottom)

0.881

6.1

0.79

4.3

6 [16]

SGT-137 + HC-A1/SGT-021 + HC-A4 (parallel)

0.878

22.1

0.76

14.6

7 [19]

D35/Y123

1.92

5.9

0.62

7.1

8 [19]

D35/Y123/HD-2-mono

2.63

3.9

0.74

7.7

9 [19]

D35/D35/Y123/Y123/Y123

4.67

2.4

0.38

4.3

10 [20]

RR9 (Fe, single cell)

1.42

2.8

0.47

1.9

11 [20]

RR9 (Fe)/D35 (Co)/Y123 (Co)

3.18

2.2

0.49

3.5

12 [20]

RR9 (Fe)/Y123 (Co)/Y123 (Co)

3.34

1.9

0.56

3.5

13 [21]

D35/B11/B11 CYTOP/Oil

2.29

5.7

0.76

10.1

14 [21]

D35/D35/Y123/B11/B11 CYTOP

4.07

2.5

0.64

6.7

15 [22]

D102 (single cell)

0.810

8.8

0.58

4.1

16 [22]

OPV (ZnPc, single cell)

0.550

14.3

0.54

4.2

17 [22]

D102/OPV

1.36

8.2

0.54

6.0

18 [23]

N719 (single cell)

0.810

24.0

0.60

11.6

19 [23]

PSC (bottom)

0.620

8.1

0.45

2.2

20 [23]

N719/PSC

0.760

28.7

0.53

11.6

21 [24]

DX3 (single cell)

0.552

30.3

0.60

10.0

22 [24]

PSC (single cell)

1.12

20.7

0.79

18.4

23 [24]

DX3/PSC

–

–

–

21.5

24 [25]

Y123 (I, single cell)b

0.74

8.3

0.66

4.1

25 [25]

Y123 (Co, single cell)c

0.85

9.0

0.53

4.1

26 [25]

CIGS (single cell)

0.51

27.1

0.65

9.0

27 [25]

Y123 (I)/CIGS

1.05

8.1

0.65

5.6

28 [25]

Y123 (Co)/CIGS

1.13

8.2

0.66

6.1

29 [26]

N719 (single cell)

0.815

13.9

0.73

8.3

30 [26]

CIGS (single cell)

0.627

29.7

0.63

11.7

31 [26]

N719/CIGS

1.44

14.1

0.61

12.4

32 [27]

SGT-021 (single cell)

0.90

16.8

0.76

11.4

33 [27]

c-Si (single cell)

0.53

36.3

0.69

V OC (V)

J SC (mA/cm2 )

FF

PCE (%)

13.2 (continued)

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A. Daniel and J. H. Delcamp

Table 1 (continued) Entry

Devicea

V OC (V)

J SC (mA/cm2 )

FF

PCE (%)

34 [27]

SGT-021/c-Si

1.36

18.1

0.69

17.2 (18.1)d

a “top” and “bottom” refer to the subcell being measured at that position in the multijunction device

as a single-junction system. A dye code + a dye code indicates as co-sensitized subcell, while dye code/dye code indicates two separate subcells in a DSC device. b Indicates an iodine electrolyte was used. c Indicates a cobalt-based electrolyte was used. d Maximum value observed among 65 devices

Fig. 5 Dyes used in DSC-based devices

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this strategy does allow for the overcoming of practical limitations leading to record setting performances. Delcamp, Cheema, and Rodrigues have recently pioneered the use of varied optical gap dyes in multijunction systems with more than two subcells with a focus on dividing photons between subcells according to energetic value in addition to photon flux distribution (Table 1, entries 7–14) [19–21]. Such a system wired in series (termed: sequential series multijunction dye-sensitized solar cell, or SSMDSC) can lead to an overall higher theoretical maximum PCE relative to strategies focused on photon flux aiming to sum photocurrent values (parallel wiring) when only photons higher in energy than the Shockley–Queisser limit are used (Fig. 1). This increase in PCE from a multijunction series system can be obtained since each of the front subcells can produce a higher photovoltage than the narrow optical gap materials below. A parallel wired system in this spectral region would use the same number of photons to generate current but would limit the photovoltage to that of the lowest photovoltage system resulting in substantial thermal losses from high energy photons. For an overall high-performance series system, the photocurrent between each subcell must be evenly matched to avoid current bottlenecking at a particular subcell leading to thermal losses. One of the foremost limitations to this strategy presently is the lack of a dye and redox shuttle pair that can produce photovoltages near the value of the photons being used in the shorter wavelength ranges. As an example, photons at 500 nm have 2.5 eV of energy, yet the highest photovoltage DSC device to date provides 1.5 V which is co-record holding with PSCs when this value is compared across solar cells in general [28, 29]. Unfortunately, this 1.0 V loss severely limits this approach from showing dramatic improvements in efficiency for overall record numbers in the DSC field; however, the initial proof-of-concept studies have been informative and promising. The initial report shows that by using between 2 and 5 subcells, exceptional photovoltages can be obtained for the series wired devices, and that photon flux to each subcell can be regulated by selecting dyes with complementary optical gaps, controlling optical layer thicknesses, and using dyes of varied molar absorptivities (Table 1, entries 7–9) [19]. The original report on the sequential series multijunction SSM-DSC strategy shows that photovoltages ranging from 1.9 V for a two-subcell SSM-DSC to 4.7 V for a five-subcell SSM-DSC device could be obtained (Table 1, entries 7 and 9). PCEs were found to increase from 7.1% with a two-subcell device to 7.7% for a three-subcell device, which illustrates the value in moving toward >2 junction systems. The increase in PCE for the threesubcell system was made possible by a careful balancing of photocurrent between two organic D-π-A dyes (D35 and Y123) and a ruthenium-based dye, HD-2-mono (Table 1, entries 7–8). Up to five-subcell multijunction devices were demonstrated with a PCE of 4.3% obtained (Table 1, entry 9). This drop in PCE as more subcells are incorporated is likely due to light losses as photons change mediums through and between each subcell. Notably, this approach allows for the direct powering of photovoltaic driven electrochemical cells (PV-ECs). PV-EC systems require a threshold voltage to be obtained before catalysis can start. In the original report of on the SSM-DSC approach, both water splitting and CO2 reduction coupled to water oxidation are demonstrated with solar-to-fuel conversion efficiencies of ~3% with a

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3 subcell SSM-DSC device. This is a significant step forward for DSCs in that for the first time these two processes were definitively shown with observed O2 output using only DSC devices. Two later iterations of this SSM-DSC approach were recently shown focusing on improving the photovoltage output of the top subcell by using a high voltage dye (RR9) and a relatively positive oxidation potential redox shuttle, Fe(bpy)3 3+/2+ , for a 1.4 V front subcell (Table 1, entries 10–12) [20]. This gives a SSM-DSC device at 3.3 V (a record for a three-subcell system); however, the photocurrent was limited due in part to the strong absorption of Fe(bpy)3 3+/2+ in the front subcell which limits the overall PCE of the system to 3.5%. In this system, a gradient of photon absorber wavelengths (RR9 < D35 < Y123) was demonstrated to provide a higher photocurrent than a system using the same absorber twice (RR9 > Y123 > Y123). This illustrates a key feature of higher order multijunction systems, which requires chromophore development in each spectral region for maximal performance (Fig. 2). Despite the low PCE for these devices, the SSM-DSC device illustrates that if photovoltages can be obtained near the maximum for a particular spectral region then the theoretical limit of a single DSC device can be overcome since the photovoltages were observed to be summed with no notable limits observed. Additionally, these systems are relatively low photocurrent (typically < 5 mA/cm2 ) which alleviates any concerns about mass transport issues in the solar cell electrolyte while maintaining high performances [30–34]. Most recently, a >10% PCE has been demonstrated using a three-subcell approach with broadly absorbing ruthenium dye B11, in addition to the use of anti-reflective coatings and an immersion oil between the subcell layers to limit light losses in the system (Table 1, entries 13–14) [21]. The anti-reflective coating and immersion oil use is particularly important to mechanically stacked SSM-DSCs since these devices have several solvent-glass-air interfaces where light can be reflected or diffracted. The three-subcell device gives a >6% solar-to-fuel conversion directly from the SSM-DSC device with no added bias for CO2 conversion in a PV-EC system. This is possible since a high photovoltage of 2.3 V is obtained which can power low overpotential electrocatalysts. Additionally, the five-subcell system was found to be improved with the light guiding anti-reflective coating CYTOP to give a 6.7% PCE device compared to the prior 4.3% record device.

4 DSC/OPV Multijunction Systems In general, OPV-based approaches to solar cells are able to more easily access nearinfrared absorbing systems than DSC devices due to less strict energy level alignments being required since a wide range of molecular acceptors are possible in OPV relative to TiO2 traditionally in DSCs. Early research on organic DSC dyes often resulted in chromophores absorbing until about 600 nm with rare exceptions past 700 nm. Thus, pairing a top DSC subcell with a bottom OPV subcell could provide a high photovoltage from the DSC subcell for shorter wavelength photons with significant photocurrent from the OPV subcell. The use of D102 in a DSC subcell with a

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zinc phthalocyanine dye in an OPV subcell led to an overall increase in PCE for the tandem device relative to either single device (6.0% versus 4.2%, Table 1, entries 15–17) [22]. The tandem device was constructed in a monolithic fashion (Fig. 4), with a silver layer separating the DSC and OPV subcells. This leads to a series connection by default. The active layer thicknesses were controlled to balance the photocurrent in each subcell leading to a good fill factor (FF) and the summing of the subcell photovoltages with the DSC device providing a significant photovoltage enhancement over the OPV device. This approach highlights the strengths of the two fields in synergistically bringing together low bandgap and high voltage subcells to form an overall more efficient device.

5 DSC/PSC Multijunction Systems PSCs are exceptional for single cell systems with a band gap onset of 800 nm and minimal overpotential losses for the highest performance systems. In general, the devices can give >1.0 V open-circuit photovoltages and >24% PCE. While there are some DSC devices with >1.0 V in the literature which could be used as a front subcell for a tandem device with a PSC back subcell, these DSC devices are rare. An initial report makes use of a DSC/PSC multijunction system employing a relatively low photovoltage PSC at 0.62 V, which is used as the bottom subcell in a tandem system with a N719 DSC as the top subcell (Table 1, entry 19). The use of a DSC (N719 dye)/PSC parallel wired multijunction system led to a high photocurrent of ~29 mA/cm2 which is near the theoretical limit possible for materials with onset incident photon-to-current conversion efficiencies (IPCEs) of ~800 nm (Table 1, entries 18–20). This system shows very few photon losses; however, the overall PCE relative to DSC devices alone is nearly identical at ~11%. This is likely due to the use of two similar optical gap materials, and the use of a higher voltage system (i.e., a wider bandgap DSC) with a series wiring could boost this performance with photons being equally distributed across the subcells [23]. Given the relatively less tunable band gap of the PSC device, opportunities exist for the pairing of a narrow band gap DSC device with a PSC device as the top subcell. For this to occur, a narrow band gap dye is required, and the invention of DX3, which produces electricity until 1000 nm, fulfilled this requirement [24]. This high current DSC dye was shown to give >30 mA/cm2 of photocurrent (a field record, Table 1, entry 21). The DSC subcell was wired to the PSC subcell via a series connection to sum the photovoltages (0.56 V and 1.12 V, respectively), and a dichroic mirror was used to divide the solar spectrum such that optical transparency of the top active layer subcell is not a concern (Fig. 4). Through this approach a PCE of 21.5% is obtained for the tandem system (Table 1, entry 23), which is higher than that of the DSC device or PSC device separately at 10.2% and 18.4%, respectively (Table 1, entries 21–23). This example highlights the importance of designing NIR chromophores for DSC

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devices as their application in relatively high photovoltage systems can complement the absorption spectrum of high efficiency perovskite active layers to synergistically raise the overall multijunction device efficiency.

6 DSC/CIGS Multijunction Systems DSCs have also been used as top subcells of multijunction devices with CIGS as the bottom subcell (Table 1, entries 24–31) [25, 26]. In one approach, the DSC is the wide optical gap absorber using dye Y123 while the CIGS is the narrow optical gap absorber [25]. A rare monolithic design was used to integrate the CIGS and DSC into a device with no air–solid interfaces within the multijunction device. By default, this system is series connected internally which leads to a summing of photovoltages with the photocurrent limited by the lowest current subcell. CIGS have very high photocurrents in relation to DSCs and very low photovoltages. In this setup, the DSC was current limiting at 9 mA/cm2 regardless of electrolyte choice (Table 1, entries 24–25), which is substantially below the >27 mA/cm2 obtained with the CIGS device alone or 15 mA/cm2 with a DSC filtered measurement (Table 1, entry 26). This dramatically reduced the photocurrent of the tandem system relative to the single CIGS system leading to a drop of PCE from 9% to ~ 7% with relation to the non-tandem CIGS cell (Table 1, entries 26–28). The DSC does provide a larger photovoltage (850 mV) relative to that of the CIGS device (500 mV) which does offset some of the current losses. Ideally, the photocurrent could be divided among three subcells (2 DSC + 1 CIGS) to allow each subcell to generate 9 mA/cm2 of photocurrent with summed photovoltages. This would dramatically increase the performance of the multijunction device, but the intermediate subcell needed would have to efficiently utilize photons beyond 550 nm in order to provide 9 mA/cm2 after the top cell filters photons. This would require an efficient NIR dye of which there are few of in DSC literature extending beyond 800 nm [17]. However, a critical advance of this work was the demonstration of a multijunction device with very high durability which was demonstrated to last 1000 h under continuous irradiation with negligible PCE loss. In a prior example using DSC and CIGS in a mechanically stacked configuration, a metal-based dye (N719) was used in the DSC subcell which better divides the photocurrent between the DSC and CIGS due to the broader IPCE of N719 relative to Y123 [26]. In this system, the DSC still remains current limiting at about 14 mA/cm2 (Table 1, entry 29). However, this is very closely matched to half the photocurrent of the CIGS system at about 15 mA/cm2 (Table 1, entry 30). Combining these two systems together with a series connection gives a photocurrent of 14 mA/cm2 for the tandem system with a summed photovoltage of 1.44 V and a PCE of 12.4% (Table 1, entry 31). This PCE is higher than that of either individual subcells with the DSC at 7.9% or the CIGS at 11.7%. This example demonstrates the synergistic use of both a classically broad absorbing inorganic solar cell and a DSC which have specialized performances in different spectral regions.

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7 DSC/Silicon Multijunction Systems A DSC subcell has also been monolithically combined with a silicon subcell to give a series connected multijunction system with an 18.1% PCE [27] which is a significant improvement in PCE relative to earlier work with DSCs and silicon subcells (Table 1, entries 32–34) [35]. This PCE is also significantly higher than either individual device, with the individual DSC device giving a PCE of 11.4% and the silicon device reaching up to 13.2% PCE (Table 1, entries 32–33). This large gain in PCE is possible due to the higher voltage supplied by the DSC subcell as the top device which reduces thermal waste from the broader absorbing silicon subcell. The photocurrent in this system is very well balanced at approximately 18 mA/cm2 through each subcell. This is a very high photocurrent in a DSC device with a good photovoltage made possible through the invention of the broadly absorbing porphyrin dye SGT-021. This is an excellent example of the potential of a multijunction strategy if materials with well-matched energetics are chosen. A further subdividing of the solar spectrum is certainly possible for large multijunction systems which could further reduce thermal losses and increase PCEs further if the solar spectrum can be well divided among the subcells. This result compares favorably to the use of PSCs or OPVs with inorganic solar cells based on CIGS and a-Si (amorphous silicon) as well as to DSC devices using GaAs [27, 36].

8 Conclusions In the sections above, multijunction systems using DSC subcells with DSCs, OPVs, PSCs, CIGSs, and silicon solar cells were presented and discussed. Examples using GaAs are present in the literature as well, which face a similar set of challenges to the PSC subcell systems in that the DSCs used in these systems need either a very high voltage DSC dye for short wavelength photons to contribute productively or a narrow bandgap DSC dye to collect substantial photons beyond 800 nm in order to balance the photocurrent in each device for a synergistic system. This is because both PSCs and GaAs systems use chromophores with IPCE onsets at 800–850 nm with good photovoltages in this region. These technologies are exceptional in this region, and DSCs have a high tunability that can be used to pair with these technologies when matched chromophores are invented. The use of DSCs with varying technologies is summarized below in Table 2 along with a few notable examples from the other two solution processable technologies for comparison with a PSC/CIGS and a OPV/Si system. The DSC systems with broad absorbers relative to common DSC dyes have shown the best performances using porphyrin and ruthenium dye-based subcells (Table 2, entries 1, 3, 4, and 6). Substantial improvements remain possible for even broader absorbing DSC chromophores in these systems especially with respect to PSC and GaAs subcells (Table 2, entries 3 and 5). However, an under-utilized approach relies on the invention of DSC dyes

96 Table 2 Comparing notable solar cell efficiencies for multijunction systems using at least one solution processable technology (PSC, OPV, DSC) with an inorganic subcell

A. Daniel and J. H. Delcamp Entry

Device

PCE (%)

1 [16]

SGT-137 + HC-A1/SGT-021 + HC-A4

14.6

2 [22]

D102/OPV

3 [24]

DX3/PSC

21.5

4 [26]

N719/CIGS

12.4

5 [36]

D131/GaAs

7.6

6 [27]

SGT-021/c-Si (crystalline silicon)

7 [27]

PSC/CIGS

8 [27]

a-Si/OPV (triple)

13.2

9 [27]

a-Si/OPV

11.6

6.0

18.1 7.7

which can effectively use early photons to give maximal photovoltage outputs which can pair with all of the existing technologies to minimize thermal losses and boost multijunction device PCEs dramatically. This area of research is relatively young with encouraging results already [20, 29, 37–45]. Despite the absence of this key component to future multijunction device designs, DSCs compare favorably to multijunction device attempts using PSCs and OPV with inorganic non-solution processable solar cell technologies (Table 2, entries 7–9). This is in part due to the high photovoltages commonly observed with DSCs relative to other solar cell technologies as well as the ability to fabricate transmissive DSC devices. Additionally, DSCs operate uniquely efficient under low photon flux conditions relative to many technologies. Acknowledgements That authors acknowledge support from the Department of Energy Basic Energy Sciences program for grant DE-SC0019131 which supported background literature research with relation to the high-voltage systems reported herein. The authors also acknowledge support from the National Science Foundation for grant 1954922 which supported background literature research with relation to the narrow energy gap systems reported herein.

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Delving Charge-Transfer Excitations in Hybrid Organic–Inorganic Hetero Junction of Dye-Sensitized Solar Cell: Assessment of Excitonic Optical Properties Using the GW and Bethe–Salpeter Green’s Function Formalisms Pabitra Narayan Samanta and Jerzy Leszczynski Abstract First-principles modeling of charge-neutral excitations with the recognition of charge-transfer and Rydberg states and probing the mechanism of chargecarrier generation from the photoexcited electron–hole pair for the hybrid organic– inorganic photovoltaic materials remain as a cornerstone problem within the framework of time-dependent density functional theory (TDDFT) . The many-body Green’s function Bethe–Salpeter formalism based on a Dyson-like equation for the two-particle correlation function, which accounts for the exchange and attractive screened Coulomb interactions between photoexcited electrons and holes, has emerged as a decent approach to study the photoemission properties including the Frenkel and charge-transfer excitations in an assortment of finite and extended systems of optoelectronic materials. The key ideas of practical implementation of Bethe–Salpeter equation (BSE) involving the computations of single-particle states, quasi-particle energy levels, and the screened Coulomb interaction with the aid of Gaussian atomic basis sets and resolution-of-identity techniques are discussed. The work revisits the computational aspects for the evaluation of electronic, spectroscopic, and photochromic properties of the dye-sensitized solar cell (DSSC) constituents by considering the excitonic effects that renormalize the energy levels and coalesce the single-particle transitions. The most recent advancements in theoretical methods that employ the maximally localized Wannier’s function (MLWF) and curtail the overall scaling of BSE calculations are also addressed, and the viable applications are subsequently illustrated with selected examples. Finally, the review

P. N. Samanta · J. Leszczynski (B) Interdisciplinary Center for Nanotoxicity, Department of Chemistry, Physics and Atmospheric Sciences, Jackson State University, Jackson, MS 39217, USA e-mail: [email protected] P. N. Samanta e-mail: [email protected] © Springer Nature Switzerland AG 2021 J. K. Roy et al. (eds.), Development of Solar Cells, Challenges and Advances in Computational Chemistry and Physics 32, https://doi.org/10.1007/978-3-030-69445-6_5

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reveals some computational challenges that need to be resolved to expand the applicability of BSE in designing solar cell materials, and to unravel the intricate mechanism of ultrafast excited-state processes.

1 Introduction To improve the quantum efficiency of dye-sensitized solar cell (DSSC) , it is fundamentally important to comprehend the crucial electronic factors underpinning the electronic transitions mediated by photoinduced intramolecular (Frenkel) excitons that further transforms into charge-separated (CS) states via charge-transfer (CT) excitations [1–3]. To date, the time-dependent density functional theory (TDDFT) has been widely deployed to acquire the atomistic details of energy and chargetransfer processes in DSSC and proposed to be a reliable and efficient approach in assessing photovoltaic performance of the photosensitizers [4–6]. However, for an accurate description of inter- and intramolecular CT excitations in concomitant with dissociation and diffusion dynamics of excitons, one has to cope with computational challenges emanating from the scarcity of long-range electron–hole interactions that materializes owing to the exploitation of (semi) local exchange– correlation (XC) kernels within the framework of TDDFT [7–10]. Stimulated by the quest for promising DSSC materials, the electrochemical and optical properties of the various donor–acceptor based dye-semiconductor systems comprising organic–inorganic hybrids have been evaluated by performing TDDFT computations in conjunction with local, hybrid, and range-separated hybrid XC functional followed by solvent correction within polarizable continuum model [5, 11–21]. Despite their success in reproducing optical spectra of the photosensitizers and deriving solar cell device performance parameters, radical issues arise in depicting Frenkel and CT excitations together at the chromophore-charge transport layer interface on the grounds of fundamentally different physicochemical properties of hybrid organic–inorganic composites including dielectric, electron–phonon interactions, spin–orbit coupling, excitons as well as charge mobility [22, 23]. The efficiency of DSSC is primarily controlled by the kinetics of electron injection and charge recombination that depend upon the band alignment of the photosensitizer and the semiconductor as well as the redox potential of the electrolyte. Accordingly, it is indispensable to estimate the ground state oxidation (GSOP) and the excited-state oxidation potential (ESOP) of the dyes that are customarily approximated by the eigenvalues of the frontier molecular orbitals, viz. HOMO and LUMO energy levels of the dyes. Albeit, the evaluation of ESOP relies on the mode of electron injection that could be categorized as the transport of electrons to the semiconductor by dint of the unrelaxed excited state of the chromophore (i.e., the absorption maximum) and the relaxed form of the excited state (i.e., the emission maximum) [6]. Furthermore, the solar energy-to-electricity conversion efficiency of a DSSC is determined by the combined effects of several factors especially the short-circuit current densityJsc , the open-circuit voltageVoc , the fill factor and the intensity of the incident light. The

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photocurrent density is strongly associated with the electron dynamics phenomena of the solar cell device under illumination and led by the optical gap of the dye molecule and the efficiency of charge-carrier generation from the photogenerated excitons. TheVoc , on the other hand, is determined by the quasi-Fermi level of the conduction band of the semiconductor and the redox potential of the electrolyte. Therefore, the understanding of quantum transport behavior of quasi-particles at nanoscale dye/semiconductor oxide (typically TiO2 ) interfaces through the estimation of energy levels of the ground and excited states of the DSSC materials, as well as both the charged and neutral excitations as required for the evaluation of band edges of the TiO2 and optical gap of the photosensitizer, respectively, are central to assess the robustness of the photosensitizers in the context of solar energy applications. In practice, the implementation of charged excitations followed by accounting excitonic effects, attributable to the two-body interactions between the excited electron-and-hole pair, is a formidable task within the framework of DFT [24]. Although the TDDFT provides superior accuracy—feasibility trade-offs compared to the wave function-based ab initio methods like MP2, CCSD(T) and ability to reckon the equilibrium and non-equilibrium solvation effect, vibronic couplings as well as the relativistic spin–orbit effects in a cost-effective manner [25–32], however, it fails to account Rydberg states and CT excitations for the sake of improper treatment of the asymptotic long-range exchange, and does not allow to capture double excitation character on the potential energy hypersurface [10, 33–36]. In this regard, the so-called GW method [24, 37–41], and the Bethe–Salpeter equation (BSE) formalism [42–45], which are based on the many-body perturbation theory (MBPT) engaging perturbative expansion of the one-particle and two-particle (electron–hole) Green’s functions, respectively, have been emerged as a viable approach to assess the charge-neutral excitations and estimate the quasi-particle (QP) energy levels in functional photochromes grafted on the surface of semiconductor [46– 48], and simulate the optical spectra and excitons in donor–acceptor complexes [49, 50]. For instance, by deploying the GW-BSE formalism for the donor–acceptorbased complex comprising zinc-tetraphenylporphyrin (ZnTPP) and C70 -fullerene, Duchemin and Blase [51] have identified the presence of several excitons lying between the lowermost intramolecular ZnTPP* donor excitation and the undermost charge-transfer (CT0 ) exciplex. The GW-BSE results also unveil that the hot electron–hole states possessing a hybrid intramolecular and charge-transfer character are resonant in energy with the ZnTPP* excitation, which in turn allows the transitions leading to the electron–hole separation. In another study [52], many-body Green’s function GW approximation has been demonstrated to be an effective strategy to estimate the relative energy levels alignment of the dye molecule and the photoanode material, enabling the computation of maximum attainable Voc for a DSSC with the alteration of degree of polarity of the solvent molecules. Nonetheless, the introduction of explicit solvent model during the estimation of optical absorption spectrum within the GW framework is suggested to be a tedious job due to the detrimental N 4 scaling with reference to the size of the system. Recently, to overcome the shortcomings of state-of-the-art BSE approach in its planewave implementation, Umari

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and co-workers [53] have implemented a suitable GW-BSE scheme based on maximally localized Wannier’s functions, allowing the reduction of overall scaling of the GW-BSE calculations from N 4 to N 3 for the estimation of excitonic eigenstates and optical absorption spectra of the nanostructures and the complex photovoltaic materials like photochrome-TiO2 interface. Herein, the fundamental principles and computational aspects for the estimation of QP energy levels in the DSSC functional materials followed by the simulation of optical spectra that incorporate the influence of screened electron–hole interactions are discussed. This work also provides discussion of the recent developments in theoretical methods and models for the GW-BSE calculations emphasizing on interfacial excited-state energetics in both finite and extended systems of hybrid organic–inorganic DSSC constituents. The performance of the GW and Bethe–Salpeter methods in examining photoinduced charge-transfer processes is subsequently illustrated with examples focusing on donor-bridge-acceptor based organic chromophores.

2 Theoretical Framework The many-body perturbation theory GW approach, which is based on approximating the self-energy as  ≈ i GW , with G being the single-particle Green’s function and W being the screened Coulomb potential, allows one to calculate the QP band gaps for a wide range of materials starting from bulk semiconductors, metals, and insulators to nano-wires, polymers, organic molecules as well as photovoltaic organic–inorganic hybrids through the Gaussian-basis implementation of the GW formalism [40, 54– 56]. The BSE, on the other hand, includes the electron–hole interaction kernel and permits to incorporate the excitonic effects and compute the optical properties with enhanced accuracy for both the isolated and extended periodic systems. Instead of providing detailed programmatic implementations of the GW/BSE method and the mathematical derivations using functional derivative techniques or the Feynman diagrammatic language that are readily available in seminal articles or reviews [24, 57], the basic ideas behind the formulation of generalized eigenvalue problem within the framework of GW approximation and Bethe–Salpeter approach are subsequently discussed.

2.1 GW Formalism The key quantity in the many-body GW approach is the Green’s function in lieu of charge density as considered in DFT. The one-particle time-ordered Green’s function can be expressed as

Delving Charge-Transfer Excitations …

     φi (r)φi∗ r   φa (r)φa∗ r  G r, r , ω = + ω − εi − iη ω − εa + iη a i 





103

(1)

where {εi , εa } refer to the exact charged excitation energies as determined by the direct and inverse photoemission spectroscopy. The virtual and occupied energy levels can be defined as εa = E(N + 1, a) − E(N , 0) and εi = E(N , 0) − E(N − 1, i), respectively; where E(N + 1, a) designates the total energy of the (N + 1)-electron system in its a th quantum state, E(N − 1, i) is the total energy of the (N − 1)-electron system in its ith quantum state, and E(N , 0) corresponds to the ground-state energy of the N-electron system. In Eq. (1), η is a positive infinitesimal that restricts the proper analytic properties of G in the complex energy plane. The {φi , φa } are entitled as “Lehman amplitudes,” and signify the extent of overlap between the wavefunctions corresponding to the N -electron ground state with one removed/added electron in (r) and the i th /a th excited states of the (N − 1)/(N + 1) electron systems, respectively. The function G accounts all many-body effects incorporating all interactions between the N-electrons and the supplemental electrons into the systems and satisfies the following Dyson equation G(1, 2) = G 0 (1, 2) + ∫ d34G 0 (1, 3) H XC (3, 4)G(4, 2)

(2)

where 1[= (r 1 , t1 )] represents a space–time coordinate, G 0 corresponds to the independent-electron Green’s function  evaluated  by substituting {εn , φn } in Eq. (1) by 0 0 the independent-electron eigenstates ε , i.e., the eigenstates of the one-electron , φ n n  

operator h 0 associated with the Kohn–Sham (KS) eigenvalue equation of DFT. The  H XC operator is called the self-energy operator and describes all the electron– electron interactions involving Hartree, exchange and correlation counterparts. The self-energy  is a two-body operator that is identical to the exact exchange operator in Hartree–Fock (HF) theory, albeit the  H XC is dynamical, i.e., energy-dependent, and is a functional of Green’s function G, i.e.,  H XC =  H XC (G), instead of a functional of electron density or density matrix as held in DFT and HF, respectively. The substitution of expression for G into the time Fourier transform of the Dyson equation gives rise to the well-known eigenvalue equation for the (photoemission) excitation energies,   hˆ 0 φn (r) + ∫ d r   XC r, r  ; εn φn (r) = εn φn (r)

(3)

where the exchange–correlation self-energy  XC is both non-local and energy dependent; and the Hamiltonian h 0 includes the kinetic, ionic, and classical Hartree operators. In the GW approximation, the  XC is obtained by 

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      i ∫ dωeiωη G r, r  ; E + ω W r, r  ; ω  XC r, r  ; E = 2π

(4)

where G and W refer to the one-particle time-ordered Green’s function and the screened Coulomb potential: 





G r, r ; E =

 n

  φn (r)φn∗ r  E − εn + iη × sgn(εn − E F )

      W r, r  ; ω = v r, r  + ∫ d r 1 d r 2 v(r, r 1 )χ0 (r 1 , r 2 ; ω)W r 2 , r  ; ω

(5) (6)

  where E F denotes the energy of the Fermi level, v r, r refers to the bare Coulomb potential, and χ0 is the independent-electron susceptibility represented by 





χ0 r, r ; ω =

 i, j

    φi∗ (r)φ j (r)φ ∗j r  φi r    fi − f j εi − ε j − ω − iη × sgn εi − ε j 

(7)

  where f i/j correspond to the occupation numbers, the {εn , φn } eigenstates are typically KS eigenstates which are corrected by substituting the DFT exchange– correlation potential with the GW self-energy contributions,

εnGW = εnK S +

φnK S

GW   GW  εn − V XC |φnK S |

 (8)

In practice, the dynamical correlations are computed by deploying contour deformation technique without any plasmon-pole approximation, implementing the frequency integration along the imaginary axis accompanied by the estimations of    the poles of the Green’s function G r, r ; E + ω . The correlation contributions are given by        φn (r)φn∗ r  vn r, r  ; E CGW r, r  ; E =

(9)

n ∼

with interpolating W = W − v, and the Heavyside step function θ ,   vn r, r  ; E

  = W˜ r, r  ; εn − E [θ (E − εn ) − θ (E F − εn )] +∞ dω   E − εn − ∫ W˜ r, r  ; iω 2 2 0 π (E − εn ) + ω

(10)

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105

GW The predicted εa/i eigenvalues and the screened Coulomb potential W can be considered as input variables for the BSE excitation energy computations.

2.2 Bethe–Salpeter Equation Within the BSE framework, the excitation energies are computed by accounting the poles of a generalized susceptibility χ (1234) = ∂G(12)/∂ V ext (34), where V ext (34) defines a non-local external perturbation. Substituting the Green’s function G with Dyson Eq. (2) introduces the derivative ∂ XC /∂G that is comparable with the exchange–correlation kernel within DFT. Representing the 4-point susceptibility   L(r 1 , r 2 , r 3 , r 4 ; ω) in the transition space between occupied and virtual φi/a onebody eigenstates   allows to express the excitonic Hamiltonian in the two-body product basis φi (r)φa∗ r , and the excitation energies are obtained by solving the following generalized eigenvalue problem:

A B −B ∗ −A∗



Xλ Yλ

=

λB S E

Xλ Yλ

(11)

where λB S E corresponds to the BSE excitation energies. X λ refers to the components of the two-body electron–hole ψλ (r e , r h ) over the φi (r h )φa (r e ) transition basis, whereas the de-excitation φi (r e )φa (r h ) components are represented by Yλ . The linear algebraic representation (Eq. 11) is reminiscent of Casida’s equation of LR-TDDFT while possessing amended matrix elements. The first diagonal block describes the resonant Hamiltonian that can be expressed as BSE Aai,bj

         = δab δi j εaGW − ∈iGW − φa (r)φi∗ r  W r, r  φb (r)φ ∗j r         + 2 φa (r)φi (r)v r, r  φb∗ r  φ ∗j r  (12)

GW where εa/i indicate the energy of the virtual/occupied molecular orbital obtained by GW approximation. The matrix elements ai|W |bj reckon the electron–hole interaction terms through the screened Coulomb potential W , while the matrix elements ai|bj account the exchange contribution term. The second diagonal block (−A∗ ) in Eq. (11) considers the non-resonant contributions stemming from the unoccupied to occupied energy levels (de-excitation process). The off-diagonal B terms account the coupling between resonant and non-resonant transitions as well as incorporate a direct and an exchange term that can be evaluated from the resonant-block by swapping the (b, j) indexes.

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3 Applications 3.1 Estimation of Electronic Band Gap and Optical Spectra of DSSC Photoanode Material (TiO2 ) The ground and excited-state properties of two crystalline phases of TiO2 , namely, rutile and anatase, have been explored to evaluate the adequacy of the quasi-particle GW approximation and the inclusion of exciton correlation effect via the BSE formalism as well as to interpret the photoemission spectroscopy experiments [58]. The structural relaxations of the rutile and anatase phases of TiO2 with space groups P42 /mnm and I 41 /amd were performed using the Perdew–Wang exchange–correlation functional within the framework of density functional theory-local density approximation (DFT-LDA). In Fig. 1a and b, the electronic band structure of the rutile TiO2 obtained by DFT-LDA is compared with those calculated by using the one-shot GW (G0 W0 ) where the self-energy is evaluated only once, and the quasiparticle self-consistent GW (QPscGW) method, respectively. The comparative study suggests that the valences bands are not significantly perturbed by the quasi-particle energy correction, whereas the conduction bands are considerably shifted to higher energy on account of their quasi-particle character and the consideration of dynamical

Fig. 1 a and b Band structure for TiO2 rutile: LDA in red dashed line, G0 W0 and QPscGW in black full lines. [Reprinted with permission from Ref. 58 Copyright (2019) IOP Publishing]

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Fig. 2 a and b Band structure for TiO2 anatase: LDA in red dashed line, G0W0 and QPscGW in black full lines. [Reprinted with permission from Ref. 58 Copyright (2019) IOP Publishing]

screened Coulomb interaction via the plasmon-pole approximation. The calculated direct band gaps at  and R points corresponding to the band structure of rutile TiO2 within the G0 W0 and QPscGW formalisms are found to be 3.12 eV and 3.53 eV, respectively, which are in accordance with the experimental reference values 3.3 ± 0.5 eV as determined by photoemission spectroscopy (PES) and inverse photoemission spectroscopy (IPES) [59]. The DFT-LDA method yields a reduced band gap of 1.75 eV. Figure 2a and b demonstrates the upward and downward shifts of the valence and conduction bands of the anatase TiO2 due to the inclusion of G0 W0 and QPscGW corrections to DFT-LDA, respectively. The estimated indirect band gap values considering the lowest level of the conduction band positioned at  point and the utmost point of the valence band existing along the X − M branch are found to be 2.05, 3.92, and 4.18 eV, respectively, for the implementation of DFT-LDA, G0 W0 , and QPscGW formalisms. The calculated band gap values for the anatase phase corroborate well with the previous reported values of 3.68–3.90 eV obtained from experimental measurements [60, 61], and 3.73–4.05 eV predicted by employing GGA + G0 W0 and HSE06 + G0 W0 level of theory [62]. To elucidate the impact of dynamical exchange–correlation effects of electron–hole pairs, the computed dielectric function and optical absorption spectra of the anatase TiO2 employing the BSEG0 W0 method are further compared with those obtained from KS-DFT and G0 W0 in conjunction with random phase approximation (RPA-KS, RPA-G0 W0 ) as well as with the experimental spectra [63]. The calculated real and imaginary parts of the

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Fig. 3 Optical dielectric function of TiO2 anatase [real part 1 (ω) and imaginary part 2 (ω)] a 2 (ω) b 1 (ω) spectra where the propagation of E perpendicular to c-axis, d 2 (ω) e 1 (ω) spectra, where the propagation of E is parallel to the c-axis, and c and f are the optical absorption spectra. [Reprinted with permission from Ref. 58 Copyright (2019) IOP Publishing]

dielectric function with the RPA-KS reveal that the features of major peaks are well reproduced with respect to the experimental peaks, however, the peaks are redshifted owing to the typical issues stemming from the band gap underestimation within the KS-DFT, as displayed in Fig. 3a, b, d, and e. In case of RPA-G0 W0 , the simulated peaks are blueshifted relative to the experimental spectra due to the exclusion of screened Coulomb interaction even though the exchange repulsion between the electron and hole is considered. The peak features corresponding to the dielectric function as well as the optical absorption spectra estimated by employing the BSE-G0 W0 are in reasonable agreement with the experimental spectra especially for E parallel to the c-axis of the bulk anatase TiO2 lattice.

3.2 Calculations of Low-Lying Charge-Transfer Excitation Energies of Coumarin-based DSSC Photosensitizers The pertinence of GW/BSE formalisms to reckon the charge-transfer excitation energies and the oscillator strengths have been assessed by Faber et al. [64] by computing singlet transition energies for the low-lying excited states of the coumarin-based

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Fig. 4 Schematic illustration of the studied coumarin-based dyes: a parent C343, b NKX-2388 (cis), c NKX-2311 (cis), d NKX-2586 (cis), and e NKX-2677. Black, white, red, blue, and yellow atoms represent carbon, hydrogen, oxygen, nitrogen, and sulfur, respectively. [Adapted with permission from Ref. 64 Copyright (2012) American Physical Society]

donor-bridge-acceptor dye molecules as displayed in Fig. 4 and comparing the GWBSE results with the earlier computational studies achieved by TDDFT and coupledcluster (CC) calculations [12, 13]. Figure 5a delineates the variation of computed singlet excitation energies of the coumarin dyes obtained by TD-B3LYP, TD-LCBLYP, and GW-BSE levels of theory against the coupled-cluster CC2 reference values. The mean absolute error (MAE) over the available data points for TD-B3LYP is estimated to be 0.2 eV as compared to the CC2 results. The deviation amounts to be as much as 0.48 eV for the NKX-2677 dye molecule even though the functional includes the 20% of exact exchange. The estimated excitation energies employing GW-BSE formalism corroborate well with the CC2 reference data, and the calculated MAE is found to be 0.06 eV. The GW-BSE results are also in conformity with the data obtained by TDDFT deploying optimized range-separated hybrid (RSH) functionals [14]. The results acquired by TDDFT with LC-BLYP functional agree well with the CC2 data, with a MAE of 0.03 eV. Despite the illustrious correlation, the excitation energies substantially depend on the range-separation parameter μ in LC-BLYP functional which was deemed to be 0.17 a.u. for these systems regardless

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Fig. 5 a Comparison of calculated lowest singlet excitation energies (in eV) as a function of the coupled-cluster CC2 reference values. The coumarins’ names are indicated by their number (removing the NKX prefix) with c standing for -cis and t for -trans; b Comparison of estimated oscillator strengths as a function of the GW-BSE excitation energies (eV). Results for the NKX2677 and NKX-2586 (s-cis) in the dashed box are reproduced in the upper-right inset. [Reprinted with permission from Ref. 64 Copyright (2012) American Physical Society]

of the deviation from the original value (μ = 0.33) proposed by Iikura et al. [65]. Next, in Fig. 5b, the calculated oscillator strengths using BSE perturbation theory are compared to those obtained by CC2, RSH-BNL, and LC-BLYP methods against the BSE excitation energy. The oscillator strengths derived from BSE are in line with TD-LC-BLYP results, albeit the predicted values using both BSE and LC-BLYP are underestimated compared to the CC2 results. The deviation is highest for the NKX2677 dye molecule with a difference of 22% between the GW-BSE and CC2 values. The charge-transfer (CT) character of the lowest singlet excitations of the studied chromophores is significantly influenced by the length of the π-conjugated bridge, as evident by the spatial distribution of electron and hole for the lowest singlet excited states of the C343 molecule and the longest NKX-2677 dye predicted by accounting the expectation value of the electron position operator over the two-body BSE excitonic wave function ψ(r e , r h ). Figure 6 portrays the isocontour plots of the spatial localization of electron and hole for the smallest and longest coumarinbased molecules. The average electron–hole separation distance is calculated to be 3.2 Å in case of C343 molecule. The prominent CT character for the NKX-2677 dye with longest π-conjugated bridge is substantiated by the augmented electron–hole separation distance of 4.6 Å. The robust light-harvesting efficiency of the longest NKX-2677 dye is further vindicated by the minimization of HOMO-LUMO quasiparticle energy gap and exciton binding energy computed by employing GW/BSE formalism.

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Fig. 6 Isocontour representation of the electron (yellow) and hole (light blue) probability distribution for the lowest singlet excited states of a C343 and b NKX-2677, respectively, as obtained within BSE. [Adapted with permission from Ref. 64 Copyright (2012) American Physical Society]

3.3 Estimation of Quasi-Particle Energy Levels in Organic Chromophores and Dye/Semiconductor Interfaces and Simulation of Photoelectron Spectroscopy of Organic–Inorganic Hybrid The deviation of quasi-particle (QP) energy levels owing to the enhancement of the conjugation and the length of linker group have been evaluated for a series of DSSC dyes [66] comprising the same donor moiety [triphenylamine (TPA)] and the same anchor group (conjugated cyano-acrylic acid) as displayed in Fig. 7. The

Fig. 7 Schematic representation of the triphenylamine (TPA)-based organic dyes. [Adapted with permission from Ref. 66 Copyright (2013) AIP Publishing]

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Table 1 Computed vertical ionization potential (IP) and electron affinity (EA) within the GW framework for the dyes: L0, L2, L3, and L4. [All the values are reproduced with permission from Ref. 66 Copyright (2013) AIP Publishing] Dye

IP (eV)

Eox (exp) (eV)

EA (eV)

L0

6.87

5.81

1.66

L2

6.48

5.57

2.31

L3

6.37

5.51

2.28

L4

6.21

5.45

2.21

vertical ionization potential (IP) and electron affinity (EA) for each dye calculated from HOMO and LUMO QP energies within the framework of GW approximation are represented in Table 1. The IP decreases with increasing the length of the conjugated moiety, and follows the similar trend as revealed by the experimental oxidation potentials (E ox ), although the structural relaxation effect in solvent core environment has not been taken into account. The EA considerably increases from L0 to L2; however, the predicted EAs for L2–L4 are not interrupted remarkedly due to the enlargement of conjugated anchor group. In order to examine the efficacy and robustness of the GW-based calculations, the computed valence electronic density of states (DOS) spectra of L0 and L2 dyes are compared with the photoemission spectra conducted on thin films of the respective dyes [67]. The calculated HOMO level with the GW method is found to be upshifted by about 0.4 eV on going from L0 to L2 (Table 1), which agrees well with the observed value of 0.2 eV measured by photoemission spectra for thin films. The positions and the relative intensities of the three major peaks seeming in the electron photoemission spectra with energy values lying between –4 and –10 eV are almost retained in the electronic DOS spectra of L0 and L2, as delineated in Fig. 8. A computational model of photochrome-TiO2 was further introduced to unveil the kinetics of electron injection at the dye-semiconductor interface. The dye molecule L0 was subjected to adsorb onto the (101) surface of anatase TiO2 slab model comprising 24 TiO2 units, in a bidentate bridging mode. All the DFT computations were carried out by dint of Quantum ESPRESSO code [68] and employing normconserving pseudopotential for all the atoms involved except for the Ti, for which adapted pseudopotential aiding semi-core 3s and 3 p orbitals as valence orbitals was implemented. The computed GW electronic band gap for the TiO2 (101) slab possessing two layers and a width of about 8 Bohr is found to be 4.31 eV which is 20% higher than the predicted GW band gap of 3.63 eV for the bulk anatase. Despite such overestimation due to the exploitation of simulation cells of restricted size, the position of the energy level of the valence band maximum (VBM), which appears at -8.3 eV, is in accordance with the experimentally measured values of -8.4 eV and -8.0 eV for the rutile TiO2 (110) surface [69, 70]. Moreover, due to the anchoring of L0 dye on the surface of anatase slab, the HOMO-LUMO energy gap of the pristine dye is lowered by about 1 eV. In Fig. 9, the calculated valence DOS for the L0 dye adsorbed on TiO2 surface is compared with the experimental photoelectron

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Fig. 8 Valence DOSs calculated with the GW approach (black) and experimental photoemission spectra (red) from Ref. 67 for L0 and L2. A Gaussian broadening of 0.25 eV has been used for the GW lines. [Reprinted with permission from Ref. 66 Copyright (2013) AIP Publishing]

spectrum recorded for the adsorption of single monolayer of L0 molecules on the surface of nanostructured TiO2 [67]. The major features of the photoemission spectrum are approximately recaptured through the GW valence DOS. The difference in line intensities between the experimental and theoretical spectra possibly emanates from the smaller penetration depth of the photoelectron spectroscopy as well as the limited size of the TiO2 slab model. The relative offset between the HOMO and the emission peak at about -9 eV is fairly captured within ~ 0.5 eV. In another study, the relative alignment of the HOMO and LUMO of the dye molecule (L0) and the valence band maximum (VBM) and conduction band minimum (CBM) of the anatase TiO2 (101) slab owing to the co-adsorption of solvent molecules such as water and acetonitrile has been evaluated by Verdi and co-workers [52]. In both the solvents, the lowest energy structure of the L0/TiO2 hybrid composite derived from DFT calculations corresponds to a dissociated monodentate structure involving transfer of proton to a nearby surface oxygen, as portrayed in Fig. 10. The computed GW energy levels in dye/semiconductor interfaces using the GWL

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Fig. 9 Computed valence DOS using the GW approximation for the L0 dye adsorbed on the TiO2 (101) surface (black), and experimental photoelectron spectrum (red) of L0 dyes sensitized on TiO2 taken from Ref. 67. The experimental spectrum has been aligned in order the HOMO level to match the theoretical one. [Adapted with permission from Ref. 66 Copyright (2013) AIP Publishing]

Fig. 10 Schematic illustration of DSSC model structures: L0 dye adsorbed on the anatase TiO2 (101) surface in the presence of water (left) and acetonitrile (right) molecules. [Reprinted with permission from Ref. 52 Copyright (2014) American Physical Society]

package of the Quantum ESPRESSO DFT code are displayed in Fig. 11. The quasiparticle energy levels are further compared to DFT-BLYP results. The calculated HOMO–LUMO energy gaps of the dye with DFT-BLYP method remain unaltered in the presence of solvent molecules. With acetonitrile the HOMO and LUMO energy levels of the dye L0 are lowered by 0.1 eV and 0.2 eV, respectively. Figure 11 clearly

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115

Fig. 11 Calculated energy levels with respect to the vacuum of the L0 HOMO (blue bold) and LUMO (blue dashed) and VBM (red bold) and CBM (red dashed) of the TiO2 slab obtained from the DFT-BLYP and the GW method. The thin black line is a guide for the eye. [Reprinted with permission from Ref. 52 Copyright (2014) American Physical Society]

demonstrates that the inclusion of many-body effects significantly alters the electronic energy levels of the photosensitizer. The estimated HOMO–LUMO energy gaps of L0 within the GW formalism are found to decrease by 0.9 eV and 1.3 eV, respectively, due to the co-adsorption of water and acetonitrile solvent molecules. The substantial alteration of electronic energy levels in the presence of acetonitrile is mainly attributed to the dipole interaction with the solvent molecules as well as the enhanced polarizability of the medium. Similarly, for the TiO2 energy levels, a prominent upward shift of the CBM is observed due to the interaction of acetonitrile molecules with the TiO2 surface, and this is in accordance with the previous theoretical and experimental studies [71, 72].

3.4 Determination of Rate of Interfacial Electron Injection and Open-Circuit Voltage in DSSC The rate of electron injection was computed for the adsorption of L0 dye on the surface of TiO2 (101) slab employing the Newns–Anderson (NA) model [73, 74]

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within the many-body Green’s function GW formalism and compared with the result obtained by DFT-BLYP method, to elucidate the impact of hybridization between the adsorbate and the substrate states on the interfacial electron injection. The NA model provides the ability to evaluate the effects of adsorption on the sensitizer electronic levels especially by accounting the coupling between the conduction band (CB) of the semiconductor (TiO2 ) and the LUMO of the photosensitizer that is characterized in terms of energy shift relative to the free dye and the lifetime broadening . The LUMO energy of the adsorbed dye is expressed as the weighted average of the  QP , computed QP energies εi  QP pi i εi E LU M O (ads) =  i pi

(13)

where pi corresponds to the squared projection of the i th empty state of the adsorbed dye system over the LUMO of the free dye L0. After that the LUMO broadening is obtained by enumerating mean deviation of a Lorentzian distribution centred at E LU M O (ads)  i pi |εi − E LU M O (ads)|   = (14) i pi The electron transfer lifetime, which is equivalent to the electron injection lifetime, is estimated as τ ( f s) =

658 (meV )

(15)

The computed values of  for the L0/TiO2 system using GW and DFT-BLYP methods are found to be 0.246 eV and 0.231 eV, respectively, yielding a shorter injection lifetime (2.67 fs) for the GW approach in contrast to the DFT-BLYPderived result of electron transfer lifetime (2.85 fs). The obtained result with GW approximation is in accordance with the experimental ultrafast injection rates [75, 76]. The maximum limiting value of the open-circuit voltage Vocmax for the dye/TiO2 model systems including single layer of co-adsorbed solvent molecules, e.g., water or acetonitrile was estimated by ignoring the recombination effects and accounting the difference between quasi-Fermi level of the TiO2 and the redox potential   the electron of the electrolyte I − /I3− [52]. The values of standard redox potential of the I − /I3− redox shuttle with reference to the normal hydrogen electrode (NHE) and vacuum in water and acetonitrile medium along with estimated values of CBM and Vocmax within GW formalism are represented in Table 2. The calculated Vocmax is in vicinity of the experimentally predicted values of open-circuit voltage for the DSSCs incorporating TiO2 as the semiconductor and I − /I3− as the electrolyte lying between 0.65 to 0.9 V in acetonitrile [77, 78].

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 max  Table 2 Calculated maximum attainable open-circuit voltage of the cell Voc along with electrochemical properties for the co-adsorption of water and acetonitrile solvent molecules employing the GW approximation. [All the values are reproduced with permission from Ref. 52 Copyright (2014) American Physical Society] H2O CBM (eV)   E 0 I − /I − 3 (V)

–

V max oc (V)

0.9

a Relative b Relative

CH3 CN

4.1a

0.53b

– 3.6a

(–4.97a )

0.31b (–4.74a ) 1.1

to vacuum to NHE

3.5 Large-Scale GW-BSE Formulation for Evaluating Excitonic Energies and Optical Absorption Spectra of Dye/Semiconductor Systems in DSSC The perturbative GW/BSE scheme has been effectively exploited to estimate the quasi-particle energy levels in diverse organic chromophores and dye/semiconductor interfaces in DSSC, and the BSE formalism has been demonstrated to be an adequate approach in describing the intra- and inter-molecular charge-transfer (CT) excitations due to the non-local nature of the implemented screened Coulomb potential that couples the nonoverlapping electron and hole distributions. However, the practical implementation of the GW-BSE formalism in reckoning the excitonic effects in large organic–inorganic hybrids, as often required for determining photoinduced chargetransfer mechanism in DSSC, is hindered by their N4 scaling needed for computing the complex dielectric function. To ease the computational constraints, Marsili et al. [53] have proposed an efficient GW-BSE scheme based on maximally localized Wannier’s function (MLWF) allowing considerably on large  computations   faster systems by minimizing the overall scaling from O N 4 toO N 3 . Within the Tamm–Dancoff approximation, focusing only on the singlet excitonic eh



states, the Hamiltonian-like operator H can be expressed as

that accounts electron–hole interactions

eh ˆ ˆx ˆd Hˆ vc,v

c = Dvc,v c + 2 K vc,v c + K vc,v c



(16)



where v and v and c and c indices go over the occupied and unoccupied single



x



d

particle states, respectively. D , K , and K refer to the diagonal, electron–hole exchange, and direct screened Coulomb operators, respectively. Now, within the framework of second quantization, a generic excited state in the Tamm–Dancoff approximation can be represented as | =

 vc

Avc aˆ v aˆ c† | ψ0



(17)

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Where aˆ i and aˆ i† correspond to the annihilation and creation operators for the i th state, and |ψ0 is the ground state wave function. The operators in Eq. (16) can be expressed in the Avc representation as follows: Dvc,v c = (εc − εv )δvv δcc

(18) qp



where εc and εv are the eigenvalues of the quasi-particle Hamiltonian H .       x   K vc,v

c = ∫ ψv (r)ψc (r)v r, r ψv r ψc r d rd r

(19)

      d   K vc,v

c = − ∫ ψc (r)ψc (r)W r, r ψv r ψv r d rd r

(20)

and

where v and W refer to the bare and static screened Coulomb operators, respectively. The explicit computation of unoccupied single-particle states can be eliminated by deploying density functional perturbation theory (DFPT)-based approach and  expressing the excitonic states in terms of single-particle functions ξv (r) = c Avc ψc (r) such that  | =

      ˆ ψˆ † r   r, r  ψ0 d rd r  ψ(r)

(21)

with       r, r  = ψv (r)ξv r 

(22)

v

where ψˆ † and ψˆ denote the creation and annihilation field operators. Now, the action of in Eq. (16) to a generic state can be written as    excitonic  the  operators defined  x  ξ

= Kˆ d |{ξv } with  ξ = D|{ξ ˆ v } ,  ξv

= Kˆ v,v

|{ξv } , and v v v,v  qp

ξv (r) = H − εv I ξv (r) 

ξv

(r) = ∫ dr Pc (r, r )ψv (r ) ξv

(r) = − ∫ dr Pc (r, r )





(23)

v [∫ dr

v(r , r

)ψv (r

)ξv (r

)]

(24)

ξv (r )[∫ dr

W (r , r

)ψv (r

)ψv (r

)]

(25)

v

where the operator Pc has been introduced for projections onto the manifold of unoccupied one-body states:

Delving Charge-Transfer Excitations …

119

        

Pc r, r = ψc (r)ψc r = δ r − r − ψv (r)ψv r

(26)

v

c



A further improvement to overall scaling is achieved by computing ξvv in real space utilizing MLWF representation {wv } of the excitonic state such that

ξ˜v

(r) = − ∫ dr Pc (r, r )



ξ˜v (r )[∫ dr

W (r , r

)wv (r

)wv (r

)]

(27)

v

with ∼

ξ v (r) =



Uvv ξv (r)

(28)

v

where U is a unitary matrix. By excluding the explicit calculations of nonoverlapping pairs of Wannier’s function, and introducing a threshold s for which a given pair of Wannier’s function can overlap, 

 2 |wv (r)|2 wv (r) d r > s

(29)

it is possible to reduce the scaling of computation of ξv

from O(N 4 ) to O(N 3 ). To assess the efficacy of GW-BSE formalism based on MLWF, the optical absorption spectrum and ionization potentials were estimated for a large DSSC model comprising an organic photosensitizer JK2 [3-{5 -[N,N-bis(9,9-dimethylfluorene-2yl)phenyl]-2,2 -bisthiophene-5-yl}-2-cyano-acrylic acid] adsorbed on the surface of an anatase TiO2 cluster. The unsymmetrical JK2 sensitizer encompasses the bisdimethylfluoreneaniline moiety as the electron donor unit, the cyano-acrylic acid moiety as the acceptor unit, and the thiophene moieties as the bridging unit making conjugation between the donor and the anchoring groups. The dimethylfluoreneaniline moiety prevents degradation upon exposure to light and high temperature and suppresses dye aggregation. The model of TiO2 cluster includes 32 TiO2 units producing 204 atoms and 1174 valence electrons. For the estimation of GW-BSE energy levels with higher accuracy, the polarizability operators were expanded on an optimal basis set involving 2500 vectors. The optical absorption spectrum was calculated by varying the thresholds, viz. 500, 50, and 10 Bohr−3 yielding 2295, 7653, and 12,711 total number of Wannier’s function products, respectively. The computed optical gap using s = 500 is found to be 2.40 eV, which is very close to

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the predicted value of 2.47 eV usings = 10, as manifested by the position of the first peak corresponding to the simulated optical absorption spectra. The simulated optical absorption spectra for the JK2 photosensitizer adsorbed on TiO2 cluster are depicted in Fig. 12. The GW-BSE spectra display a lowest energy absorption band at 2.5 eV, which is in decent agreement with the experimental value of 2.6 eV [79]. The inception of light absorption in the experimental ultraviolet-visible (UV-vis) spectrum appears at 1.9 eV which is retained well in the GW-BSE spectra of the JK2-TiO2 composite. The second lowest energy absorption band centred at 3.2 eV in the simulated spectra is in conformity with the experimental UV-vis spectrum of the isolated JK2  dye [80]. In Table 3, the estimated groundstate  dye ionization  potential D/D + , excited-state dye ionization potential D ∗ /D ∗+ , CBM of TiO2 ,

Fig. 12 Simulated optical absorption spectra for the adsorption of JK2 dye on the TiO2 surface within the framework of GW-BSE formalism with s = 10 Bohr−3 (black), s = 50 Bohr−3 (blue), and s = 500 Bohr−3 (red). A Lorentzian broadening of 0.1 eV has been applied. [Reprinted with permission from Ref. 53 Copyright (2017) American Physical Society]   Table 3 Computed energy values of the estimated ground state dye ionization potential D/D + ,  ∗ ∗+    excited-state dye ionization potential D /D , CBM of TiO2 , and optical gap E g of the JK2TiO2 complex using the GW-BSE formalism. The GW-BSE values in parentheses include the solvent effects. The experimental values are obtained from Ref. 80. [All the values are reproduced with permission from Ref. 53 Copyright (2017) American Physical Society] Expt. (eV)

GW-BSE (eV)

D/ D+

−5.4

−5.9 (−5.8)

D∗ / D∗+

−3.5

−3.9 (−3.8)

CBM

−4.0

−4.3 (−4.1)

Eg

2.6

2.5 (2.5)

Delving Charge-Transfer Excitations …

121

  and optical gap E g of the JK2-TiO2 complex are further compared with the experimental data. Except the value ofE g , all the values are shifted by about -0.4 eV. The deviation further reduces to -0.3 eV upon solvation correction, as revealed by the data shown in parentheses. The solvent effect was included by exploiting implicit solvent model within the DFT formalism.

4 Summary and Outlook The quantitative assessment for the effectiveness of photovoltaic materials relies on the delicate analysis of the electronic states involving charge and energy transfer, as well as exciton dissociation and charge recombination. In the present study, we have epitomized recent achievements emphasizing on reckoning the intra- and intermolecular charge-transfer excitations and the localized (Frenkel) excitons in modeling the photochrome-TiO2 interface associated with the solar energy-to-electricity conversion efficiency of a DSSC. In contrast to the TDDFT method that commonly shows strong dependence on exchange–correlation functional in reproducing experimental optical absorption spectra, the many-body Green’s function GW-BSE approach allows one to account Rydberg states and charge–transfer excitations as well as simulate optical spectra more accurately due to the inclusion of exchange and attractive screened Coulomb interactions between the electrons and holes produced upon photoexcitation. The computational cost of the BSE formalism based on standard Gaussian atomic basis sets and resolution-of-identity techniques as implemented in several quantum chemistry codes such as Turbomole [81], CP2K [82], and Fiesta [49, 83, 84] is comparable to TDDFT in the alleged Casida’s formulation. The exploitation of a full frequency GW algorithm in a Gaussian-type basis enables the computations of quasi-particle energies for the larger systems with thousands of atoms including molecules and nanostructures in the gas, liquid, or condensed phase [85]. The latest formulation of BSE with the aid of maximally localized Wannier’s function presents a very good compromise between computer cost and accuracy by eliminating the explicit computations of summations over the empty state manifold as well as the screened Coulomb interaction W matrix. As evident by the predicted spectroscopic and photochromic properties of prototypical donor-bridge-acceptor organic dyes adsorbed on semiconductor oxide (TiO2 ) , the GW-BSE formalism is demonstrated to be a competent first-principles approach for determining crucial factors responsible for charge injection and recombination processes through the evaluation of optical gap of the photosensitizer followed by accounting energy shift of the TiO2 bands with the alterations of size of the linker groups and the dipole layer induced by co-adsorbed solvent molecules on the TiO2 surface. The estimated DSSC device performance parameter such as the open-circuit voltage Voc within the GW approximation is found to correlate well with the experimental data. The implementation of GW approximation for the estimation of ultrafast injection rate at the photochrome-TiO2 interface using the Newns–Anderson model does not give rise to a considerable change compared to the DFT-BLYP result, even though the

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band gaps are substantially underestimated by the DFT-BLYP method with reference to the experimental data. Despite the feasibility of the GW-BSE formulation in reproducing the experimental photo-electron spectroscopic and electrochemical data of the photochromes, the calculated indirect and direct band gaps with the GW approximation for the anatase and rutile phases of TiO2 are deviated to some extent compared to the experimental measurements, which is probably attributed to the eradication of vertex correction for the irreducible polarization function [86]. Albeit the state-of-the-art Bethe–Salpeter formalism is manifested to be a decent method to probe photovoltaic materials with weak dielectric screening and strongly bound excitons, there is still plenty of work that needs to be done to assess the efficacy of solar cell materials which are characterized by strong coupling between electronic and vibrational degrees of freedom, and to estimate the rates of radiative and nonradiative transitions in which the states are coupled by spin − orbit coupling (SOC) or influenced by nonadiabatic and spin − orbit coupling simultaneously. Delving and recognizing these effects in intricate hybrid organic–inorganic solar cell materials necessitate further improvement of the theoretical models within the many-body perturbation theory approach, which can reinforce the experimental interpretation. Acknowledgements This work has been supported by the Department of Energy (Grant number: DE-SC0018322) and the NSF EPSCoR (Grant number: OIA-1757220).

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Promising DSSCs Involving Organic D–π–A and Similar Structures for nand p-type Semiconductors—A Theoretical Approach Anik Sen Abstract This chapter discusses the need for energy and a process to address such need with the help of a renewable source of energy—solar energy––when the primary sources such as oil, natural gas, and coal are being depleted while also polluting the atmosphere. It discusses the rise of dye-sensitized solar cells (DSSC) and the invention of organic dyes. Several reports suggest that molecular modeling is an important key to understanding and developing new and efficient organic dyes for DSSC.

1 Introduction 1.1 Requirement of Energy In today’s world scenario, one of the most common questions is related to the sources and uses of energy in different fields. In 1807, Thomas Young first used the term “energy,” which is defined as a quantitative property that can be shifted in order to perform work or to heat. However, the law of conservation of energy states that Energy can be converted from one form to another but not created or destroyed. For example, a dynamite explosion is chemical energy converted to kinetic energy. The familiar forms of energy include kinetic energy, potential energy stored by an object’s position (gravitational, electric or magnetic), elastic energy, chemical energy, radiant energy carried by light, thermal energy, etc. Every living organism requires energy to stay alive, so humans get that energy from food. Every civilization also needs energy to function, and they get it from different energy resources as stated in the next section of the chapter.

A. Sen (B) Department of Chemistry, GITAM Institute of Science, GITAM (Deemed To Be University), Visakhapatnam, Andhra Pradesh 530045, India e-mail: [email protected] © Springer Nature Switzerland AG 2021 J. K. Roy et al. (eds.), Development of Solar Cells, Challenges and Advances in Computational Chemistry and Physics 32, https://doi.org/10.1007/978-3-030-69445-6_6

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In chemistry, energy is a characteristic of a substance due to its atomic, molecular, or collective structural changes. In contrast, in biology, energy is a characteristic of all biological systems. Energy is solely accountable for the development of biological cells or organelles. The cells in the molecules of substances can store energy as different compounds such as carbohydrates (including sugars), lipids, and proteins. They can release energy when reacting with oxygen in respiration.

1.2 Sources of Energy With the population increase and invention of newer systems, we will have a continuous rise in the demand for energy around the world. The world’s energy resources are mostly fossil fuels, nuclear fuels, and renewable resources. Still, the primary sources are fossil fuels: oil, coal, and natural gas. Estimating the residual amount of the fossil fuels on the planet requires a thorough investigation of Earth’s crust. Nevertheless, since these resources have been used for a long time, they are being depleted, and they are sources of pollution and thus not environmentally friendly. Still, the primary sources of energy are coal and oil, i.e., fossil fuels (see Fig. 1). Political issues, depleting amounts, and environmental pollution issues are helping us to move away from fossil fuels toward renewable energy Fig. 1 Different sources of energy

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Fig. 2 Renewable energies

sources. Nuclear power sources could be a vital alternative, but they have a high risk of radiation. So, renewable sources of energy are the best alternative (Fig. 2).

2 Why Solar Energy? Sun is the primary source of energy. Adequate solar energy needed for the survival of every living organism reaches Earth every hour. It is a clean, renewable, and sustainable source of energy. The quantity of energy from the Sun that reaches Earth per annum is 4 × 1018 J, whereas the amount of energy consumed annually by the world’s population is about 3 × 1014 J. Solar energy is chosen over all the other renewable energy sources because it has some important advantages: (i) (ii) (iii) (iv) (v) (vi) (vii)

it is a permanent, natural, and free source; it is obtainable in abundance; it is non-polluting; it does not produce or release any greenhouse gases; it offers devolution in most (sunny) locations, meaning independent societies; it is not affected by politics and price unpredictability that characterize fossil fuel markets; it does not negatively affect forests and eco-systems, unlike most fossil fuel operations.

Plants capture the solar energy to use in photosynthesis to transform carbon dioxide and water into high-energy compounds: carbohydrates, proteins, and lipids. Therefore, during photosynthesis, the trees produce adenosine 5 -triphosphate (ATP)

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O

O

Dye

Dye

P

Dye

SH

OH

O

OH

Dye

OH H

OH

Dithiocarboxylic Acid (2)

Carboxylic Acid (1)

Phosphonic Acid (3)

O

O

O

Dye

Catechol (4)

Dye

Dye

N

OH

N

Acetyl acetone (6)

Pyridine (5)

H

OH

Aldehyde (8)

CyanocarboxylicAcid (7) O

Dye

OH

Dye

O

H

Salicylic Acid (10)

Benzaldehyde (9)

S

OH

Dye +

O

OH

O

N

OH

Dye NH

N

Hydroxamate (13)

Hydroxyl Benzonitrile (14)

Fig. 3 Schematic diagram of different anchors for DSSC Fig. 4 UV-Vis absorption spectra of [Ru(CN)4 L]2− /TiO2 complex in three different solvents a water, b methanol, and c dimethyl sulphoxide [Reused with permission from Ref. [67], Copyright 2010, American Chemical Society]

–

Nitro (12)

Dye OH

OH

O

O

Sulphonate (11) OH

O

Dye

Dye

Resorcinol (15)

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energy. Creating such types of devices that can utilize solar energy to produce the energy needed for our household and other needs is the goal of solar energy scientists.

2.1 What Are Photovoltaic/Solar Cells? A photovoltaic cell can be defined as an electrical device that can convert light energy to electrical energy. It is a physical and chemical phenomenon [1–4]. One can relate the photovoltaic effect to the photoelectric effect. In either case, light is absorbed, causing the electron to excite or other charge carriers to a higher energy state. However, the key variation lies in the aftereffect of the electrons. In the photoelectric effect, the electron is expelled out of the material (usually into a vacuum), whereas in the case of the photovoltaic effect, the excited electron or charge carrier is contained within the material. Edmond Becquerel in 1839 first gave a demonstration of the photovoltaic effect through the first solar cell, consisting of a coat of selenium covered with a thin film of gold, which was experimented by Charles Fritts in 1884 [5]. The source of light or energy may vary from sunlight to artificial light, but as in most applications, the radiation is sunlight, so the devices are named “solar cells.” The first prominent use of solar cells was for the Vanguard 1 satellite in 1958, where they were mainly used as an alternative power source.

2.2 Different Kinds of Solar Cells Solar cells are usually named after the semiconductor material used to make them. These materials have individual distinctiveness to absorb sunlight and are designed to be used on Earth and in space. The most commonly known solar cell is made from silicon, which has a large-area p–n junction. The solar cells are classified into first-, second-, and third-generation solar cells on their evolve timings. The first generations of solar cells are based on crystalline silicon (mono- and polycrystalline). They are very heavy and costly but very efficient. The second-generation solar cells are known as thin-film solar cells, including amorphous silicon, CdTe, etc. Third-generation solar cells are also based on thin-film technology and are mostly in the development phase. Other possible solar cell types are dye-sensitized solar cells, perovskite solar cells, organic solar cells, and quantum dot solar cells, etc., which are the subject of current research.

3 Why DSSCs Are Important In recent years, designing and manufacturing flexible, lightweight, and highly efficient solar cells is a prime research area. Silicon-based solar cells are very heavy

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and costly. Therefore, researchers have been exploring other options to design new lightweight and less expensive materials for solar cell studies. A few different solar cells on which current research is focused are perovskite solar cells, organic/polymer cells, DSSCs, and quantum dots. Perovskite solar cells include a perovskite-structured material (ABX3 type) as the active layer. The efficiencies of perovskite solar cells have increased from below 5% in the early 2000s to over 25% in 2019 [6]. Organic solar cells and polymer solar cells are manufactured from thin films of semiconductors, including polymers such as polyphenylene vinylene and small molecules such as fullerene derivatives, copper phthalocyanine, etc. The polymer solar cells showed very low conversion efficiency to date. However, a recent study showed an efficiency of 8.3%. Both perovskite and organic solar cells are much cheaper than silicon and have excellent prospects in the future, but their main issue is stability and not being able to be commercialized. DSSCs are based on a device formed with a photo-sensitized anode or a semiconductor that interacts with a dye sensitizer in the presence of an electrolyte or a redox media. The present version of a dye-sensitized solar cell was invented by Brian O’Regan and Michael Grätzel in 1988 at UC Berkeley [7]. Such solar cells are less expensive and also less heavy than the older solid-state cell designs based on silicon. The efficiency for such DSSCs is found to be lower than that of the silicon solar cells, but their price/performance ratio is higher. The most common DSSC research is based on metal–organic dyes as they were found to be more efficient and mostly based on the rare metal ruthenium. The advantages of such dyes over silicon-based dyes are their low weight, low cost, easier production, and higher flexibility [8–16]. In DSSCs, the dye first absorbs light, and then the charge is generated at the semiconductor–dye interface and transferred through the electrolyte. In a broad view, DSSCs consist of five different components: (a) (b) (c) (d) (e)

a material that can be coated with a transparent and conductive oxide; the base or the photo-electrode (semiconductor, n-type, or p-type); a dye sensitizer (metal-based or purely organic), which will be interacting with the semiconductor; the electrolyte or the redox mediator (M/M− ); and a counter electrode, which has the capability to regenerate the redox mediator [17, 18].

For an n-type DSSC, as shown below, at first ‘S’ sensitizer is excited by a photon and then this excited sensitizer S*injects an electron into the CB, or the conduction band, of the n-type semiconductor. This injected electron excites the electrolyte to produce the electricity required, later an electron from the counter electrode flows back to minimize the semiconductor’s charge. Some other processes such as back electron transfer also occur, which reduces the efficiency of the device. S(absorbed) + hν −→ S*(absorbed) − S*(absorbed) −→ S+ (absorbed) + e(absorbed) − M + e− (CE) −→ M(CE)

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− S+ (absorbed) + M −→ S(absorbed) + M − S+ (absorbed) + e(injected) −→ S(absorbed) − M + e− (injected) −→ M

The overall efficiency of the device depends on the optimization and compatibility of each of the constituents. In the case of p-SC, hole transports from the dye to the semiconductor. Several hole transport materials are known: NiO, CuI, CuSCN, CsSnI3, etc. A similar working principle is observed for the p-type semiconductor-based DSSC. The difference lies in the sensitizer’s excited state, which after excitation transfers its electron to the electrolyte or to the attached catalyst. In this case, the semiconductor injects electrons into the dye and thereby creates holes in the valence band of the SC. It can also be stated in a different way that the dye injects hole to the valence band of the semiconductor. Although the standard design of the dyes for n- and p-type DSSCs consists of electron-donor (D) and electron-acceptor (A) linked with π conjugation (D–π–A) , the main difference between the two lies in the position of the acceptor or the anchoring groups. For n-type, it is attached on the electron-acceptor part, while the group is attached on the electron-donor part for p-type dyes. S(absorbed) + hν −→ S*(absorbed) + S*(absorbed) −→ S− (absorbed) + h(injected) − M + h+ (CE) −→ M(CE) − S− (absorbed) + M −→ S(absorbed) + M

DSSCs are currently the most efficient third-generation solar technology available due to their low cost and high durability (Scheme 1). DSSCs are attractive as a replacement for existing technologies in “low” applications such as rooftop solar collectors, where they are better than the heavy glass-based silicon solar cells. However, DSSCs are still not used for large-scale development because higher device

Scheme 1 Schematic diagram of n- and p-type DSSCs

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efficiencies are still hovering over the cost-efficiency. But continuous research in the field of DSSCs is being done to increase the efficiency of the DSSC devices, and in the near future, they may replace the costly solar cells in every field. Moreover, DSSCs work in low-light conditions, so they can work when it is overcast or in nondirect sunlight. Even in bright lights in home, unlike traditional solar cells, which causes solar energy companies to suffer losses during the rainy season. Therefore, DSSC can very aptly soon take over and be used for indoor energy purposes. Photocatalysis is the acceleration of a photoreaction in the presence of a catalyst. In photogenerated catalysis, the photocatalytic activity (PCA) depends on the catalyst’s capability to create electron–hole pairs that generate free radicals that can undergo reactions. A more advanced form of photocatalysis tries to perform multiple lightinduced electron-transfer steps, accumulate these charges at the catalytic center, and perform multielectron catalytic conversions. Photocatalysis is generally of two types, based on the phase of the catalyst and the reactant. If the reactants and the catalysts exist in the same phase, it is known as homogeneous photocatalysis and if different, it is known as heterogeneous photocatalysis. Photocatalysts can be applied in various fields such as (i) conversion of water to hydrogen gas through photocatalytic water splitting [19]; (ii) generation of free radicals by TiO2 , which helps in the oxidation of organic matter; (iii) oxidation of organic contaminants using magnetic particles coated with TiO2 nanoparticles [20]; (iv) the ability of TiO2 in presence water and a suitable electron donor to help in the conversion of carbon dioxide into gaseous hydrocarbons [21]; (v) removal of unwanted fingerprints from sensitive optical and electrical instruments and sterilization of surgical instruments; and (vi) disinfection of water by supported titanium dioxide photocatalysts [22, 23] etc. Photocatalytic splitting of water is of tremendous importance in the present day as it has a great prospect for solving the crisis of energy [24–26]. However, very little is known about the interplay of light absorption, directional electron transfer, and catalytic processes. The current understanding of experimental methods is limited to the first electron transfer, while hydrogen evolution requires two electrons and water oxidation four. In other words, the total mechanism of the overall catalytic process is unclear. Theoretical methods have been involved in solving specific problems, but some information is obtained [27, 28], a general mechanism is still not established. Within this context, photoelectrochemical cells or PECs [29] are very interesting as they may offer not only a technically feasible proof of concept. They also limit the amount of collision-induced processes essential for the overall catalytic mechanism. In detail, they may be seen as solar cells that is often used to electrolyze water to hydrogen and oxygen gas by irradiating both electrodes with electromagnetic radiation. This type of work is referred to as artificial photosynthesis as it resembles the actual photosynthesis process and has been suggested to store solar energy in hydrogen for use as fuel. Two types of photochemical systems are known. One is with semiconductor surfaces as catalysts, which absorbs solar energy and acts as an electrode for water splitting at the same time. The other methodology uses insolution metal complexes as chromophore and catalysts, while the electrode servers are electron acceptors or donors.

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Involvement of the dye sensitizer was inaugurated in this photocatalysis when O’Regan and Grätzel published their pioneering work on DSSCs in 1991 [7]. In recent years, Youngblood et al.; Li et al.; Song et al. [30–36] focused on the DSPEC research based on mostly water oxidation with chromophore catalyst, but studies on dye-sensitized photocathodes for reduction of water or carbon dioxide are much less frequent [37, 38]. The aim of the recent studies including my research is intimately related to the field of energy conversion and renewable energy sources, which are of uttermost importance for our society. Energy research is a field focusing on making available adequate major energy sources and minor energy forms to meet the needs of society. This includes the production of conventional, substitute, and renewable sources of energy and the revival and recycling of energy. Renewable energy is produced by natural resources such as sunlight, rain, wind, waves, tides, and geothermal heat. Since the direct combustion of fossil fuels causes the most significant amount of air pollution, continuous incremental progress in developing renewable energy technologies is required. The hydrogen fuel cell is one of the promising alternatives to fossil fuels. Hydrogen fuel may reduce the threat of fossil fuels’ depletion in the near future. It can be produced from waste, biomass, solar, hydro, wind, nuclear power, or geothermal energy and may offer the greatest long-term potential to radically reduce the usage of non-renewable sources. Renewable hydrogen can be produced in numerous ways: i. ii.

iii.

splitting of water into oxygen and hydrogen using electricity or electrolysis; conversion of biomass either by thermochemical or biochemical alteration to intermediate products that can form hydrogen or direct hydrogen formation through fermentation techniques; and conversion of solar energies which can be obtained by thermolysis, using solargenerated heat in which the solar photons are used to produce hydrogen directly by involving biological or electrochemical systems.

For practical environmental applications, the immobilization of the photocatalyst on appropriate support is extremely attractive for several reasons. Attaching the catalytically active materials to supports allows a spatial separation of the reduction and oxidation processes and their products so that unwanted recombination reactions are avoided. Immobilization of the photocatalyst suppresses potential intermolecular reactions between highly oxidizing species thus preventing possible decomposition. And through nanostructuring the support, the immobilized catalysts can be dispersed efficiently. The best-studied support material for photocatalytic hydrogen evolution is NiO; however, its performance is limited by some severe drawbacks such as unfavorable charge transport properties and its own catalytic activity leading to side reactions [39]. The already relatively well-established photocatalytic water oxidation catalyst immobilized on TiO2 electrodes [35] have not reached their full potential as the potential generated is insufficient for hydrogen evolution at the counter electrode. The recently published first report on a NiO-based molecular photocatalytic system for hydrogen evolution [39] is based on a photosensitizer, Ruthenium–polypyridyl complex, a bridging ligand, and a coordinated cobalt center as the catalytic center.

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Here, photoexcitation of the ruthenium unit leads to intramolecular charge transfer to the catalytic cobalt center. The NiO-electrode donates an electron to the oxidized ruthenium center, closing the first redox cycle. The subsequent events are not known; however, upon several hours of irradiation, catalytic hydrogen formation occurs via the cobalt center. The stability of the charge-separated state, Ru(III)–Co(II), versus charge injection from the electrode NiO to the Ru(III) is one key aspect determining overall catalytic efficiency. Theoretical calculations to understand the process, describing the formation of the barrier so that the flow of electrons or holes is possible for the photocatalysts to work are very important. Many theoretical calculations on dye-sensitized solar cell with TiO2 have been done, although the same for photo electrocatalytic processes for water splitting on such NiO surfaces are scarce. Recently, M. Shen et al. discussed the photocatalytic activity of porous NiO nanowires [40]. They have performed experimental studies and theoretical calculations to understand how to improve NiO’s electro- and photocatalytic activities and exhibited a possible route for the development of structurally steady and chemically active catalysts in new energy applications with high performance. Such artificial photosynthesis studies can be performed with p- and n-conjugated DSSCs which are commonly known as tandem cells, and the theoretical efficiency of tandem cells is higher than the single-junction DSCs. The tandem cell is a sandwich configuration with an intermediate electrolyte layer of both n-DSSC and p-DSSC. The matching of photocurrent is vital for the construction of highly efficient tandem pn-DSCs. Though, n-DSCs have a fast charge recombination, but the much slower hole injection process for p-DSCs results in a low efficiency of the p-DSC and thus hampers the overall device’s efficiency. Some major disadvantages for the DSSC uses: 1.

The usage of the liquid electrolyte has stability problems due to its temperatures: a. b.

2.

at lower temperatures, the electrolyte may freeze, and thus power production is halted, which leads to physical damage; at very high temperatures, the liquid expands and makes the panels seal, which causes a serious problem. So, liquid electrolyte is a serious problem for such devices.

The second disadvantage is the use of costly ruthenium or such metal dyes for the dye sensitizer. This can be avoided by the use of low-cost metal dyes or organic-based dye sensitizers. Many researchers are developing other low-cost metal-centered dye sensitizers and organic dye sensitizers for DSSC.

Quantum dot solar cells (QDSCs) are the new development in solar cells and are based on the Gratzel cell, or DSSCs architecture. In such devices, the semiconductor nanoparticles have low band gaps and are fabricated with crystallite sizes minute enough to form quantum dots as an alternative of the organic or organometallic dyes used in the normal DSSCs (e.g., CdS, CdSe, Sb2 S3 , PbS, etc.). Environmentally friendly green materials such as CuInS2 , CuInSe2, and CuInSeS) [41] are used in QDSC. Like the normal DSSCs, in QDSC the backbone is formed by a mesoporous

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layer of titanium dioxide nanoparticles, which can be made photoactive by coating with semiconductor quantum dots, using chemical soak deposition, electrophoretic deposition, or ionic layer adsorption and reaction. Recently, it has been observed that the efficiency of QDSCs has increased [42] to ~5% for both liquid junction and solid-state cells [43]. One report has also shown efficiency of 11.91% [44]. However, limitations are still present as the adsorption is weak at room temperature for such quantum dots (QDs) in the QDSCs [45].

4 Development of New Dye Sensitizers Ruthenium-based metal dyes are still known to be the highly efficient DSSCs for n-SC [46–59]. The use of polypyridyl–metal complexes as photosensitizers or photocatalysts is well known for the last two decades [38, 60–63]. These photosensitizers immobilized on the semiconductor surfaces (SC) in a DSSCs are responsible for the conversion of energy. For n-type DSSCs, Ru–polypyridyl complexes have shown the best photo-voltaic properties among the metals, whereas their use is limited for p-type DSSCs [8]. But Ru– or Re–polypyridyl complexes have been used [64, 65] for hydrogen evolution or photo-catalytic CO2 reduction on p-type SCs like NiO or TaON. Meyer and co-workers [66] reported about dual sensitization of TiO2 using iron-based metal-centered dyes and electron injection through cyano-ligand.

4.1 Studies on Metal-Centered Dyes The metal-centered dyes generally have two parts, the metal complex and the anchor group interconnected with a ligand. The anchors are the important part that connects the dye with the semiconductor surface. Mainly the metal complex part has the most important component to absorb the sunlight. The photovoltaic performances are analyzed based on terms of conversion yield and long-term stability, and it has been observed that polypyridyl complexes of ruthenium and osmium are the best. General structures that are mostly preferred to be good sensitizers are ML4 or ML2 (X)2 , where M can be Ru or Os and L is 2,2 -bipyridyl-4,4 -dicarboxylic acid, and X can be a cyanide, halide, acetyl acetonate, thiacarbamate, thiocyanate, or water substituent group [67–71]. Polypyridyl complexes of the d6 transition metals (RuII, OsII, and ReI) are mostly used in DSSC as they have a rich photochemistry due to prolonged MLCT excited states [52, 56, 72–74]. Polypyridyl complexes of these metals are commonly known as DSSC for n-type semiconductors like TiO2 [75–84]. Iridium complexes have also been studied for use in DSSC in recent years [85]. Karmakar et al. showed many diverse metal complexes used in this field for n-type semiconductors, but according to their research, ruthenium complexes were observed to be the most competent ones [86].

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Ruthenium-based dyes can be classified under phosphonate ruthenium dyes, carboxylate polypyridyl ruthenium dyes, and polynuclear bipyridyl ruthenium dyes [87, 88]. In 1993, Grätzel reported cis-[Ru(dcbH2)2 (NCS)2 ], known as N3 dye, which was one of the most promising dye sensitizers [89]. Other efficient dyes were explored based on Ruthenium metals, namely N719, N749, and Z907, to list a few [90–92]. Research on near IR dyes as sensitizer for DSSC has been carried out, including ruthenium complexes containing 1,8-naphthyridyl or biquinoline moieties, osmium polypyridyl complexes, cyclometallated ruthenium complexes, and phthalocyanine and perylene dyes [93–95]. Crown ether-based Ru-dyes have also been synthesized but showed a very low efficiency of 2% and IPCE of 31% at 530 nm [96]. Osmium sensitizers were also examined and found to be 50% less efficient than Ru complexes, but they have better photochemical stability than the previous. Different complex dyes have been synthesized based on osmium metal such as [OsII(H3 tcterpy)(CN)3 ]−(H3 tcterpy = 4,4 ,4 -tricarboxy 2,2 :6 ,2 -terpyridine) and osmium sensitizers including 2,2 -bipyridine-4,4 -bisphosphonic acid ligand, but the IPCE values were still lower than the Ru complex [97]. Dyes based on such scarce and heavy metal ions are difficult to synthesize and not environmentally friendly. Thus, research has been executed in recent years to develop cheaper dyes based on more abundant metals as well as nonmetal organic dyes. Iron (fourth abundant element in Earth’s crust) has very recently been used for DSSC with TiO2 [98, 99]. Research also showed applications of nickel, chromium, copper, and zinc metal ions (some other abundant metal ions) for the DSSC [100–103]. Nickel(II) polypyridyl complex is also newly used as a catalyst for hydrogen production from water [104, 105].

4.2 Studies on Organic Dyes Organic dyes have attracted considerable attention as they are capable of high sunlight-to-electricity conversion, high molar absorption coefficient. Also, their ease of synthesis and low production costs are significant attractions to researchers in this field [106]. Metal-free organic dyes naturally have a simple D–l–A structure, where D is the donor moiety (electron-rich) and A is the acceptor (electron-poor) moiety connected with a l-spacer. Since the invention and successful synthesis of the novel organic dye polyene–diphenylaniline, also known as D5, with an overall efficiency of ~5% [107–111], many theoretical and experimental calculations have been performed to progress the DSSC performance through sensible alteration of donor [112], π-spacer [113–115], and acceptor [116–120] subunits. Recently, novel organic dyes with a D–A –π–A design have been introduced with an additional acceptor A into the conventional D–π–A structure. These auxiliary electron-withdrawing groups ‘A ’ [121–124] in this kind of organic sensitizer “D–A –π–A” moieties display outstanding photovoltaic properties for many systems [125–132] but also have some unpleasant effects [133–135]. In the previous topic, we also discussed the tandem cells, which consist of an n-type photo-anode linked with a p-type photo-cathode. But the efficiency of such

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devices is restricted to the low efficiency of the p-type DSSCs. After the research on NiO DSSC studies based on erythrosine-based (organic dye) studies by Lindquist et al. [136], numerous studies have been performed to increase the efficiency of ptype DSSCs such as coumarin, [137, 138] perylene monoimide [139–141], porphyrin [142, 143], amine [144], etc., donor groups.

5 My Contributions Improving the efficiency of the DSSCs is a complex crisis and a demanding job. Different features related to the dye contribute to the efficiency of the DSSCs—(i) accurate choice of an appropriate anchor to interact on a semiconductor surface; (ii) absorbance of light in the visible spectrum; (iii) high electron injection efficiency from the dye (excited state) to the semiconductor surface; (iv) easy regeneration of the sensitizer molecule with the help of the counter electrode and the electrolyte; (v) the control on the slow undesired charge recombination processes that are present between the LUMO of the dye and TiO2 conduction band, etc. [67–70, 93, 94]. Recently, many theoretical and experimental studies have been performed on various organic dye sensitizers based on cyanines, hemicyanines, triphenylmethanes, perylenes, coumarins, porphyrins, squarines, etc., donor groups. Several studies have also been carried out with various π-linkers such as ethenyl [125–127], phenylene [128], and thiophene derivatives [129], to name a few. Different acceptors have been studied that are more frequently known as anchor groups as they immobilize on the semiconductor surface directly. Anchoring groups like carboxylic acid (1), cyanoacrylic acid (7), and phosphonic acid (3) are very common for DSSCs studies [130–132, 145, 146]. Another compound that is frequently used for anchors is catechol (4) [147–150]. The pyridine-based anchoring group (5) and its properties have been found to be comparable with a traditional phenyl carboxylate anchor that was first developed by Ooyoma et al. [151, 152]. Acetylacetone is another well-known anchoring group (6), which is also well known for its coordination properties in the direction of transition metals [153, 154] and has been effectively utilized as a linker for DSSCs [155–157]. A recently developed anchor group dithiocarboxylic acid (2) for p-type semiconductors is also very fruitful [158, 159]. Several other anchoring groups have been used for DSSCs studies and are well studied in literature: aldehyde and benzaldehyde (8, 9) [160, 161], salicyclic acid (10) [162, 163], sulfonic acid (11) [164–166], nitro (12) [167], hydroxamate (13) [168–170], hydroxyl-benzonitrile (14) [171, 172], and resorcinol (15) [173]. Metal–organic dyes have been used with the anchoring groups 10 and 13 for n-SCs, whereas organic dyes are used for the other anchors 8, 9, 11, 12, 14, and 15 (Fig. 3). Theoretical investigation of the challenges for both experiment and theory to understand many fundamental properties decisive for the efficiency of the DSSCs is still very important. In order to improve the performance of dye sensitizers first the physical properties of known dyes need to be analyzed and then novel dyes that promise a higher performance need to be suggested based on the gained insights. This

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would be a much more environmentally friendly and lower cost way to gain better and more efficient dyes. In this regard, my work has been dedicated to significantly contribute to this field and understanding the ways of enhancing the efficiency of the metal–organic and organic dyes for both n-type and p-type semiconductors.

5.1 Theoretical Calculation Strategy The conversion efficiency for a DSSC is generally given by the symbol η and is given by the following equation [109]: η = FF

JSC VOC Pinc

(1)

In this case, FF is the Fill Factor; VOC is the open-circuit photovoltage, and the short-circuit current density is given by J SC. Pinc stands for the incident solar power. The short-circuit current density is given by the equation: 0 Jsc =

LHE(λ)inject .ηcollect .ηregen Is (λ).dλ

(2)

λ

where LHE is the light-harvesting efficiency at wavelength λ of photon, Φ inject is the hole injection, and ηregen is the efficiency for regeneration for the oxidized dye. The charge collection efficiency is given by the term ηcollect [109]. It has been observed from Eq. 2 that the short-circuit current density is directly proportional to the LHE, Φ inject , ηregen, and ηcollect. The LHE or the light-harvesting efficiency can be calculated by the theoretical method by calculating the oscillator strength of the adsorbed dye molecule at the respective absorption maximum, λmax using the following equation: LHE(λ) = 1−10− f

(3)

For n-type DSSC, Φ inject is the efficiency for electron injection, ïcollect denotes the charge collection efficiency, and the ïregen is the regeneration efficiency. Φ inject is similar to ΔGinject , i.e., the driving force for the electron injessction from the excited state of the dye to the semiconductor. The calculations of the ΔGinject can be performed theoretically and are very well described in the previous articles [109, 174]. They calculated the oxidation potential of the excited state (E dye* ), and the conjugate band edge of the semiconductor used and the difference of these two gave the ΔGinject . G inject = E dye∗ − E C B ,

(4)

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whereas the regeneration efficiency, which is closely related to the free energy change of the regeneration (ΔGregen ), can be calculated from the difference of the oxidation potential of the dye and the redox potential of the electrolyte. redox G regen = E dye − E A/A −

(5)

The previous articles on this topic also revealed that the open-circuit photovoltage (V oc ) is directly dependent on the perpendicular dipole moment or the normal dipole moment of the dyes on the semiconductor. An increase in the normal dipole moment directly increases V oc . For the case of p-type DSSC, Φ inject is the hole injection efficiency and ΔGinject , i.e., the driving force of the injection of electron from the dye’s excited state to the semiconductor or also given as the hole injection from the semiconductor to the dye and ΔGregen is the regeneration efficiency of the dye. The equation for calculating the hole injection efficiency is given as below [175]:   G inject = E VB (NiO) − (E 00 (S∗ ) + E(S/S− )

(6)

Here, in the equation the E 00 (S∗ ) is the electronic excitation energy equivalent to the maximum absorption, whereas E(S/S− ) symbolizes the sensitizer’s reduction potential. The E VB (NiO) indicates the valence-band energy level of the semiconductor [147, 148]. A detailed description can be observed in the previous article by Sen et al. [175]. Theoretically, the reduction potential of the sensitizer can be calculated, and its difference from the redox energy denotes the regeneration efficiency as observed in the article by Sen et al. [175–177]. The open-circuit photovoltage V oc , for the p-type can also be determined from the variation of the Fermi levels between the redox couple electrode and the NiO semiconductor [175]. The excited-state lifetime calculation was also described briefly in the article by Sen et al. [175].

5.1.1

Pendant Catechol Functionality Using a New Tetracyanato Ruthenium(II) Polypyridyl Complex [67]

In this work, comprising both experimental and theoretical collaborative work, a new ruthenium (II)–polypyridyl complex ([Ru(CN)4 L]2− having a pendant catechol functionality was synthesized for binding to the nanoparticulate of TiO2 surfaces (Scheme 2). A detailed report was presented in the work on the interfacial electron transport dynamics linking the conjugate band of the TIO2 and the photoexcited states of the sensitizer molecule, using femtosecond transient absorption spectroscopy. This report was the first of its kind that gave a detailed understanding of the ultrafast electron transfer dynamics for sensitization of nanocrystalline TiO2 based on tetracyano ruthenium–polypyridyl complex (solvatochoromic dye). The Emission spectra, as well as the steady-state optical absorption, were recorded for the complex

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Scheme 2 Synthetic procedure for the complex [Reused with permission from Ref. [67], Copyright 2010, American Chemical Society]

in various solvents and their mixtures, which showed the solvatochromic behavior of the dye molecule. The steady-state absorption studies also recommended the catecholate moiety binds through a pendant mode to the TiO2 surfaces through though the complex possessed two varied binding functionalities (coordinated CN− and the pendant catecholate group) (Fig. 4). At higher wavelengths, the 1/TiO2 system showed a broader band when compared to the complex, which can be explained by the formation of a stronger chargetransfer complex. DFT studies further explained this observation. Electron injection was observed to be single exponential (0.1) bond order of a C atom, and f) ESP-minimum net atomic charge for H atom would decrease the %PCE value of FDs. The developed model will help predict new FDs for the future as an acceptor component for PSCs. Kar et al. [16] developed one of the first QSPR models, using a combination of C60 and C70 FDs [52 C60 and 7 C70 ] as solar cell acceptors to predict the %PCE. The authors employed an MLR approach based on a genetic algorithm (GA) as a variable selection tool to develop the best QSPR model. Later, the developed model was introduced to screen a series of 169 FDs, collected from 18 different literature sources that had never been used or checked in the PSC system. Along with predicting and quantifying the structural features responsible for higher %PCE values of FDs as polymer-based solar cell acceptor (Fig. 4), the developed model offers helpful insights regarding the use of virtual screening approaches to the identification of lead FDs. Fragment A (Fig. 4) has positive effects on the %PCE value; it represents a four-atomic fragment labeled by partial charges induced by -ortho directing groups in the substituted benzene rings (Fig. 1). While fragment B has a negative impact on the %PCE related to the van der Waals attraction between three or more –ortho substituents in benzene ring decrease, the %PCE value represents a five-atomic fragment [X-C(benz)-C(benz)-C(benz)-X]. Fragments C define two types of fullerene substituent linkages, including fragment type one (first one) that corresponds to the presence of aromatic rings (X = phenyl, pyrrole, thiophene) attached via a linker to the fullerene, and fragment type two (the second one) that corresponds to the presence of only a phenyl ring fused to fullerene via a linker. Fragment D defines partial charges and negatively affects the modeled equation, where A is an aromatic ring, R1 an alkane substituent, and the cross line shows the bond attaching the fullerene. Fragment E has a negative effect: it replicates substituents attached near a pentagon of

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Fig. 4 Identified structural features of FDs as an efficient acceptor molecule for PSCs

the fullerene core, which is chemically and electrochemically more stable than twopoint substituted FDs. A large number of attachments in the fullerene core decreases the unsaturation and aromaticity properties, reducing the acceptor property of FDs. The fragments F are connected to partial charges with a negative impact on the %PCE values. They represent the transmission of charge through a chain of saturated carbons induced by a C=O group. However, when the C=O is attached to an aromatic ring, it can induce a mesomeric effect, which is stronger than an inductive effect. Therefore, the C=O group in the saturated carbon chain produces an inductive effect (the reason for lower %PCE). When it is connected to an aromatic ring, the mesomeric effect leads to higher %PCE. The presence of saturated carbon chains such as [C(sp3 )- C(sp3 )- C(sp3 )- C(sp3 )-H]) and the solvent-accessible surface area of polar atoms, which is essential when calculating free energy changes due to transferring the molecule from a polar to a non-polar solvent during the formation of PSCs with BHJ layers, has a negative impact on %PCE. Virtual screening of large FDs has enabled the authors to identify 12 lead FDs with high %PCE values, then the studied FDs. An FD (ID: 41) showed the most promising %PCE value of 12.11, which offered a 200% increase in %PCE compared to the existing FDs at that time. The authors also established SiRMS-based descriptors, which can be used efficiently for QSPR modeling of FDs. The developed QSPR model is incredibly valuable for predicting and characterizing the nature of donor–acceptor relationships critical for photoconversion. The partial least squares-based (PLS-based) QSPR modeling followed by designing and optoelectronic properties were checked for ten future power-efficient FDs as acceptors for PSCs by Roy et al. [26]. For the QSPR modeling purpose, experimental %PCE measured according to bulk-heterojunction (BHJ) devices, where FD acts as the electron acceptor and Poly(3-hexylthiophene) (P3HT) as donor polymer

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were considered. The modeling dataset comprises 52 C60 and 7 C70 FDs. The PLSbased QSPR model helped to interpret the mathematical equation, which assists in understanding the following structural analysis for designing and mechanistic interpretation purposes: The -ortho directing groups in the benzene and aromatic rings such as phenyl, pyrrole, thiophene, attached to the fullerene are significant features for better %PCE of PSCs. For higher %PCE, the saturated carbon chains or higher –ortho substituents in benzene rings and a higher number of attachments in the parent fullerene core along with structural fragments with a lower solvent accessible surface area of polar atoms need to be avoided. Introspecting the structural features, the authors designed ten novel FDs consisting of C60 and C70 derivatives, and the predicted %PCE of FDs ranged from 7.96 to 23.01. The obtained encouraging results led the authors to perform a further theoretical analysis of the energetics and UV–Vis spectra of isolated FDs, employing DFT and TD-DFT calculations using PBE/631G(d,p) and CAM-B3LYP/6-311G(d,p) level calculations, respectively. Frontier orbital energies and UV–Vis absorption spectra of the isolated poly(3-hexylthiophene (P3HT) oligomer, Phenyl-C61-butyric acid methyl ester (PCBM), and FDs were analyzed to estimate the optoelectronic properties of identified top four FDs (FD1, FD2, FD4, and FD10) as an acceptor in future PSCs. FD4 is recognized as the best C60 -derivatives for PSCs as it shows the lowest exciton binding energy, strong absorption in the UV region, and up-shifted LUMO energy level that assist in increasing V OC (Fig. 5). While in the case of C70 -derivatives, FD7 is a likely candidate for future PSCs due to its strong absorption in the UV–Vis region and lower exciton binding energy with higher V OC . Combining the analyses of QSPR prediction and optoelectronic properties, the FD4 is proposed as the lead donor system of the future PSC by the authors.

Fig. 5 Top four potential lead acceptor FDs for PSC

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4.3 QSPR Modeling of Absorption Maxima Another important property of a dye, the absorption maxima (λmax ) of organic dyes for DSSCs can also be modeled using QSPR analysis and was first performed by Xu et al. [27]. The authors employed linear regression analysis to model 70 structurally diverse dyes as sensitizers for DSSCs. All the dyes were pre-optimized using MM+ force field applying Polak–Ribiere algorithm in the HYPERCHEM. It was followed by final geometries of the minimum energy conformation that were obtained by the semiempirical AM1 method at a restricted Hartree–Fock level with no configuration interaction, applying a gradient norm limit of 0.02 kcalÅ−1 mol−1 as a stopping criterion. After that, the DRAGON software was employed to calculate 763 3D descriptors from the optimized molecular geometries. Once the pool of descriptors was prepared, the author divided the dataset, using Kennard and Stones algorithm and developed the model with a training set, employing stepwise multilinear regression analysis (MLRA). The ten-descriptor model reported a squared correlation coefficient (R2 ) of 0.95. The consistency of the developed model was additionally checked using diverse validation techniques such as the leave-one-out cross-validation procedure, validation through the external test set, and randomization tests. Based on the significance, the authors illustrated the modeled descriptors in the following order: RDF020v > R3v > R8m+ >Hy > ALOGP2 > G1u > Mor30m > Mor21m > Mor05u > P1u, where, RDF020v is the Radial Distribution Function—2.0/weighted atomic van der Waals volumes; Mor21m and Mor30m are the 3D-MoRSE-signal 21/weighted and 30/weighted by atomic masses, respectively, Mor05u is the 3D-MoRSE-signal 05/unweighted, G1u is the first component symmetry directional WHIM index/unweighted, P1u is the first component shape directional WHIM index/unweighted, R3v is the R autocorrelation of lag 3/weighted by atomic van der Waals volumes, R8m+ is the R maximal autocorrelation of lag 8/weighted by atomic masses, ALOGP2 is the squared Ghose–Crippen octanol– water partition coefficient (log P2), and Hy is the hydrophilic factor. The derived descriptors will be helpful to estimate the λmax of future dyes before they are even synthesized. The same set of dyes was further explored by Xu et al. [28] employing artificial neural networks (ANN). The authors used similar optimization protocols applied under the previous study [A], followed by a total of 1164 descriptors that were calculated from the optimized molecular geometries, employing DRAGON software. The descriptors range from 0D to 3D descriptors (constitutional, functional groups and atom-centered fragments, topological, BCUT (Burden Chemical Abstract Service University of Texas), autocorrelations, walk and path counts, information indices, connectivity indices, eigenvalue-based indices, topological charge indices, Randic molecular profiles from the geometry matrix, geometrical, GETAWAY descriptors and weighted holistic invariant molecular (WHIM)). Then, the authors modeled λmax , using seven descriptors selected on the training set by genetic algorithm (GA) followed by a non-linear model using ANN with the squared correlation coefficient R2 = 0.991. The modeled descriptors were HOMA, Mor09u, RDF095v, G1p,

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Mor26v, R6mþ, and R2m, indicating that the λmax values of the dye sensitizers rely significantly on the size, mass, polarizability, and aromatic plane of the dyes. Additionally, the molecular conformational changes have an immense effect on the λmax values as per the ANN model.

5 Designing of Solar Cells, Employing QSPR and Machine Learning Models Rational designing of solar cells can help manufacture low-cost and efficient cells under scalable techniques, allowing to reach competitive performance-to-price ratios [29]. How QSPR, machine learning (ML) tools, and artificial intelligence (AI) can be employed for designing, followed by the quantum chemical study, is explained in the schematic workflow in Fig. 6. Interestingly, all the theoretical predictions of %PCE need to be confirmed through multiple quantum chemical studies and computation of optoelectronic parameters before final confirmation by experiment. Thus, many times although QSPR and ML approaches suggest a system can be efficient for future solar cells, it can fail to achieve the required optoelectronic parameters. In these specific cases, the systems need to be redesigned based on the interpretation to maintain required optoelectronic parameters for an efficient solar cell, as explained in Fig. 6. This process may continue in a loop until all parameters and the %PCE value optimize. This redesigning approach is a more rational and strategical one than

Fig. 6 Designing and redesigning scheme of efficient solar cells, employing QSPR and ML models

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a simple designing idea. For modeling and designing purposes, the following data, tools, and software are required: (a)

(b)

(c)

(d)

(e)

(f)

Experimental %PCE along with Voc and Jsc values for at least 25+ data points (more data points along with structurally diverse one lead to statistically better model) for the QSPR modeling purpose. The data points can be dye as the acceptor for DSSCs or acceptor (FD/NFA)/donor (Polymer) for PSCs. Structural and physicochemical properties can be calculated employing PaDEL software [30], Dragon [31], ChemAxon [32], etc., while quantum descriptors can be computed utilizing Gaussian (DFT and TD-DFT analysis using different levels of calculations) [33] and MOPAC (PM6 and PM7 semiempirical calculations) [34] software outputs. Chemometric approaches such as multiple linear regression (MLR), partial least squares (PLS), stepwise regressions, linear discriminant analysis, random forest, supervised, unsupervised machine learning approaches such as a neural network, deep learning, decision tree, etc. There are multiple open-access pieces of software available to perform these mentioned analyses, for example, DTC Lab Software Tools [35], QSARINS [36], WEKA workbench [37], etc. Once the statistically accepted model is ready, interpret the mathematical QSPR equation to understand the features responsible for the augmentation of %PCE value along with identity features accountable for lower %PCE. Use this information in designing new systems for solar cells. Optoelectronic parameters such as the driving force of electro injection (G I n ject ), charge recombination, shift of conduction band (CB) edge, intramolecular charge transfer (ICT), exciton binding energy, the spontaneity of dye regeneration (G Reg ), exciton binding synergy (E b ), charge transfer length (dC T ), reorganization energy (λT otal ), the shift of CB of TiO2 (E C B ), projected density of states (PDOS), and chemical reactivity parameters as well as excited-state lifetime and photostability of the complex need to be computed to check the ideal characteristics of a solar system [38]. If there is a problem with the value of any optoelectronic parameter, the system needs to be redesigned, followed by %PCE prediction and recalculation of the optoelectronic properties.

6 Databases of Solar Cells for Modeling The databases are one of the starting points for computational and in silico modeling studies (QSPR, machine learning, high-throughput screening). A series of databases related to drug design and discovery (Super Natural II [39], DrugBank [40]), chemicals’ toxicity and ecotoxicity (ACToR [41], ITER [42], RiskIE [42]), and agrochemicals (NPIRS [43], PAN [44]) exists for modeling and virtual screening purposes. Similarly, solar cell databases covering single or multiple types are the best source to start the modeling process. But, unfortunately, most of the existing databases for solar cells cover the solar cell panel information, cell types, dimensions, and efficiency

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without offering too much detailed information for modeling personnel. Recently, a handful of databases have been available for solar cell research, which is a matter of great concern. The public databases are discussed below: 6.1 The Dye-Sensitized Solar Cell Database (DSSCDB) is one of the finest additions in solar energy research by Venkatraman et al. [45], which consists of over 4000 experimental observations spanning multiple dye classes for DSSCs and can be accessed at THQ7 > THQ8 > THQ2 > THQ1 > THQ3 > THQ5 while the

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length of IA -IB is following: THQ5 > THQ3 > THQ1 > THQ2 > THQ8 > THQ7 > THQ9. Moreover, the sequence of the S1 –I2 bond length (except THQ1 and THQ2) is THQ5 > THQ7 > THQ8 > THQ9 > THQ3, and the trend for IC –ID is THQ3 > THQ9 > THQ7 > THQ8 > THQ5. In both cases, the iodine dimer’s separation distances increase with the increase of dye and iodine bond lengths [33]. The additives like N-methyl-benzimidazole (NMBI), 2-methylquinoline (MQ), and 4-t-butylpyridine (TBP) are commonly used to lessen the iodine concentration in the proximity of TiO2 . The bond lengths of the optimized additive–I2 adducts are 2.56 Å, 2.64 Å, and 2.55 Å, respectively, which are smaller than that of the dye–I2 complexes, indicates that the photophysical characteristics of the designed sensitizers are sufficient to reduce the iodine concentration near the TiO2 surface [8].

4.3 Interfacial Properties Interfacial phenomena like electronic properties and the interaction of specific dye with the surface play a key role in photovoltaics. Cluster and periodic DFT methodologies have been explored by many researchers to describe the interface and in most of the cases, the choice of model is case-specific [19, 33]. Both models have advantages and disadvantages over one another. To implement continuum solvent models with hybrid exchange–correlation functional, cluster models are suitable. However, sometimes cluster models fail to globally describe the surface electronic structures. In contrast, a periodic approach to be preferred for the detailed description of the surface properties without finite-size effects [52]. A shortcoming of the periodic approach is long-range order correction is expected for the surfaces which might be eliminated by increasing supercell sizes [55]. To investigate the interfacial properties like band-level alignment of the semiconductor and adsorbed dyes with respect to electron injection or the electrolytes redox potential, cluster, and periodic methodologies have been reported in the literature [8, 21, 54, 56]. DFT approaches considered different cluster models to obtain a judicious explanation of the local properties of TiO2 and possible interactions with various individual organic dyes [8]. Very small to large TiO2 clusters such as (TiO2 )16 , (TiO2 )38 [30], and (TiO2 )6 [54] used to investigate a wide variety of organic and inorganic dyes. Multiscale simulation approaches to nonadiabatic molecular dynamics simulation also performed to gain insight into the photophysical characteristics of isolated T-shaped organic and indoline dyes, respectively [56, 57]. Newns-Anderson model could be used to estimate the interfacial electron injection rate of dye-sensitizer to the semiconductor in a much simpler fashion, compared to the classical Marcus approach [58, 59]. This approach considers only the changes in the electronic structure after the photoinduced surface electron transfer of the adsorbed dye-sensitizers, contrary to the Marcus detailed configuration interactions. The initial photoexcitation involves the HOMO to LUMO transition of the dye-sensitizers, and the anchored LUMO levels are expected to show significant overlapping with the semiconductors’ conduction band. So, it is important to perform a detailed analysis

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of the dye/TiO2 electronic structure, and the salient features can be defined in terms of the energy shift relative to the isolated dye and the lifetime broadening ( ). The term,

, is the half-width at the half-maximum of the dye’s PDOS coupled to the continuum of the semiconductor (TiO 2 ) CB states. The width of the LUMO  broadening can ads ads | with E = pi εi where pi = be defined as [57]  = pi |εi − E LU MO LU M O  A∈ads A 2 n A 2 (ci j ) / j (ci j ) , where εi is the energy of the orbital corresponding to pi j ads and E LU M O is the energy of the TiO2 bound dye’s LUMO. Then the electron injection lifetime, τin j , can be computed as follows: τin j = τin j (fs) =

 2π

658 (meV)

(16)

Persson et al. [59] computed the electron injection lifetimes of perylene derivatives dyes with the above formalism. The calculated electron transfer times are within 5 and 10 fs for formic acid and the conjugated acrylic acid bridges, whereas the saturated propionic acid bridge is about 35 fs. The calculated electron injection times are of the equivalent order of magnitude as the corresponding experimental values qualitatively follow the experimental trend concerning different substitutions.

4.4 Planar Electrostatic Average Protentional Roy et al. [33] implemented periodic DFT approaches to explore the dye/TiO2 interface in the Vienna ab initio Simulation Package (VASP) using generalized gradient approximation (GGA). Author used PBE and optB86b-vdW functionals to compute electrostatic potential difference (EPD) and charge density difference (CDD). The van der Waals (vdW) interactions are more important in the longer alkyl chain, considering this interaction vdW density functional was employed. It is well known that the default DFT always underestimates the bandgap of the semiconductor. To improve the description of the electronic structure of the onsite Coulomb interaction of 3d-states of Ti, an effective potential equal to 3.5 eV is applied under Hubbard formalism, which is called the DFT + U method. Under this framework, charge redistribution between the organic dye and TiO2 surface before and after the dye’s adsorption was investigated (Fig. 7a). The relative atomic coordinates of dyes and surface before and after the adsorption kept the same. By analyzing 3D CDD, 1D planar average CDD and EPD author confirmed that the charge is originated from the dye molecule to the interface. Besides, when the charge transfer rate avails the equilibrium state, a built-in electric field is generated at the interface of dye/TiO2 , which enhances the electron injection from dye to CB of TiO2 .

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Fig. 7 Different interfacial properties of the studied THQ1 dye. a 1D planar averaged charge density of dye/TiO2 interface where red (after absorption), dashed (free dye), and dotted (surface), b 1D planar average charge density difference as a function of position in the Z-direction, in Å. c 3D charge density difference with an isovalue of 0.006e/Å3 . Blue (Red) indicates charge accumulation (depletion) in plane. The vertical cyan line represents the interface line of dye/TiO2 system [33] [The figure is printed with permission from Scientific Reports]

4.5 Photostability in the Excited State of the Dyes The longevity of DSSCs also depends on the photostability of the oxidized dyes. DFT and TDDFT approaches can be implemented to build a swift and robust technique to screen the most photostable dyes based on their aligned ESOP and GSOP. Roy et al. estimated the photostability and excited-state lifetime (τe ) of D−D−π−A-based NNdPA dyes using B3LYP/6-311G(d,p) level of theory. Figure 8 depicts the GSOP, ESOP, and the FMOs of dye@cluster complexes. Theτe , which aids the efficient

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Fig. 8 Alignment of the energy of NNdPA dyes@cluster complexes along with the frontier molecular orbitals (HOMO, LUMO) and CB edge of TiO2 (dotted violet line) [13]

charge transfer, is vital for evaluating the dye’s long-term stability. Stable cationic forms with extended excited-state lifetime help to qualitatively evaluate the charge transfer phenomenon from dye to CB edge of TiO2 . The τe of the NNdPA dyes estimated by the relation τe = 1.499/ f E 2 , where E is the excitation energy (cm −1 ) of the lowest electronic state and f is the oscillator strength. The trend of the τe values is NNdPA06 < NNdPA01 < NNdPA08 < NNdPA07 < NNdPA10 < NNdPA03 < NNdPA04. Among seven dyes, NNdPA04 with the largest extended lifetime ensures efficient electron injection into the CB of TiO2 , and stability after electron injection. The judicious choice of effective conjugation length and a co-acceptor (BTD unit) improved the excited-state lifetime of NNdPA dyes. A deeper understanding of structural attributes in the designed NNdPA dyes leads to achieving improved excited-state properties. By looking into the structure and results of NNdPA04 and NNdPA06 dyes, one can conclude that three different factors are responsible for the extended excited-state lifetime (i) planar fused-π-conjugation, (ii) co-acceptor like BTD, and (iii) the number of heteroatoms present in the dyes [13].

4.6 TDDFT Nonadiabatic Molecular Dynamics (NAMD) Simulation Chiu et al. [57] implemented a TDDFT atomistic nonadiabatic molecular dynamics (NAMD) simulation in the femtosecond scale to understand the fast photoinduced electron transfer process from the donor to acceptor of D–A–π–A-based organic dyes. The CT mechanism that stems from the thermal energy after photoexcitation

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is addressed by the NAMD simulation. The thermal fluctuation of the atoms at the photoexcited state affects the molecular structures (in both ground and excited state), and energies of donor/acceptor along with the CT behavior. Also, the bond strength of the photoexcited molecules is weaker than that of the ground state. TDDFT NAMD simulation explores the fluctuation of excited electron density, between internal and terminal acceptors, due to the thermal energy gradient allows the electron density not to flow significantly toward the terminal acceptor. The photoexcited electron density delocalized over the BTD and CAA fragments of the TPA-BTD-Th-CAA. This study revealed that the thermal energy’s vibrational modes are not populated enough to push a significant amount of photoexcited electron density on the internal acceptor to the terminal acceptor.

5 Conclusions In this chapter, we have outlined different approaches to estimate/predict the photophysical properties of dye-sensitizers for DSSCs by employing the DFT/TDDFT framework. We emphasized the two critical factors responsible for the dye performance: short-circuit current density (JSC ) and open-circuit voltage (VOC ). Both properties can be tuned by molecular engineering for the isolated dye-sensitizers. To predictJSC , one might consider the absorption spectra of isolated dyes, intermolecular charge transfer (ICT), spatial CT index, reorganization energy, and the band-level alignment of the dyes and semiconductors. We have also outlined the modeling of VOC by considering the E C B of TiO2 after dye adsorption and non-covalent halogen bond interactions. The details of DFT modeling of the interfacial phenomena of dye/TiO2, including charge transfer, planar average electrostatic potential, and the photostability of the dyes in the excited state, have also been described. However, one needs to remember that DSSCs consist of many individual components, which are critical to the operation of the device. Particular failure of any single component may result in lower photoconversion efficiency. We anticipate that further developments in DFT formalism will be able to take care of multiscale, complete description of all the various mechanism occurred in a DSSC, including regeneration of sensitizers by the electrolyte and reducing the I3− ions by the metal cathode. The availability of such details will facilitate the development of efficient DSSCS. Acknowledgements The authors appreciate the financial support of this work from the National Science Foundation under Grant Number NSF OIA-1757220 and the Department of Energy under Grant Number DE-SC0018322. Conflicts of Interest The authors declare no conflict of interest.

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Chemometric Modeling of Absorption Maxima of Carbazole Dyes Used in Dye-Sensitized Solar Cells Jillella Gopala Krishna, Probir Kumar Ojha, and Kunal Roy

Abstract The present chapter reports a partial least squares (PLS)-regression-based chemometric model for the carbazole class of dyes used in dye-sensitized solar cells (DSSCs) to predict the absorption maxima (λmax ) values. Quantitative prediction of the λmax values can be an important criterion for molecular design of new dye molecules. We have used only 2D descriptors for the model development purpose as the quantum chemical and electrochemical analyses are time consuming. The developed model was validated extensively using internationally acceptable statistical and validation parameters. A seven-descriptor PLS model with one latent variable (LV) was developed. The statistical results suggested that the model was statistically significant. The majority of the descriptors involved in the model are easily interpretable 2D atom pair descriptors. The model suggests that presence of nitrogen and sulfur atoms at the topological distance of 8, presence of nitrogen and oxygen atoms at the topological distance of 4, higher frequency of oxygen and sulfur atoms at the topological distance of 5, higher frequency of two nitrogen atoms at the topological distance of 5, presence of two oxygen atoms at the topological distance of 4, presence of carbon atoms connected with three aromatic bonds, and presence of two sulfur atoms at the topological distance of 4 in the dye molecules shifted the λmax value toward the longer wavelength. From the information obtained from the model, it has also been suggested that highly conjugated π-systems shift the λmax values toward the longer wavelength. Finally, it can be concluded that the identified features from the PLS model for the carbazole derivatives may be employed for the design and development of new carbazole dyes and to predict λmax values before they are synthesized.

J. Gopala Krishna Department of Pharmacoinformatics, National Institute of Pharmaceutical Educational and Research (NIPER), Chunilal Bhawan, 168, Manikata Main Road, Kolkata 700054, India P. K. Ojha · K. Roy (B) Drug Theoretics and Cheminformatics Laboratory, Department of Pharmaceutical Technology, Jadavpur University, 188 Raja S C Mullick Road, Kolkata 700032, India e-mail: [email protected] URL: http://sites.google.com/site/kunalroyindia/ © Springer Nature Switzerland AG 2021 J. K. Roy et al. (eds.), Development of Solar Cells, Challenges and Advances in Computational Chemistry and Physics 32, https://doi.org/10.1007/978-3-030-69445-6_9

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1 Introduction Energy is a vital force in human life. Until now, non-renewable energy sources like fossil fuels, crude oil, and natural gas have been used as major energy resources, which are also the reason for environmental problems. This problem can be solved by using one of the potential sources of renewable energies, i.e., solar energy, which contributes to sustainability, cleanliness, and low risk. If we were able to use solar energy (renewable energy source) to the full extent for day-to-day life activities, it would have a great impact on humans. In the eighteenth century, a French scientist named Edmond Becquerel first discovered the photovoltaic effect. It becomes the first step for the evolution of solar energy harvesting applications [1]. In the firstgeneration solar cells, silicon was used for attaining the photovoltaic effect. In the year of 1887, German scientist Hertz first examined the photoelectric effect and found that photons present in the light can eject free electrons from a solid surface (usually conductor) to create power [2]. However, the early results from the study showed that the same process produced more power when the conductor is experienced with the UV light instead of extra intense visible light. The evolution of the solar cells is majorly categorized into three different types based on the properties of materials and time period of generation [1]. For example, crystal and amorphous (silicon based) materials are a part in the first-generation solar cells, whereas the secondgeneration solar cells are made up of semiconductor materials (III–IV group chalcogenides/phosphide materials). Emerging materials such as dye-sensitized solar cells (DSSCs), quantum dots, and perovskites are the third-generation solar cells. During 1953 to 1956, the physicists worked in the Bell laboratory to initiate fabrication of the solar cells using silicon solar cells with the efficiency of 6% which was quite efficient compared to the earlier used selenium. This incident motivated the use of solar cells to power up the electrical equipment and led to this kind of efforts to get the new devices with better performance for commercialization. After 10 years, this continuous effort produced the second-generation thin film solar cells. These are emerging thin film solar cells having capability to convert 30% solar radiation to electrical energy. In this generation, copper indium gallium selenide (CIGS), cadmium telluride (CdTe), and gallium arsenide (GaAs) were used as the semiconductor materials. Till 1990, second-generation solar cells made from above materials were commercially available [3]. Later, the third-generation solar cells have emerged; this generation includes DSSCs, organic/polymer solar cells, quantum dot solar cells, perovskite solar cells, etc. This generation has PCE values ranging from respectable to very high power conversion efficiencies values [4], and they have their own advantages such as low processing costs and less environmental impact that induce the intensive research and development in this area. All the generations of solar cells with suitable examples are depicted in Fig. 1. The dye-sensitized solar cell (DSSC) is a photovoltaic equipment which employs a dye to absorb the solar energy to generate charge/power carriers to be collected as harnessed solar electricity. The structure of DSSCs constitutes a photo-sensitive dye coated with TiO2 , deposited on a transparent electrode, redox couple (I− /I3 − ) with

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Fig. 1 Evolution of the solar cells

an electrolyte solution, and a counter electrode which is a platinized conductive glass substrate. To upgrade the efficiency of DSSC, the HOMO and LUMO of dyes should locate under iodide redox couple (I− /I3 − ) and position on the top of the conduction band (CB) of the TiO2 semiconductor for improving the electron regeneration and efficient electron injection. In addition, the dye should be sensitive to all visible colors (UV/Visible (UV/Vis), and near-IR range) of the solar spectrum to increase broadband light harvesting. Most of the incident light energy (around 50%) falls in the infrared region, the remaining about 30% of light energy falls in the visible region. The UV and visible range cover photons which have sufficient energy to pump electrons in semiconducting material, and this may be efficiently used for charge generation. The ideal dye sensitizer must possess a wide absorption range in visible light, and it might contain anchoring groups like carboxylic or phosphonic acids. The DSSC working procedure requires the solar energy to be absorbed by the sensitizers (dyes) that result in the ground state dye molecules going to the excited state. These excited electrons are released into the conduction band of TiO2 [5, 6] after the process in which the dye gets oxidized. The oxidized dye is then neutralized to the ground state by I3 − /I− redox system. The basic structure of a DSSC is given in Fig. 2. In recent years, dye-sensitized solar cells (DSSCs) are gaining more popularity because of their promising performance and cost-effectiveness. So, molecular design and synthesis of organic functional dyes with high yield ratio have become a focus of

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Fig. 2 Basic structure of dye-sensitized solar cell

current research in view of their potential applications as sensitizers in dye-sensitized solar cells (DSSCs). So far, different types of organic dyes have been used as a sensitizer in DSSCs, among which the most successful dyes to date are based on ruthenium (Ru) complex systems (N3 and N719 dyes) [7, 8], for which power conversion efficiencies (PCE) of up to 10–11% under standard global air mass (AM) 1.5 solar conditions [9, 10]. Unfortunately, Ruthenium is of immoderate and minimal availability. Therefore, researchers have developed “metal free or organic dyes” as alternatives for Ru-complexes to surpass the disadvantages and adopt the advantages like high molar coefficient, facile modification, low-cost materials, and high photoconversion efficiency.

1.1 Mechanism of DSSCs The following stages reveal how DSSCs convert the light (photons) into power. Stage 1: In the initial stage, all the dye molecules (photosensitizer) lie in the ground state. When the incident photon (light) falls on the photosensitizer present on the TiO2 surface (non-conductive), the dye molecules get excited from their ground state to a higher energy state (S* ) D ye + P hot on → D ye∗

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Stage 2: After the excitation, the dye molecules transfer the electrons to conduction band of the semiconductor, then the dye gets oxidized. Here, the electrons move freely because the semiconductor (TiO2 ) energy level becomes conductive, electrons get transferred to the counter electrode. + D ye∗ + T i O 2 → e− (T i O 2 ) + D ye − e− (T i O 2 ) + C ount er el ect r ode(C.E) → T i O 2 + e(C.E) + El ect r i cal ener g y

Then the transported electrons from TiO2 are collected in the current collector via diffusion process. Stage 3: The oxidized dye molecules regain the electron from the iodide electrolyte solution. D ye+ + I − → D ye + I − 3 Stage 4: Reciprocally, iodide electrolyte is regenerated by reduction of tri-iodide on the counter electrode. − I− 3 + E−(C.E) → I + C.E

The efficiency of dye-sensitized solar cell mainly depends on four energy levels of the components: Excited (LUMO) and the ground states (HOMO) of the dye molecules, the conduction band edge of the TiO2 electrode and the redox potential of the mediator (I− /I3 − ) in the electrolyte [1]. The detailed mechanism is depicted in Fig. 3.

1.2 Ideal Characteristics of the Dye Used in DSSCs The ideal dye sensitizer should follow certain considerations necessarily. The dye must securely apply on the semiconductor surface and it should penetrate electrons into the conduction band with a quantum yield of unity. They must possess high redox potential for rapid regeneration via donation of electrons from the electrolyte, and it should last not less than 108 turnovers under illumination which is equivalent to 20 years exposure under sunlight. Calculation of all necessary parameters and then synthesizing a dye is much difficult to practice. Thus, here, “a trial and error method” may help to find appropriate dye sensitizers [7, 8]. Quantitative prediction of the absorption maxima (λmax ) using the molecular structure of a dye can be a significant criterion for molecular design of new dye molecules. Thermodynamic studies such as density functional theory (DFT) and ab initio calculations have been performed previously for the prediction of the absorption maxima (λmax ). Although such calculation methods are tedious, time consuming, and the results are not easy

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Fig. 3 Detailed mechanism of dye-sensitized solar cells (DSSCs)

to analyze [11]. Furthermore, it was shown that the DFT calculations for some of the dyes give poor results. So, there is a need to predict a large number of dyes in a fast and accurate manner. In this perspective, quantitative structure–property relationship (QSPR) using easily computable descriptors to furnish promising results for the prediction of λmax values of the dyes based on descriptors derived solely from the molecular structure to fit experimental data. QSPR has many advantages as compared with the other techniques such as utilization of limited resources, less expense, and time efficient outcome [12]. Because of these motivating qualities, one can recommend QSAR/QSPR in early stages of property detection. Till now, many researchers developed QSPR models for DSSCs using PCE properties of several classes of dyes [11, 13–21]. But, using λmax values of dyes, there are very few reported QSPR models. Some of them are mentioned here. Xu et al. developed a QSPR model correlating the experimental absorption maxima (λmax ) values of 70 organic dyes using 3D molecular descriptors calculated from Dragon [11] software. Venkatraman and colleagues [12] used a supervised machine learning approach for developing a non-linear model for absorption data of 1861 metal-free dyes. Quashie

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[13] used DFT to study the electronic structure and molecular orbital data of the carbazole dyes. Xu et al. [14] performed a quantitative structure–property relationship study between descriptors representing the molecular structures and the λmax of organic dyes; those descriptors were then used for development of the artificial neural networks (ANN). The present study reports a QSPR model correlating the absorption maxima (λmax ) values of carbazole dyes. Only easily computable 2D descriptors have been employed in the modeling, as they give definite physicochemical meaning and easy interpretation of the derived models. Model validation was carried out using internationally acceptable validation metrics. The applicability domain study was performed to check whether any of the test set molecules are situated outside the chemical region space of the training set molecules. To the best of our knowledge, this is the first QSPR report of carbazole class of dyes using λmax values.

2 Materials and Methods 2.1 Dataset Preparation The absorption maxima values used for modeling of 85 carbazole dyes were collected from the Dye-Sensitized Solar Cell Database (DSSCDB) (https://www.dyedb.com/) [13, 22]. This is a large database consisting of around 4,000 entries for various chemical classes of dyes used for DSSCs. After initial analysis, the mixtures of dyes were discarded from the database. After that, the remaining classes of dyes were screened based upon the solar simulator (AM 1.5G 100 mW/cm2 ) and TiO2 electrode. Next, we have separated the database based on chemical classes of dyes. In this study, we have used only carbazole derivatives having defined absorption maxima (λmax ) values for modeling. We have removed one compound as an outlier due to high residual value. So, we have used 84 compounds for the modeling purpose. The details of the dataset are provided in Table 1. In case of any biological QSPR, the response variable should be in the logarithmic scale; but in this case, endpoint (λmax ) refers to the energy terms; so, the modeling procedure was carried without any logarithmic conversion of the response.

2.2 Structure Representation The chemical structures of carbazole dyes with proper aromatization with explicit hydrogens were carefully drawn manually using MarvinSketch tool [23] and saved in MDL.mol format, a recommended format for descriptor calculation.

SMILES of the carbazole dyes

N#C/C(=C\c1ccc(s1)c1ccc(s1)c1ccc(cc1)n1c2ccc (cc2c2c1ccc(c2)C(C)(C)C)C(C)(C)C)/C(=O)O

N#C/C(=C/c1ccc(s1)c1ccc(cc1)n1c2ccc (cc2c2c1ccc(c2)C(C)(C)C)C(C)(C)C)/C(=O)O

N#CC(=Cc1ccc(s1)c1ccc2c(c1) c1ccccc1n2c1ccc2c(c1)C(C)(C)c1c2cccc1)C(=O)O

N#CC(=Cc1ccc(s1)c1ccc(s1)c1ccc2c(c1) c1ccccc1n2c1ccc2c(c1)C(C)(C)c1c2cccc1)C(=O)O

N#CC(=Cc1ccc(s1)c1ccc2c(c1)c1ccccc1n2c1ccc(cc1) C=C(c1ccccc1)c1ccccc1)C(=O)O

OC(=O)CN1C(=S)SC(=Cc2ccc(s2)c2ccc3c(c2) c2ccccc2n3c2ccc3c(c2)C(C)(C)c2c3cccc2)C1=O

OC(=O)CN1C(=S)SC(=Cc2ccc(s2)c2ccc(s2) c2ccc3c(c2)c2ccccc2n3c2ccc3c(c2)C(C)(C)c2c3cccc2)C1=O

N#CC(=Cc1ccc(s1)c1ccc(c2c1nsn2) c1ccc(cc1)n1c2ccccc2c2c1cccc2)C(=O)O

N#CC(=Cc1ccc(s1)c1ccc(c2c1nsn2) c1ccc2c(c1)c1ccccc1n2c1ccccc1)C(=O)O

CCCCC(Cn1c2ccc(cc2c2c1cccc2) c1ccc(c2c1nsn2)c1ccc(s1)C=C(C(=O)O)C#N)CC

CCCCC(COc1ccc(cc1)n1c2ccc(cc2c2c1cccc2) c1ccc(c2c1nsn2)c1ccc(s1)C=C(C(=O)O)C#N)CC

N#CC(=Cc1ccc(s1)c1ccc(c2c1nsn2) c1ccc2c(c1)n(c1ccccc1)c1c2cccc1)C(=O)O

CCCCC(COc1ccc(cc1)n1c2ccccc2c2c1cc(cc2) c1ccc(c2c1nsn2)c1ccc(s1)C=C(C(=O)O)C#N)CC

N#CC(=Cc1ccc(cc1) n1c2ccccc2c2c1cccc2)C(=O)O

N#CC(=Cc1ccc(cc1)C#Cc1ccc(cc1) n1c2ccccc2c2c1cccc2)C(=O)O

CCCCn1c2cc(ccc2c2c1cc(cc2)N (c1ccccc1)c1ccccc1)c1ccc(s1)c1ccc(s1)/C=C(/C(=O)O)\C#N

N#CC(=Cc1ccc(s1)C#Cc1ccc(cc1) n1c2ccccc2c2c1cccc2)C(=O)O

CCCCn1c2cc(ccc2c2c1cc(cc2)N (c1ccccc1)c1ccccc1)c1ccc(s1)/C=C(/C(=O)O)\C#N

N#CC(=Cc1ccc2c(c1) c1ccccc1n2CC)C(=O)O

Sl. No

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2a

3

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6

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10a

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Table 1 Carbazole dye structures with observed and predicted absorption maxima (λmax ) values

504

572

555

579

548

527

557

560

595

628

589

557

600

619

538

595

528

585

589

Observed

Absorption maxima (λmax )

(continued)

505.69

531.39

585.24

586.24

507.63

506.51

539.43

539.93

593.33

596.44

593.82

594.69

610.87

556.17

529.82

585.31

530.40

531.88

586.35

Predicted

214 J. Gopala Krishna et al.

SMILES of the carbazole dyes

CCCCCCn1c2ccc(cc2c2c1ccc(c2)C=C1SC(=S)N (C1=O)CC(=O)O)C=C1SC(=S)N(C1=O)CC(=O)O

N#CC(=Cc1ccc(cc1)c1ccc2c(c1) c1ccccc1n2c1ccc2c(c1)C(C)(C)c1c2cccc1)C(=O)O

CCCCCCN1c2ccc(cc2Sc2c1ccc(c2) C=C(C(=O)O)C#N)c1ccc(cc1)C=C(c1ccc(cc1) n1c2ccccc2c2c1cccc2)c1ccc(cc1)n1c2ccccc2c2c1cccc2

CCCCCCn1c2ccc(cc2c2c1ccc(c2) C=C(C(=O)O)C#N)c1ccc(cc1)C=C(c1ccc(cc1) n1c2ccccc2c2c1cccc2)c1ccc(cc1)n1c2ccccc2c2c1cccc2

CCCCCCCCCCCCn1c2ccc(cc2c2c1ccc(c2) c1ccc(c2c1nsn2)c1ccc2c(c1) n(CCCCCCCCCCCC)c1c2cc(cc1)/C=C(/C(=O)O)\C#N)/C=C(/C(=O)O)\C#N

N#CC(=Cc1ccc(s1)c1ccc(c2c1nsn2) c1ccc2c(c1)c1ccccc1n2c1ccc2c(c1)C(C)(C) c1c2cccc1)C(=O)O

N#CC(=Cc1ccc(o1)c1ccc(c2c1nsn2) c1ccc2c(c1)c1ccccc1n2c1ccc2c(c1)C(C)(C)c1c2cccc1)C(=O)O

N#CC(=Cc1ccc(cc1)c1ccc(c2c1nsn2) c1ccc2c(c1)c1ccccc1n2c1ccc2c(c1)C(C)(C)c1c2cccc1)C(=O)O

N#CC(=Cc1ccc(o1)c1ccc2c(c1) c1ccccc1n2c1ccc2c(c1)C(C)(C)c1c2cccc1)C(=O)O

CCCCCCn1c2ccc(cc2c2c1ccc(c2)/C=C(/c1ccc(cc1)c1ccc(cc1)/ C=C\1/SC(=S)N(C1=O)CC(=O)O) \C#N)C=C(c1ccc(cc1)c1ccc(cc1)/C=C/1\SC(=S)N(C1=O)CC(=O)O)C#N

CCCCCCn1c2ccc(cc2c2c1ccc(c2)/ C=C(/c1ccc(cc1)c1ccc(cc1)/C=C(\C(=O)O)/ C#N)\C#N)C=C(c1ccc(cc1)c1ccc(cc1)/C=C(\C(=O)O)/C#N)C#N

Sl. No

20

21a

22a

23a

24

25a

26

27

28a

29a

30

Table 1 (continued)

487

506

480

565

596

601

560

551

537

495

521

Observed

Absorption maxima (λmax )

(continued)

504.75

548.50

505.54

570.30

580.55

593.80

592.17

561.13

535.99

506.88

546.80

Predicted

Chemometric Modeling of Absorption Maxima of Carbazole Dyes … 215

SMILES of the carbazole dyes

CCCCCCCCn1c2ccc(cc2c2c1ccc(c2) c1ccc(s1)c1ccc(s1)/C=C(/C(=O)O) \C#N)c1ccc(s1)c1ccc(s1)/C=C(/C(=O)O)\C#N

CCCCCCCCn1c2ccc(cc2c2c1ccc(c2) c1ccc(s1)/C=C(/C(=O)O)\C#N)c1ccc(s1)/C=C(/C(=O)O)\C#N

CCCCCCCCC(n1c2ccc(cc2c2c1ccc(c2) c1sc(cc1CCCCCC)c1ccc(s1)/C=C(\C(=O)O)/ C#N)c1sc(cc1CCCCCC)c1ccc(s1)/C=C(\C(=O)O)/C#N)CCCCCCCC

CCCCCCCCC(n1c2ccc(cc2c2c1ccc(c2) c1ccc(s1)c1ccc(s1)c1ccc(s1)/C=C(/C(=O)O) \C#N)c1ccc(s1)c1ccc(s1)c1ccc(s1)/C=C(\C(=O)O)/C#N)CCCCCCCC

CCCCCCCCC(n1c2ccc(cc2c2c1ccc(c2) c1ccc(s1)c1ccc(s1)/C=C(\C(=O)O)/C#N)c1ccc(s1)c1ccc(s1)/ C=C(\C(=O)O)/C#N)CCCCCCCC

CCCCCCn1c2ccc(cc2c2c1ccc(c2)c1sc(cc1CCCCCC) c1ccc(s1)/C=C(\C(=O)O)/C#N)c1sc(cc1CCCCCC)c1ccc(s1)/ C=C(\C(=O)O)/C#N

CCCCCCn1c2ccc(cc2c2c1ccc(c2)c1ccc(s1)c1ccc(s1) c1ccc(s1)/C=C(/C(=O)O)\C#N)c1ccc(s1) c1ccc(s1)c1ccc(s1)/C=C(\C(=O)O)/C#N

CCCCCCn1c2ccc(cc2c2c1ccc(c2)c1ccc(s1)c1ccc(s1)/ C=C(/C(=O)O)\C#N)c1ccc(s1)c1ccc(s1)/ C=C(\C(=O)O)/C#N

CCCCCCn1c2ccc(cc2c2c1cccc2)c1ccc(cc1)/ C=C/1\SC(=S)N(C1=O)CC(=O)O

CCCCCCn1c2ccc(cc2c2c1cccc2)c1ccc(cc1)/ C=C(\C(=O)O)/C#N

CCCCCCn1c2ccc(cc2c2c1cccc2)/ C=C(\c1ccc(s1)C=C1C(=O)NC(=O)NC1=O)/C#N

CCCCCCn1c2ccc(cc2c2c1cccc2)/ C=C(\c1ccc(s1)/C=C\1/SC(=S)N(C1=O)CC(=O)O)/C#N

CCCCCCn1c2ccc(cc2c2c1cccc2)/ C=C(\c1ccc(s1)/C=C(/C(=O)O)\C#N)/C#N

Sl. No

31

32

33a

34

35

36a

37

38

39

40

41

42a

43

Table 1 (continued)

630

640

624

546

550

606

606

600

582

617

610

559

610

Observed

Absorption maxima (λmax )

(continued)

585.31

610.92

642.59

509.07

505.50

609.23

610.17

610.09

610.30

611.25

611.16

553.50

609.36

Predicted

216 J. Gopala Krishna et al.

CCCCn1c2cc(ccc2c2c1cc(cc2)N(c1ccc(cc1) c1ccc2c(c1)C(CC)(CC)c1c2cccc1)c1ccc(cc1) c1ccc2c(c1)C(CC)(CC)c1c2cccc1)c1ccc(s1)/C=C(/C(=O)O)\C#N

OC(=O)CCCCCCn1c2cc(ccc2c2c1cc(cc2) N(c1ccccc1)c1ccccc1)c1ccc(s1)c1cnccn1

CCCCn1c2cc(ccc2c2c1cc(cc2) N(c1ccccc1)c1ccccc1)c1ccc(s1)c1cnccn1

OC(=O)CCCCCCn1c2cc(ccc2c2c1cc(cc2) N(c1ccccc1)c1ccccc1)c1ccc(s1)c1ccncc1

OC(=O)CCCCCCn1c2cc(ccc2c2c1cc(cc2)c1ccncc1) N(c1ccccc1)c1ccccc1

CCCCn1c2cc(ccc2c2c1cc(cc2) N(c1ccccc1)c1ccccc1)c1ccc(s1)c1ccncc1

c1ccc(cc1)N(c1ccc2c(c1)[nH]c1c2ccc(c1) c1ccc(s1)c1ccncc1)c1ccccc1

CCCCn1c2cc(ccc2c2c1cc(cc2)c1ccncc1) N(c1ccccc1)c1ccccc1

c1ccc(cc1)N(c1ccc2c(c1)[nH]c1c2ccc(c1) c1ccncc1)c1ccccc1

CCCCn1c2cc(ccc2c2c1cc(cc2) N(c1ccccc1)c1ccccc1)c1ccc(cc1)C(=O)O

50

51

52

53

54

55

56a

57

58a

59

CCCCCCn1c2ccc(cc2c2c1cccc2) c1ccc(cc1)C=C1C(=O)NC(=S)NC1=O

47

CCCCCCn1c2ccc(cc2c2c1cccc2) c1ccc(cc1)C=C1C(=O)NC(=O)NC1=O

CCCCn1c2cc(ccc2c2c1cc(cc2)c1ccc(s1)/ C=C(/C(=O)O)\C#N)N(c1ccc(cc1)OCCCC)c1ccc(cc1)OCCCC

46

CCCCn1c2cc(ccc2c2c1cc(cc2)N(c1ccc(cc1) c1ccc2c(c1)C(CC)(CC)c1c2cccc1) c1ccc(cc1)c1ccc2c(c1)C(CC)(CC)c1c2cccc1)c1ccc(s1)c1ccc(s1)/C=C(/C(=O)O)\C#N

CCCCOc1ccc(cc1)N(c1ccc2c(c1)n(CCCC) c1c2ccc(c1)c1ccc(s1)c1ccc(s1)/ C=C(/C(=O)O)\C#N)c1ccc(cc1)OCCCC

45

49

CCCCCCC(Cc1cc(sc1c1sc2c(c1)c1nonc1c1c2sc(c1) c1sc(cc1CC(CCCCCC)CCCC)c1ccc2c(c1)c1ccccc1n2CC)/ C=C(/C(=O)O)\C#N)CCCC

44

48a

SMILES of the carbazole dyes

Sl. No

Table 1 (continued)

442

423

423

465

464

425

467

478

477

545

575

578

618

565

570

702

Observed

Absorption maxima (λmax )

(continued)

456.81

455.96

458.51

456.10

458.66

456.88

457.02

458.34

456.71

531.03

585.88

566.33

566.73

530.83

585.69

646.00

Predicted

Chemometric Modeling of Absorption Maxima of Carbazole Dyes … 217

SMILES of the carbazole dyes

OC(=O)c1ccc(cc1)c1ccc2c(c1)[nH]c1c2ccc(c1) N(c1ccccc1)c1ccccc1

CCCCCCn1c2ccc(cc2c2c1ccc(c2)N(c1ccc(cc1) c1ccc(s1)c1ccc(s1)/C=C(/C(=O)O) \C#N)c1ccc(cc1)OCCCCCC)N(c1ccc(cc1) c1ccc(s1)c1ccc(s1)/C=C(/C(=O)O)\C#N)c1ccc(cc1)OCCCCCC

N#C/C(=C\c1ccc2c(n1)ccc(c2)n1c2ccc (cc2c2c1ccc(c2)OC)OC)/C(=O)O

CCCCCCCCn1c2ccccc2c2c1ccc1c2c2c3cc(ccc3n(c2cc1) CCCCCCCC)/C=C(/C(=O)O)\C#N

N#CC(=Cc1ccc(cc1)C#Cc1ccc2c(c1)n (c1ccc(cc1)C(F)(F)F)c1c2ccc(c1) n1c2ccc(cc2c2c1ccc(c2)C(C)(C)C)C(C)(C)C)C(=O)O

N#CC(=Cc1ccc(cc1)C#Cc1ccc2c(c1) n(c1ccc(cc1)C(F)(F)F)c1c2ccc(c1) C#Cc1ccc(cc1)n1c2ccc(cc2c2c1ccc(c2)C(C)(C)C)C(C)(C)C)C(=O)O

N#CC(=Cc1ccc(cc1)C#Cc1ccc(s1)c1ccc(s1) C#Cc1ccc(cc1)n1c2ccc(cc2c2c1ccc(c2)C(C)(C)C)C(C)(C)C)C(=O)O

N#C/C(=C\c1ccc2c(c1)c1c(n2C) ccc2c1c1c3ccccc3n(c1cc2)C)/C(=O)O

CCCCCCn1c2ccc(cc2c2c1ccc(c2)/ C=C(/c1ccc(s1)C=C(C(=O)O)C(=O)O)\C#N)/ C=C(/c1ccc(s1)C=C(C(=O)O)C(=O)O)\C#N

CCCCn1c2ccc(cc2c2c1ccc(c2) c1ccc(s1)c1ccc(cc1)C(=O)O)c1ccc(s1)c1ccc(cc1)C(=O)O

CCCCn1c2ccc(cc2c2c1ccc(c2) c1ccc(s1)c1ccncc1)c1ccc(s1)c1ccncc1

CCCCn1c2ccc(cc2c2c1ccc(c2)c1ccc(s1)c1ccc(c(c1)O)O)c1ccc(s1)c1ccc(c(c1)O)O

CCCCn1c2ccc(cc2c2c1ccc(c2) c1ccc(s1)c1ccncc1)c1ccc(s1)c1ccc(cc1)C(=O)O

CCCCn1c2ccc(cc2c2c1ccc(c2) c1ccc(s1)c1ccncc1)c1ccc(s1)c1ccc(c(c1)O)O

N#C/C(=C/c1ccc(s1)c1scc(n1) c1ccc(cc1)n1c2ccccc2c2c1cccc2)/C(=O)O

Sl. No

60

61

62

63

64

65a

66

67

68

69

70a

71

72

73

74a

Table 1 (continued)

565

465

464

412

448

461

661

561

540

545

524

556

550

647

438

Observed

Absorption maxima (λmax )

(continued)

585.48

469.82

458.07

480.49

459.15

457.00

657.30

546.06

562.59

526.47

525.64

550.62

557.05

652.26

454.26

Predicted

218 J. Gopala Krishna et al.

CCCCn1c2ccccc2c2c1cc(cc2)c1ccc(cc1) c1csc(n1)c1ccc(s1)/C=C(\C(=O)O)/C#N

CCCCCCOc1ccc(cc1)c1ccc2c(c1) c1cc(ccc1n2c1ccc(cc1)c1ccc(s1)c1ccc(s1)C=C(C(=O)O)C#N)c1ccc(cc1)OCCCCCC

CCCCCCOc1ccc(cc1)c1ccc2c(c1) c1cc(ccc1n2c1ccc2c(c1)C(C)(C)c1c2sc(c1)c1ccc(s1)C=C(C(=O)O)C#N)c1ccc(cc1)OCCCCCC

CCCCCCOc1cc(OCCCCCC)ccc1c1ccc2c(c1) c1cc(ccc1n2c1ccc2c(c1)C(C)(C)c1c2sc(c1) c1ccc(s1)C=C(C(=O)O)C#N)c1ccc(cc1OCCCCCC)OCCCCCC

CCCCCCn1c2ccc(cc2c2c1ccc(c2)c1ccc(o1)/ C=C(\C(=O)O)/C#N)c1ccc(o1)C=C(C(=O)O)C#N

CCCCCCn1c2ccc(cc2c2c1ccc(c2)c1ccc(s1)/ C=C(\C(=O)O)/C#N)c1ccc(s1)C=C(C(=O)O)C#N

CCCCCCn1c2ccc(cc2c2c1ccc(c2)c1ccc(cc1)/ C=C(\C(=O)O)/C#N)c1ccc(cc1)C=C(C(=O)O)C#N

CCCCCCc1cc(sc1c1ccc(cc1)N(c1ccc2c(c1) c1ccccc1n2c1ccccc1)c1ccc2c(c1)c1ccccc1n2c1ccccc1)c1sc(cc1CCCCCC)/C=C(\C(=O)O)/C#N

CCCCCCc1cc(sc1c1ccc(cc1)N(c1ccc2c(c1) c1ccccc1n2c1ccccc1)c1ccc2c(c1)c1ccccc1n2c1ccccc1)/C=C(\C(=O)O)/C#N

76

77a

78

79

80

81

82

83a

84

set compounds

N#C/C(=C/c1ccc(s1)c1scc(n1) c1ccc(cc1)c1ccc2c(c1)n(c1ccccc1)c1c2cccc1)/C(=O)O

75

a Test

SMILES of the carbazole dyes

Sl. No

Table 1 (continued)

641

714

494

502

486

620

570

570

568

569

Observed

Absorption maxima (λmax )

601.36

656.12

506.31

553.36

503.63

641.24

584.78

584.48

587.47

585.50

Predicted

Chemometric Modeling of Absorption Maxima of Carbazole Dyes … 219

220

J. Gopala Krishna et al.

2.3 Descriptor Calculation and Dataset Division After drawing the chemical structures, we have calculated the descriptors using the Dragon software and PaDEL-descriptor software. To prevent the difficulty in interpretation of the final model, we have calculated only selected classes of 2Ddescriptors with definite physicochemical meaning such as ring descriptors, connectivity indices, atom type E-state indices, constitutional indices, functional group counts, 2D atom pairs, atom-centered fragment, and molecular property descriptors using DRAGON (Version 7) software [24, 25]. Only extended topochemical atom (ETA) class of descriptors were calculated using PaDEL-Descriptor (Version 2.20) software [26]. From the initial pool of descriptors, we have removed the redundant, constant, intercorrelated descriptors (>0.9). After removing intercorrelated descriptors, the initial pool of descriptors was further reduced to a manageable number of descriptors using multilayered stepwise regression method [27]. The reduced pool of descriptors was used for model development purposes. The main aim of the present work was to develop a robust and significant QSPR model using the absorption maxima (λmax ) values of carbazole dyes for a precise and reliable prediction of absorption maxima values. To develop statistically robust QSPR model for absorption maxima values, we have divided the dataset into training set (used explicitly for model generation) and a test set (for model validation) in approximately 75:25 ratio [21] using k-Medoids dataset-division (ver. 1.2) tool (available at https://dtclab. webs.com/software-tools). However, in the present work, we have developed statistically robust models for carbazole dyes. The final model was obtained by using 63 compounds in the training set (ntraining ) and 21 molecules in the test set (ntest ).

2.4 Model Development and Validation Prior to the development of the final model, we have used stepwise regression in a multilayered fashion for the selection of features. To run the stepwise regression [27, 28], we have used the stepping criteria (Fischer criteria) with definite threshold value of F = 4.0 for inclusion and F = 3.9 for exclusion [13, 28]. The process was repeated many times (after deleting modeled descriptors appearing in the previous runs) in order to extract the important descriptors. Finally, a set of 33 descriptors was extracted at the end of stepwise analysis and subjected to run best subset selection. The best model was subjected for PLS analysis in order to reduce noise from the developed model, as PLS regression computes latent variables (LVs) from the original variables and can also manage a lot of noisy descriptors. In case of PLS model development, the software internally performs input data scaling (standardization) followed by calculation of latent variables scores (the actual regressing variables), although the final regression coefficients are presented in terms of the original unscaled variables (similar to multiple linear regression or MLR equations). Unlike MLR models, the determination of standard errors (SE) of regression coefficients for PLS models is

Chemometric Modeling of Absorption Maxima of Carbazole Dyes …

221

not straightforward. However, the relative importance of different descriptors can be offered in terms of variable importance plot (VIP) [29]. The acceptability of the developed models was judged by using a number of internationally acceptable validation metrics, in terms of stability, robustness, fitness, and predictivity. The determination coefficient (R2 ), internal predictive metrics [30] like Q2 LOO (leave-one-out cross-validated R2 ), and external predictivity metrics like R2 pred or Q2 ext (Q2 F1 ) and Q2 F2 were calculated for simple judgment of the errors encountered during the prediction of a test set within the model domain [31]. In addition, rm 2 parameters were calculated for both internal and external sets. This metric is calculated based on the correlations between the observed and predicted values with (r2 ) and without (r0 2 ) intercept for the least squares regression [32]. Model prediction error was evaluated by the statistical validation parameters of the model for the external set which should be within the response and chemical domain of the training set. Randomization of the model was executed to justify the robustness of developed PLS model. In this study, Y-randomization was conducted using SIMCA-P software. Randomization is a validation technique used in QSPR/QSAR models, whereby the performance of the original model in data description (r2 ) is compared with the models built with randomly shuffled response, based on the original descriptor pool and the original model building procedure. The methodology of model development is schematically summarized in Fig. 4.

Fig. 4 Schematic representation of modeling of absorption maxima values against carbazole dyes

222

J. Gopala Krishna et al.

2.5 Applicability Domain Assessment The applicability domain is a speculative region in the chemical space surrounding the training set of the specific QSPR model, within which the predictions of the model are considered to be valid. In the development of the QSPR model, the AD of the molecules has a pivotal role to judge the variability in the predictions of a compound gleaned from how much similar it is to the compounds used to build the model. In this case, we have applied the DModX (distance to model in X-space) approach using SIMCA-P software [29] to check the AD of the developed model. In the DModX approach, the indicative values of X and Y residuals are used to confirm the model quality. The standard deviation (SD) of the X-residuals of the corresponding row of the residual matrix E is relative to the distance between the data point and the model plane in X-space, often called DModX. A compound with a DModX value higher than 2.5 times the overall SD of the X residual or threshold value is considered as an outlier in case of the training set and outside AD in case of the test set.

3 Results and Discussion Based on the λmax values of 84 dyes (carbazole chemical class), we have developed a robust and reliable PLS model using only 2D descriptors. Prior to the development of the final model, we have employed variable selection strategy [27, 33–36] using multilayered stepwise regression from a large pool of descriptors to reduce noise in the input. The statistical quality of the PLS model was determined by utilizing internationally accepted various internal and external validation metrics. The reported PLS model was developed by using 7 descriptors with one latent variable. Here, ntraining and ntest are the number of compounds present in the training and test sets. The R2 (0.865), Q2 (0.792), R2 pred (0.849), and Q2 F2 (0.846) values of the PLS model were higher than 0.6 (as depicted in model 1), which indicated the acceptability and predictive ability of models. Therefore, based on the statistical results obtained from the PLS model (see in Table 2), it can be confirmed that the model is acceptable in terms of fitness, stability, and classical predictivity measures. The descriptors appearing in the model recognize the structural and functional requirements, which are essential to regulate the λmax values of carbazole dyes. The proximity of the observed and predicted values for λmax in the dataset can be further established from the scatter plot as shown in Fig. 5. To check the applicability domain (AD) of the test set dyes, we have used DModX approach. Based on the results, it has been found that compounds 23 and 42 are present outside the applicability domain (Fig. 6). Additionally, we have also performed Y-randomization test to check whether the model was obtained by any chance or not. The results (R2 intercept = −0.00943 and Q2 intercept = −0.149) obtained from the randomized models confirmed that the developed model was not obtained by any chance correlation (Fig. 7). We have discussed briefly all the contributing descriptors appearing in the model in this section. The significance

Descriptors

B08[N–S], B04[N–O], F05[O–S], SaaaC, B04[O–O], B04[S–S], F05[N–N]

Model type

PLS

0.865

R2

0.847

Ra 2 0.792

Q2 1

LV

0.729

2 rm(L O O)

0.097

2 rm(L O O)

202.65

s 51898.5

PRESS 0.849

R2 pred

0.846

Q2 F2

0.711

2 rm(test)

0.133

2 rm(test)

Table 2 Statistical quality and validation parameters of the final PLS models developed using the absorption maxima (λmax ) values of carbazole dyes

0.906

CCC

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Fig. 5 Scatter plot of the observed and the predicted λmax values of the developed PLS model

Fig. 6 Applicability domain of the test set compounds

Fig. 7 Importance of the model variables based on VIP plot

Chemometric Modeling of Absorption Maxima of Carbazole Dyes …

225

Fig. 8 Randomization plot of the PLS model

level of the modeled descriptors toward the λmax values was computed based on the variable importance plot (VIP) (Fig. 8) [29]. The VIP defines the importance of each parameter obtained from the final PLS model that is responsible for regulating the λmax values. As per the VIP plot, the significance level of the modeled descriptors are in the following manner: B08[N–S], B04[N–O], F05[O–S], F05[N–N], B04[O–O], SaaaC, and B04[S–S]. Here, all these descriptors appearing in the model contribute positively toward the λmax values as indicated by their positive regression coefficients. Model 1 λmax = 428.731 + 53.948 × B08[N-S] + 53.301 × B04[N-O] + 11.875 × F05[O-S] + 21.999 × F05[N-N] + 57.462 × B04[O-O] + 5.765 × SaaaC + 41.122 × B04[S-S] 2 ntraining = 63, R2 = 0.865, R(adj) = 0.847, Q2 = 0.792, S = 202.65,

PRESS = 51898.5, F = 309.67(1, 62) −

2 2 rm(LOO) = 0.729, rm(Loo) = 0.097, LV = 1, −

2 = 0.849, Q2 = 0.846, r 2 ntest = 21, QF1 F2 m(test) = 0.711,

r 2m(test) = 0.133, CCC = 0.906

The most significant descriptor, B08[N–S], a 2D-atom pair descriptor, denotes the presence or absence of N and S atoms at the topological distance of 8. The positive contribution of this variable suggested that the presence of this fragment may enhance the absorption maxima values of carbazole dyes as evidenced by compounds 44, 61, and 68 (λmax values of these compounds are 702, 647, and 661, respectively) and vice versa in case of compounds 54, 57, and 71 (λmax values of these compounds are

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Fig. 9 Contribution of B08[N–S] and B04[N–O] descriptors toward the λmax values

425, 423, and 412, respectively). The presence of N and S atoms at the topological distance 8 increases the photo-excitation by enhancing the localized π–π* transition of the dye [13]. The contribution of this descriptor toward the λmax values is depicted in Fig. 9. The next significant descriptor, B04[N–O], another 2D atom pair descriptor, is defined as the presence or absence of N and O atoms at the topological distance of 4. This descriptor also contributes positively toward the λmax value as evident from the carbazole dyes 41 (B04[N–O] = 1; λmax = 624), 43 (B04[N–O] = 1; λmax = 630) and 44 (B04[N–O] = 1; λmax = 702). On the other hand, dyes like 59 (B04[N–O] = 0; λmax = 442), 69 (B04[N–O] = 0; λmax = 461), and 72 (B04[N–O] = 0; λmax = 464) have low λmax values. This parameter signifies the distance between the N and the O atoms which is referred to a strong cyano acceptor and a chelating anchoring mode of the carboxylation, which play a vital role to alter the absorption maxima values of dyes [13]. Thus, the presence of strong acceptor and chelating anchors [37, 38] in the dyes results in to higher λmax values. The contribution of this descriptor toward the λmax values is depicted in Fig. 9. The positive regression coefficient of the next important descriptor, F05[O–S] (frequency of O and S atoms at the topological distance 5), another 2D atom pair descriptor, suggested that higher frequency of these two atoms at the topological distance 5 in the carbazole dyes shifts the absorption maxima toward longer wavelength [39]. This observation was evidenced by dyes 6 (F05[O–S] = 5; λmax = 619), 44 (F05[O–S] = 4; λmax = 702), and 68 F05[O–S] = 8; λmax = 661). On the contrary, absence or less number of this fragments in the dyes may shift the absorption maxima toward shorter wavelength as evidenced by the dyes like 54 (F05[O–S] = 0; λmax =

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425), 57 (F05[O–S] = 0; λmax = 423), and 60 (F05[O–S] = 0; λmax = 438). The presence of O and S atoms in the dye system may delocalize the electron density which is necessary for the π-bond conjugation. Thus, the molar extinction coefficient of the dyes increases which leads to the bathochromic shift of the absorption spectrum [13]. The contribution of this descriptor toward the λmax values is depicted in Fig. 10. The fourth highest significant descriptor, F05[N–N], another 2D atom pair descriptor, is defined as the frequency of two N atoms at the topological distance 5. This descriptor also contributes positively toward the absorption maxima as indicated by its positive regression coefficient. Therefore, higher frequency of this atom at the topological distance 5 may shift the absorption maxima value to the longer wavelength as evidenced by dyes 128 (F05[N–N] = 2; λmax = 647) and 179 (F05[N–N] = 2; λmax = 641) and vice versa in case of dyes like 120 (F05[N–N] = 0; λmax = 425) and 123 (F05[N–N] = 0; λmax = 423). The contribution of this descriptor toward the λmax values is depicted in Fig. 10. Another 2D atom pair descriptor B04[O–O] denotes the presence or absence of two O atoms at the topological distance of 4, which contributes positively toward the λmax values. We have found that in case of dyes 41 (B04[O–O] = 1; λmax = 624), 47 (B04[O–O] = 1; λmax = 618), and 68 (B04[O–O] = 1; λmax = 661), the absorption maxima values are high due to the presence of two O atoms at the topological distance 4. In contrary, the reverse is observed in case of dyes 54 (B04[O–O] = 0; λmax = 425), 59 (B04[O–O] = 0; λmax = 442), and 60 (B04[O–O] = 0; λmax = 438). This parameter denotes the oxygen in the enamine of the carbazole moiety and the anchoring functional groups (such as carboxylate, alkoxysilanes, etc.) which may

Fig. 10 Contribution of F05[O–S] and F05[N–N] descriptors toward the λmax values

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Fig. 11 Contribution of B04[O–O] and SaaaC descriptors toward the λmax values

make stronger π–π interactions of the dye system to shift the λmax values to a longer wavelength [13, 40]. The contribution of this descriptor toward the λmax values is depicted in Fig. 11. The atom-centered fragment descriptor, SaaaC, represents the sum of carbons connected with three aromatic bonds. The positive regression coefficient of this descriptor suggests that the presence of this fragment shifts the absorption maxima to a longer wavelength as evidenced by the dyes 44 and 84 (λmax values of these compounds are 720 and 641, respectively, and their corresponding descriptor values are 11.192 and 9.294) and absence of this fragment shifts the absorption maxima to a shorter wavelength as evidenced by dyes 30, 60, and 80 (λmax values of these compounds are 487, 438, and 486, respectively, and their corresponding descriptor values are 4.288, 4.428, and 4.094). The presence of the aromatic groups in the structure increases conjugation, which implies enhanced absorption maxima (λmax ) of the carbazole dye molecules [41, 42]. The contribution of this descriptor toward the λmax values is depicted in Fig. 11. The least significant descriptor, B04[S–S], a 2D atom pair descriptor, is defined as the presence or absence of two S atoms at the topological distance 4. This descriptor also contributes positively. Therefore, the presence of two S atoms at the topological distance 4 in carbazole dye molecules may shift the absorption maxima to a longer wavelength (e.g., dyes 6 (λmax = 619) and 7 (λmax = 600)) and absence of this fragment may shift the absorption maxima to a shorter wavelength [43] (e.g., dyes 19 (λmax = 504) and 30 (λmax = 487)). The contribution of this descriptor toward the λmax values is depicted in Fig. 12.

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Fig. 12 Contribution of B04[S–S] descriptor toward the λmax values

4 Conclusion In this chapter, we have reported a statistically sound PLS regression-based chemometric model based on only 2D descriptors to predict the λmax values of a set of sensitizing carbazole dyes used in DSSCs. As the quantum and electrochemical analyses for a large number of dyes are time consuming, we have explored only the 2D structural features [25] in the present chapter. Most of the parameters appearing in the model are simple interpretable 2D atom pair descriptors. From the model descriptors, we have concluded that (Fig. 13): (i) the presence of N and S atoms at

Fig. 13 The insights were obtained from the developed PLS model

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the topological distance of 8 increases the photo-excitation by enhancing the localized π–π* transition of the dye; (ii) the presence of N and O atoms at the topological distance of 4 may lead to a strong cyano acceptor and a chelating anchoring mode of the carboxylation which play an important role to alter the absorption maxima values of dyes; (iii) the frequency of O and S atoms at the topological distance of 5 should be higher in the dye system for the π-bond conjugation thus shifting the λmax values to a longer wavelength; (iv) the frequency of two N atoms at the topological distance of 5 should be more for higher λmax values; (v) the presence of two O atoms at the topological distance of 4 in the dye system may strengthen the π–π interactions of the dye system thus shifting the λmax values to a longer wavelength; (vi) the presence of an aromatic system in the dye molecules is favorable for π-bond conjugation thus shifting the λmax values to a longer wavelength; (vii) the presence of two S atoms at the topological distance of 4 may also shift the λmax values to the longer wavelength. The absorption maxima have a great impact on the selection of DSSCs as they influence the value of optical bandgap, HOMO-LUMO distance. In DSSCs, a dye is the key element to absorb the photon from solar energy. The general estimation reveals that for most of the dye molecules, the absorption range falls in the visible spectrum (in principle, the radiation down in the near IR can be exploited, and maximum photon flux occurs in the visible range). It is important to select the dyes whose absorption maxima lie in the visible range. Therefore, the interpreted features from the QSPR model should be useful in the design and development of new carbazole sensitizers with predicted λmax values for their use in DSSCs. Acknowledgements JGK thanks the Department of Pharmaceuticals, Ministry of Chemicals and Fertilizers, Govt. of India for a fellowship. KR thanks SERB, Govt of India for financial assistance under the MATRICS scheme (MTR/2019/000008).

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Index

2 2D descriptors, 172, 207, 213, 220, 222, 225–227, 229

A Absorption spectroscopy, 141, 143, 144, 147 Amsterdam Density Functional (ADF), 64 Applicability domain, 170, 173, 213, 222, 224 Artificial neural networks, 179, 213 Arylamine organic dyes, 172, 173, 192

Conduction band, 41, 42, 101, 106, 107, 113, 116, 132, 139, 144, 147, 181, 189, 191, 192, 194–198, 209, 211 Coumarin, 108–110, 139, 170, 171, 174, 175, 182

B Band gap, 93, 102, 106, 107, 112, 122, 136, 188, 199, 230 Basis set, 62, 99, 119, 121, 172, 173 Benzothiadiazole, 174, 194 Bethe–Salpeter equation, 99, 101, 105 Bulk-heterojunction, 57, 58, 177

D D-π-A, 88, 91, 133, 148, 173, 188 D−D−π−A, 194, 196, 200 Databases, 167, 169, 170, 181–183, 213 Density functional theory, 57, 59, 99, 100, 106, 172, 187, 211 DFT-D3, 64, 76 DRAGON, 171, 172, 179, 181, 212, 220 DSSCDB, 182, 213 Dye-Sensitized Solar Cells (DSSCs), 2, 82, 91, 99–102, 106, 108, 111, 114–117, 119, 121, 127, 130–141, 145, 146, 150–152, 167–170, 172–174, 179, 181, 183, 184, 187–192, 196, 200, 202, 207–213, 229, 230

C CH3 NH3 PbI3 , 1, 2, 6, 9–11, 13, 16–18, 21, 23, 24 Charge separation, 57, 59–63, 67, 74, 75, 84, 188, 193 Charge transfer, 23, 59, 60, 62, 67, 73, 75, 88, 100, 117, 136, 143, 147, 174, 181, 187–189, 193, 194, 199, 201, 202 Chemical vapor deposition, 9 Chemometric, 170, 181, 207, 229 CoMFA, 170, 171

E Electron–hole interactions, 100, 102, 105, 117 Electrostatic potential difference, 199 Excited state lifetime, 141, 147, 181, 200, 201 Excited State Oxidation Potential (ESOP), 100, 194, 195, 200 Exciton, 58, 74, 100, 101, 106, 110, 121, 122, 178, 181, 195 Excitonic, 99, 101, 102, 105, 110, 117–119

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234 F First-principles, 99, 121 Fossil fuels, 1, 57, 128, 129, 135, 187, 208 Fullerene, 57–59, 61, 62, 101, 132, 168, 176–178

G GA-MLR, 172 Green’s function, 99, 101–105, 116, 121 GSOP, 100, 194, 200 GW, 101–107, 109, 110, 112–117, 119–122

H Heterojunction solar cells, 33–36, 42–44, 47–50, 52 HOMO, 34, 41, 74, 100, 110, 112–115, 142– 144, 147, 173, 189, 195, 198, 201, 209, 211, 230

I Indoline, 173, 174, 182, 192–194, 196–198 In-silico, 188 Intramolecular Charge Transfer (ICT), 181, 188

J JSC , 48, 88, 140, 169–171, 173, 189 J–V characteristics, 37, 38, 40, 41

Index O Open-circuit voltage, 37, 88, 115–117, 169, 170, 174, 187, 195, 202 Organic Photovoltaic (OPV), 57–61, 63, 71, 73–76, 81–83, 85, 92, 93, 95, 96, 182

P P3HT, 18, 59–63, 65–75, 177, 178 PCBM, 19, 24, 25, 59–63, 65–75, 178 PEDOT, 34, 36, 43, 44 Perovskite Solar Cells (PSC), 1–6, 8–19, 21– 27, 81–83, 91, 93, 95, 96, 131, 132, 167–169, 176–178, 181–184, 208 Photocurrent, 13, 48, 51, 85, 86, 88, 91–95, 101, 136, 169, 191 Photoelectrode, 132 Photoexcited, 99, 141, 202 Photoinduced charge-transfer, 102, 117 Photophysical, 83, 167, 168, 170, 173, 184, 187, 197, 198, 202 Photostability, 181, 192, 193, 200, 202 Photovoltage, 13, 84, 85, 88, 91–96, 140, 141, 147 Photovoltaic effect, 1, 131, 208 Plasmon, 104, 107 Polypyridyl complexes, 135, 137, 138, 141, 143, 145, 146 Power Conversion Efficiency (PCE), 1, 2, 4– 6, 8–19, 21–27, 42, 43, 45, 46, 48, 51, 84, 88, 91–96, 167, 187–189, 192, 208, 210, 212 Pulsed laser deposition, 15, 23

L Light soaking stability, 43, 44, 51 LUMO, 34, 36, 42, 74, 100, 112–116, 139, 142, 144, 173, 178, 189, 192, 198, 209, 211

Q QSAR, 168 QTAIM, 59, 64, 66, 67, 69, 73 Quantitative Structure-Property Relationship (QSPR), 167–184, 188, 212, 213, 220–222, 230 Quantum dot solar cells, 131, 136, 208

M Machine learning, 167, 169, 180, 181, 212 Marcus theory, 74, 194 Microwave irradiation deposition, 11 Moisture degradation, 18 Multijunction, 81, 84–96

R Renewable energy, 1, 57, 128, 129, 135, 167, 168, 187, 208 Ruthenium, 91, 92, 95, 132, 135–138, 141, 143, 145, 146, 168, 182, 188, 210

N Newns–Anderson, 115, 121, 198

S Schottky, 34, 36–38, 40, 41, 51 Shockley-Queisser, 81, 82, 84, 85, 91

Index Silicon, 2, 33–37, 39, 42, 43, 48, 49, 81, 82, 84, 95, 96, 131–133, 168, 188, 208 Solar cell, 1, 2, 11, 15, 18, 21, 23–25, 27, 33–37, 39–52, 58, 75, 81–88, 91, 92, 94–96, 100, 101, 122, 127, 131–134, 136, 150, 167–172, 176, 180–184, 187, 188, 207–213 Spiro-OMeTAD, 14, 19 T TDDFT, 59, 62–64, 70, 74, 75, 99–101, 105, 109, 121, 144, 148, 150, 174, 187, 189, 193–195, 200–202 Thermal vapor deposition, 10 TiO2 , 13–16, 21–23, 50, 86, 88, 92, 101, 102, 106–108, 112–116, 119–122,

235 130, 134–139, 141–145, 147–149, 172, 174, 181, 189–192, 194–202, 208–211, 213 Two-step sequential coating, 6

U UV-Vis, 57, 60, 61, 73, 75, 120, 130, 178

V Valence band, 107, 112, 113, 133 Vapor-assisted solution, 7, 8 Voc , 25, 33, 36, 39–41, 48, 51, 88, 140, 141, 149, 169–171, 173, 178, 181, 189