Work Function and Band Alignment of Electrode Materials: The Art of Interface Potential for Electronic Devices, Solar Cells, and Batteries 4431568964, 9784431568964

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Work Function and Band Alignment of Electrode Materials: The Art of Interface Potential for Electronic Devices, Solar Cells, and Batteries
 4431568964, 9784431568964

Table of contents :
Preface
Contents
1 Introduction: Functions and Performances Governed by the Work Function
1.1 Why is the Work Function Important?
1.2 Contents of the Following Chapters
References
2 What is the Work Function?: Definition and Factors that Determine the Work Function
2.1 Definition of the Work Function
2.2 Origin of the Work Function
2.3 Factors Determining the Work Function
2.4 Effect of Temperature on the Work Function
2.5 Inhomogeneity of the Work Function
References
3 Modification of the Work Function
3.1 Mixing Elements
3.1.1 Substitutional Alloys
3.1.2 Interstitials (Metal Carbides and Nitrides)
3.1.3 Intermetallic Compounds (Ordered Alloys)
3.1.4 Two Elements with Miscibility Gap
3.2 Surface Termination
3.3 Adsorption or Segregation
3.4 Deposition
References
4 Measurement of Work Function
4.1 Utilizing Electron Emission Current Measurement
4.1.1 Thermal Emission
4.1.2 Field Emission
4.1.3 Photoelectron Emission
4.2 Utilizing Electron Emission Spectroscopy
4.2.1 Photoelectron Emission Yield Spectroscopy (PYS)
4.2.2 Secondary Electron Cutoff Spectroscopy (UPS, XPS, AES …)
4.3 Utilizing Contact Potential Difference Measurement
4.3.1 Kelvin Probe Method
4.3.2 Diode Method
4.4 Other Methods
4.4.1 Photoemission of Adsorbed Xenon (PAX)
References
5 Modification of Band Alignment via Work Function Control
5.1 Ideal Band Alignment
5.2 Modification of Band Alignment
References
6 Advanced Models for Practical Devices
6.1 S Parameter: Indicator of Nonideality
6.2 Origin of Nonideality
6.2.1 Metal-Induced Gap States (MIGS) Model
6.2.2 Disorder-Induced Gap States (DIGS) Model
6.2.3 Interface-Induced Gap States (IFIGS) Model
6.3 Charge Neutrality Level (CNL) and S Parameter
6.4 Modification of S Parameter by Inserting Insulator
6.5 Generalized CNL
References
7 Utilization of Interface Potential
7.1 Control of Interface-Terminating Species
7.2 Insertion of a 1-ML-Thick Material
References

Citation preview

NIMS Monographs

Michiko Yoshitake

Work Function and Band Alignment of Electrode Materials The Art of Interface Potential for Electronic Devices, Solar Cells, and Batteries

NIMS Monographs Series Editor Naoki OHASHI, National Institute for Materials Science, Tsukuba, Ibaraki, Japan Editorial Board Takahito OHMURA, National Institute for Materials Science, Tsukuba, Ibaraki, Japan Yoshitaka TATEYAMA, National Institute for Materials Science, Tsukuba, Ibaraki, Japan Takashi TANIGUCHI, National Institute for Materials Science, Tsukuba, Ibaraki, Japan Kazuya TERABE, National Institute for Materials Science, Tsukuba, Ibaraki, Japan Masanobu NAITO, National Institute for Materials Science, Tsukuba, Ibaraki, Japan Nobutaka HANAGATA, National Institute for Materials Science, Tsukuba, Japan Kenjiro MIYANO, National Institute for Materials Science, Tsukuba, Ibaraki, Japan

NIMS publishes specialized books in English covering from principle, theory and all recent application examples as NIMS Monographs series. NIMS places a unity of one study theme as a specialized book which was specialized in each particular field, and we try for publishing them as a series with the characteristic (production, application) of NIMS. Authors of the series are limited to NIMS researchers. Our world is made up of various “substances” and in these “materials” the basis of our everyday lives can be found. Materials fall into two major categories such as organic/polymeric materials and inorganic materials, the latter in turn being divided into metals and ceramics. From the Stone Ages - by way of the Industrial Revolution - up to today, the advance in materials has contributed to the development of humankind and now it is being focused upon as offering a solution for global problems. NIMS specializes in carrying out research concerning these materials. NIMS: http://www.nims.go.jp/ eng/index.html

More information about this series at http://www.springer.com/series/11599

Michiko Yoshitake

Work Function and Band Alignment of Electrode Materials The Art of Interface Potential for Electronic Devices, Solar Cells, and Batteries

Michiko Yoshitake National Institute for Materials Science Tsukuba, Ibaraki, Japan

ISSN 2197-8891 ISSN 2197-9502 (electronic) NIMS Monographs ISBN 978-4-431-56896-4 ISBN 978-4-431-56898-8 (eBook) https://doi.org/10.1007/978-4-431-56898-8 © National Institute for Materials Science, Japan 2021 This work is subject to copyright. All rights are reserved by the National Institute for Materials Science, Japan (NIMS), 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. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of applicable copyright laws and applicable treaties, and permission for use must always be obtained from NIMS. Violations are liable to prosecution under the respective copyright laws and treaties. 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. While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. NIMS and the publisher make no warranty, express or implied, with respect to the material contained herein. This Springer imprint is published by the registered company Springer Japan KK part of Springer Nature. The registered company address is: Shiroyama Trust Tower, 4-3-1 Toranomon, Minato-ku, Tokyo 1056005, Japan

Preface

Work function is one of the important physical quantities of materials that is related to various phenomena. However, systematic discussion on the work function is limited possibly because of the following two reasons. One is that the work function is not a quantity that is specific to a bulk material such as dielectric constant, elastic modulus, density, and magnetic susceptibility. Even one single crystalline material has different work function values, depending on the crystal plane. This means that work function values are influenced not only by bulk materials but also by surface conditions. The other is that the measurement of work function values of an intended surface of materials is not easy. The difficulty comes from the fact that work function values are surface sensitive as mentioned above. Surface is very reactive in general, and it is rather difficult to prepare and maintain a surface as intended states. Basic experimental researches on the work function had progressed upon the development of commercially available vacuum instruments in the 1960s–1970s, which provided tools to maintain surface conditions and observe surface compositions and structures. Most of fundamental issues were established during this time. Then, theoretical calculations of the work function have complimented experimental researches thanks to the development of first-principles calculations in the 1990s. Emergence of electronic devices had required the control of band alignment via work function control at the interface, and the origins of the deviation from ideal Schottky relation were rigorously discussed in the 1980s and later.

v

vi

Preface

This book presents issues on the work function from fundamental physics to examples of band alignment via work function control in device applications. The author hopes the book helpful for all who engage in research and development of materials whose function has related to the work function. Acknowledgements The author would like to thank the editorial teams of Springer and NIMS Monographs for their patience and support. It is grateful that the author had been stimulated by the discussion with the members of 158 committees of University-Industry Research Cooperation Societally Applied Scientific Linkage and Collaboration. Tsukuba, Japan September 2020

Michiko Yoshitake

Contents

1 Introduction: Functions and Performances Governed by the Work Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Why is the Work Function Important? . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Contents of the Following Chapters . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1 1 4 6

2 What is the Work Function?: Definition and Factors that Determine the Work Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Definition of the Work Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Origin of the Work Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Factors Determining the Work Function . . . . . . . . . . . . . . . . . . . . . . . 2.4 Effect of Temperature on the Work Function . . . . . . . . . . . . . . . . . . . . 2.5 Inhomogeneity of the Work Function . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

7 7 10 16 23 32 33

3 Modification of the Work Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Mixing Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.1 Substitutional Alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.2 Interstitials (Metal Carbides and Nitrides) . . . . . . . . . . . . . . . 3.1.3 Intermetallic Compounds (Ordered Alloys) . . . . . . . . . . . . . . 3.1.4 Two Elements with Miscibility Gap . . . . . . . . . . . . . . . . . . . . . 3.2 Surface Termination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Adsorption or Segregation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Deposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

35 35 38 40 53 56 58 60 64 67

4 Measurement of Work Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Utilizing Electron Emission Current Measurement . . . . . . . . . . . . . . 4.1.1 Thermal Emission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.2 Field Emission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.3 Photoelectron Emission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Utilizing Electron Emission Spectroscopy . . . . . . . . . . . . . . . . . . . . . . 4.2.1 Photoelectron Emission Yield Spectroscopy (PYS) . . . . . . . .

71 71 72 74 77 77 78 vii

viii

Contents

4.2.2 Secondary Electron Cutoff Spectroscopy (UPS, XPS, AES …) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Utilizing Contact Potential Difference Measurement . . . . . . . . . . . . . 4.3.1 Kelvin Probe Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.2 Diode Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4 Other Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4.1 Photoemission of Adsorbed Xenon (PAX) . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

82 88 88 91 93 93 95

5 Modification of Band Alignment via Work Function Control . . . . . . . 97 5.1 Ideal Band Alignment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 5.2 Modification of Band Alignment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 6 Advanced Models for Practical Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1 S Parameter: Indicator of Nonideality . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Origin of Nonideality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.1 Metal-Induced Gap States (MIGS) Model . . . . . . . . . . . . . . . 6.2.2 Disorder-Induced Gap States (DIGS) Model . . . . . . . . . . . . . 6.2.3 Interface-Induced Gap States (IFIGS) Model . . . . . . . . . . . . . 6.3 Charge Neutrality Level (CNL) and S Parameter . . . . . . . . . . . . . . . . 6.4 Modification of S Parameter by Inserting Insulator . . . . . . . . . . . . . . 6.5 Generalized CNL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

113 113 115 117 118 118 119 123 123 125

7 Utilization of Interface Potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1 Control of Interface-Terminating Species . . . . . . . . . . . . . . . . . . . . . . 7.2 Insertion of a 1-ML-Thick Material . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

127 127 133 135

Chapter 1

Introduction: Functions and Performances Governed by the Work Function

1.1 Why is the Work Function Important? The work function is an important property for phenomena where electron transfer between two different materials in contact or from a material into vacuum is involved. Electron transfer into vacuum or a gas phase is usually called electron emission (Fig. 1.1a). Electron emission is one of the well-known phenomena governed by the work function. In fact, electron emission has been used to measure values of the work function. Electron emitters with a low work function have been developed for a long time. Electron transfer between two materials (Fig. 1.1b) is another major application field related to electron emission. In the field of semiconductor device physics, it is well known that the ideal Schottky barrier height (SBH) at a metal–semiconductor interface is determined by the work function of the metal and the electron affinity of the semiconductor (Fig. 1.2). There are major application fields that utilize the concept of a Schottky contact, which will be discussed later in the book. Furthermore, several types of chemical reaction on a surface have been reported to be related to the work function. For example, the potential of oxidation in fuel cells has been shown to be related to the work function of the electrode materials [1]. The dissociation of molecules on catalytic metals has also been reported to be affected by the work function of metals [2, 3]. Because the work function is a factor determining electron emission, it affects most phenomena involving electrons and is important in many application fields. In Fig. 1.3, some of the application fields that utilize electron emission phenomena are shown. A scanning electron microscope (SEM) and a transmission electron microscope (TEM), which are familiar in scientific R&D fields, use an electron source whose performance is determined by the work functions of the electron source materials. Here, emitted electrons are made into a beam. Other examples of electron beam applications are electron lithography, accelerators for synchrotron radiation photon sources, and colliders for nuclear physics research. Examples of the practical use of electron emission in daily life are fluorescent lamps, neon lighting in neon © The Author(s), under exclusive license to Springer Japan KK, part of Springer Nature 2021 M. Yoshitake, Work Function and Band Alignment of Electrode Materials, NIMS Monographs, https://doi.org/10.1007/978-4-431-56898-8_1

1

2

1 Introduction: Functions and Performances Governed by the Work Function

a)

b)

vacuum

electron electron

Material B (solid) Material A (solid)

Material (solid/liquid)

Electron source for microscopes and other analycal instruments and photocathodes

Solar cells MOS Fuel cells Baeries Catalysts Sensors

Fig. 1.1 Some examples of applications related to a electron emission (electron transfer into vacuum or gas phase) and b electron transfer between two materials (see text for details) Fig. 1.2 Band alignment for ideal Schottky contact between metal and n-type semiconductor (see text for explanation)

metal

n-type semiconductor

EVAC

EVAC SBH EC

EF

EF

EV SBH =

- EA ΔE=

-

1.1 Why is the Work Function Important?

3

SEM/ TEM Electron lithography

Fluorescent lamp

Collider

Photodetector Sensor

Car plug Discharge

Plasma

Electron emission

Fig. 1.3 Applications related to electron emission phenomena. See text for explanation

signs, and car plugs. For these applications, electron emission is mostly utilized to initiate electric discharge. Electric discharge initiated by electron emission is used for plasma formation, and plasma is utilized for many industrial applications such as film deposition. Another important application is based on photoelectron emission. When light irradiates a metal, electrons are emitted if the energy of the light exceeds the work function. This phenomenon is utilized for photodetectors and gas sensors (which detect light emission from gas). Detectors or sensors for a specific photon energy or gas species can be fabricated by tuning the work function of materials. Electron emission not to vacuum or a gas phase but to another solid (electron transfer) has an even wider range of applications. The performances of almost all devices that involve an electric circuit are related to the work function. Figure 1.4 illustrates some of the application fields that utilize electron transfer phenomena. Electron transfer is controlled via the electric voltage in electric devices such as transistors and CMOS. The work function is a key factor determining the operation voltage. Light-emitting devices including organic devices convert electric energy to light, where the work function is an important factor determining the conversion efficiency. The performance of devices involving energy conversion in the opposite direction, i.e., solar cells, is also influenced by the work function. For other energy conversion devices with various types of energy, such as fuel cells and batteries

4

1 Introduction: Functions and Performances Governed by the Work Function

CMOS Transistor OLED

LED

Fuel cell

Solar cell Baery

Sensor

Electron transfer

Fig. 1.4 Applications related to electron transfer phenomena. See text for explanation

(chemical energy), the work function is a key to extracting electricity from the energy. Another field related to energy conversion is sensors, where the amount of energy to be converted is small. Again, the energy conversion efficiency is related to the work function, where the efficiency determines the sensitivity.

1.2 Contents of the Following Chapters As briefly overviewed in the above section, the work function plays an important role in a very wide range of scientific, technological, and industrial fields. In the following chapters, we discuss the physical origin of the work function, how the work function can be controlled on the basis of physics, and how to design interfaces. In this section, a guide to the following chapters is given. In Chap. 2, the definition and the origin of the work function are given, and factors that determine the value of the work function are explained. The most important point is that the work function is defined for the surface of a material as well as for bulk materials. In Chap. 3, strategies for tuning the work function are demonstrated on the basis of the discussion in Chap. 2. Examples of work function modifications using

1.2 Contents of the Following Chapters

5

these strategies are also given for concrete material systems. In Chap. 4, various methods of measuring work function are given with both their physical principles and technical issues. From Chaps. 5–7, band alignment at the interface is discussed on the basis of the relationship with the work function. In Chap. 5, band alignment is handled as an ideal case, where the modification of the work function directly controls the band alignment. The relationship between the band alignment and the work function in general, and concrete examples of band alignment modification via tuning of the work function are given. In Chap. 6, cases where the relationship between the band alignment and the work function is not ideal are discussed. Here, although the relationship is not ideal, a linear relationship with the work function is obtained in many cases. A correlation factor for the linear relationship is introduced, which is determined by the dielectric property of the material in contact. Chapter 7 discusses band alignment with interface-specific cases. By extending the idea that the work function is surface-sensitive, either an appropriate interface terminating species or the insertion of a very thin layer that can be regarded as having only a surface and no bulk is adopted to modify the band alignment. Some concrete examples are also given. Practically, the former technique is extensively adopted in the field of compound semiconductors and the latter technique is used in organic semiconductor fields. The relationship between the chapters of this book is summarized in Fig. 1.5.

Chapter 1

Chapter 2

Chapter 5

Chapter 3

Chapter 6

Chapter 7

Chapter 4

Fig. 1.5 Relationship between the chapters of the book

6

1 Introduction: Functions and Performances Governed by the Work Function

References 1. Ishihara A, Doi S, Matsushita S, Ota K (2008) Tantalum (oxy)nitrides prepared using reactive sputtering for new nonplatinum cathodes of polymer electrolyte fuel cell. Electrochim Acta 53:5442–5450 2. Lang ND, Holloway S, Norskov JK (1985) Electrostatic adsorbate-adsorbate interactions: the poisoning and promotion of the molecular adsorption reaction. Surf Sci 150:24–38 3. Brown JK, Luntz AC, Schultz PA (1991) Long-range poisoning of D2 dissociative chemisorption on Pt(111) by coadsorbed K. J Chem Phys 95:3767–3774

Chapter 2

What is the Work Function?: Definition and Factors that Determine the Work Function

2.1 Definition of the Work Function The work function (φ) is conventionally defined as the minimum energy required to extract one electron from a metal. In this definition, the final state of the electron needs to be specified. For the energy to be minimum at the final state, the electron must be finally at rest. Thus, the work function depends on the final position of the electron. Here, the magnitude relationship among the atomic distance in the metal (a), the size of the metal (L), and the distance between the surface of the metal and the final position of the electron (d ) is classified into three types (Fig. 2.1). When an electron is extracted from a metal with a finite size to the final position at a large distance (a point at infinity), the energy required does not depend on the crystal orientation (L  d , Fig. 2.1a), which is not the work function in the usual sense. If the final distance is sufficiently large compared with the atomic distance but sufficiently small compared with the size of the metal, the electron at the final position is under the influence of the ambient electric fields in vacuum and the energy required is dependent on the crystal orientation (a  d  L, Fig. 2.1b). This is the definition of the work function [1]. The condition of distance d > 103 nm is explained later in the text (Sect. 2.2). For an extremely small d value, an electron is extracted near the surface (d ∼ a  L, Fig. 2.1c). At zero temperature, by considering the energy difference between the initial state (a system containing N electrons in the ground state with energy EN ) and the final state (a system with one electron extracted, containing (N − 1) electrons), it can be seen that the work function is equal to the difference between EN and the energy in the final state, with the energy of (EN −1 + φV ), where φV denotes the electrostatic energy of the extracted electron at rest far from the surface (at distance d ). φ = (EN −1 + φV ) − EN

(2.1)

Equation (2.1) can be rewritten as © The Author(s), under exclusive license to Springer Japan KK, part of Springer Nature 2021 M. Yoshitake, Work Function and Band Alignment of Electrode Materials, NIMS Monographs, https://doi.org/10.1007/978-4-431-56898-8_2

7

8

2 What is the Work Function?: Definition and Factors …

a)

b)

c)

(local work func on) ea 103 nm) > d

d≈a

e-

e> 103 nm

a

large area atomic distance: a Fig. 2.1 Classification of the relationship among the atomic distance in the metal (a), the size of the metal (L), and the distance between the surface of the metal and the final position of the electron. The distance d > 103 nm is explained later in the text (Sect. 2.2)

φ = (EN −1 − EN ) + φV .

(2.2)

Because the work function is an intensive property, not an extensive one, the energy difference (EN −1 − EN ) is replaced by the derivative of the Helmholtz free energy with respect to the electron number N , where the temperature T and volume V are kept constant. This derivative is the chemical potential of the electrons μ.  EN − EN −1 →

∂F ∂N

 T ,V



(2.3)

Then, the general form of Eq. (2.1) for a nonzero temperature is expressed as   ∂F φ=− + φV = φV − μ. ∂N T ,V

(2.4)

When φV is used as a reference level, the work function is the same as the chemical potential but with the opposite sign. φV is called the “vacuum level” of the system, which is dependent on the surface. Because the Fermi level is the chemical potential of the system, by definition, the work function is equal to the energy difference between the Fermi level and the vacuum level at the surface of the metal. For materials with a band gap (semiconductors and insulators), the Fermi level is inside the band gap (Fig. 2.2). Therefore, the energy difference between the Fermi level and the vacuum level at the surface of the material is not equal to the minimum energy required to extract one electron. The conventional definition of the work

2.1 Definition of the Work Function

energy

9

metal vacuum level

work func on

Insulator

semiconductor IE

IE

EA

Conduc on band

Conduc on band

Fermi level Valence band

EA

Band gap Valence band

Fig. 2.2 Schematic band diagram for metal, semiconductor, and insulator (see text for explanation)

function, the minimum energy required to extract one electron, applies only for a metal. The above definition, the energy difference between the Fermi level and the vacuum level at the surface of the material, is more general definition and should apply to any material with or without a band gap. Here, one should note that the minimum energy required to extract one electron from either a semiconductor or insulator is not the work function but the ionization energy (IE). The electron affinity (EA), which is the energy released by adding one electron to a material, is a concept similar to the work function but the direction of electron transfer is opposite. For metals, the EA has the same value as the work function. However, for semiconductors or insulators, the values of EA are different from those of the work function, as illustrated in Fig. 2.2. Here we discuss the difference in the final position of an extracted electron in Fig. 2.1a, b. The potential inside a metal is exactly the same for the two cases. Therefore, the electrostatic energy of the extracted electron at rest far from the surface (at distance d) in Fig. 2.1b, φV , is different from the potential at an infinite distance (Fig. 2.1a), φB . Here, φB represents how strongly electrons are bound in the bulk of the metal, which is determined by the bulk. Then, φV − φB corresponds to the surface electrostatic potential (φS ), which depends on the surface properties such as the crystal orientation. This means that φV depends on the surface of the material. In the situation shown in Fig. 2.1c, where the distance between the extracted electron and the surface is close to the atomic distance, the final position is inside the surface electrostatic field, and thus the electrostatic potential should be different from φV . However, the recent development of scanning probe microscopy (SPM) techniques such as scanning tunneling microscopy (STM) and atomic force microscopy (AFM) allows us to experimentally obtain the potential barrier height corresponding to the situation shown in Fig. 2.1c. This potential barrier height is sometimes called the local work function or local barrier height. The potential as a function of the distance between the surface and the final position of the electron is schematically represented in Fig. 2.3.

10

2 What is the Work Function?: Definition and Factors …

≈ ≈

EVAC EVAC(∞)

EF ħ2 2 V kF XC 2m

0

~ mm

~ km



Fig. 2.3 Potential diagram as a function of the distance between the surface and the final position of the electron

Note that the work function is not an intrinsic property of bulk materials such as the lattice constant or density, but is affected by the state of the surface such as the crystal orientation, roughness, and surface contamination. The origin of the work function is explained in detail in the next section.

2.2 Origin of the Work Function The work function is the potential barrier that binds electrons inside a material. Therefore, we start by considering the energy stabilization of electrons by bond formation between atoms. When two atoms approach each other, a bonding orbital and an anti-bonding orbital are generated as a result of overlap of the wave functions of valence electrons from the two atoms. Because the bonding orbital accepts up to two electrons, the total energy of the valence electrons is lowered by the formation of a bond between the atoms (the system is stabilized by bond formation). This stabilization by bond formation occurs in all atoms except atoms whose outer shell of valence electrons is full (= He, Ne, Ar, Kr, Xe, and Rn). With an increase of the number of atoms involved in bonding, the width of the bonding orbital increases and an energy band is formed, which is called the valence band (Fig. 2.4). For an atom or cluster, the minimum energy required to extract one electron is the IE. In Fig. 2.5, the IE of Hg clusters is plotted as a function of the number of atoms contained in a cluster [2]. The energy stabilization of electrons by bond formation is understood to be one of the origins of the work function, which we call the “bulk term” in the text. In the previous section, we saw that the work function is affected by the surface electrostatic potential (φV −φB ). Here, the origin of the surface electrostatic potential is discussed. Let us consider the charge distribution near the surface. Atoms consist of ion cores and valence electrons, where ion cores are located almost regularly

2.2 Origin of the Work Function

atom

11

energy

atom

valence band electrons

atomic nucleus Fig. 2.4 Schematic illustration of band generation by bond formation among atoms (see text for explanation)

Fig. 2.5 Ionization energy of Hg clusters plotted as a function of number of atoms contained in a cluster

Number of atoms in clusters 70

17 12 7

4 3

2

1

Ioniza on energy (eV)

11 mercury cluster

10 9 8 7 6 5 4 0.0

Bulk work func on 0.1

0.2

0.3

0.4

0.5

0.6

1/R (sphere radius having the same volume as cluster, Å)

from the bulk to the surface and can be treated as a homogeneous distribution. The distribution of valence electrons, which have much lower mass than ionic cores, is determined by the electrostatic field from the ion cores. Inside a solid, valence electrons are surrounded by ion cores in all directions, and thus their distribution is uniform similar to that of the ion cores. However, at the surface, the ion cores are missing, and valence electrons are subjected to an electrostatic field considerably different from that in the bulk. Because the force attracting the valence electrons is weaker near the surface, the valence electrons are distributed outside the surface toward the vacuum, which is schematically shown in Fig. 2.6. In the right part of the figure, the positive (ion cores) and negative (valence electrons) charge distributions from the bulk to the vacuum across the surface are plotted as a function of the distance from the surface. The corresponding distribution of valence electrons near the surface is illustrated in the left part of the figure. In the bulk, positive and negative charges balance and there is no electrostatic potential. However, near the surface, some of the negative charges are distributed outside the surface owing to the weaker attractive force of the ion cores. This results in an electric dipole with negative charge toward

12

2 What is the Work Function?: Definition and Factors … Electrons spreading out vacuum

+

Ion core

charge density

Fig. 2.6 Schematic illustration of the origin of the surface term of the work function. The left picture depicts a schematic cross-sectional electron contour map near the surface and the right picture shows the charge density of electrons across the surface region

the vacuum side, which is the origin of the surface electrostatic potential. This term is called the “surface term” in the text. Here we reintroduce the energy diagram of electrons near the surface by replacing potentials with energy levels, i.e., the chemical potential μ with the Fermi level EF , φV with EV AC , and φB with EV AC(bulk) (Fig. 2.7). The work function φ is the energy difference EV AC − EF . We represent the surface term of the work function, φV − φB = EV AC − EV AC(bulk) , as φS and the bulk term of the work function, EV AC(bulk) − EF , as φB . According to density functional theory (DFT) applied to the jellium model, the bottom of the valence band is located VXC below EV AC(bulk) , where VXC is the exchange–correlation energy. Valence electrons occupy energy 2 2 kF above levels from the bottom of the valence band up to EF , which is located 2m the bottom of the valence band.

Fig. 2.7 Energy diagram of electrons near the surface obtained by replacing potentials with energy levels, chemical potential μ with Fermi level E F , φ V with E vac , φ B with E vac(bulk)

2.2 Origin of the Work Function

13

We see that the origin of the surface term of the work function is the charge distribution of valence electrons, which generates an electric dipole at the surface. For metals where the density of carriers is large, the length of the dipole is in the range of the Fermi wavelength (typically ~1 nm). However, for semiconductors with carrier density orders of magnitude less than that of metals, the electron redistribution extends far below the surface. The dipole due to the electron redistribution causes the electrostatic potential to extend rather deeply in the case of semiconductors, resulting in so-called “band bending” (Fig. 2.8a). The depth of band bending W is expressed as [3]  W =

 ε eφ . × 2π e2 N

(2.5)

Fig. 2.8 a Band bending on the surface of a semiconductor. b Flat-band realization by surface treatment. c Band diagram for negative electron affinity. See text for explanation

14

2 What is the Work Function?: Definition and Factors …

Here, ε is the dielectric constant of a semiconductor, φ is the potential induced by the surface charge distribution, and N is the carrier density. Note that band bending occurs at a clean surface of a semiconductor, although it is often introduced at the interface between a metal and a semiconductor in semiconductor physics. Because band bending is caused by the electron distribution near the surface, surface modification such as HF treatment can modify the band bending of a semiconductor. The band of n-Si, which initially bends upward on a clean surface, is flattened by HF treatment (Fig. 2.8b). For semiconductors whose Fermi level is located near the valence band (the conduction band is close to EV AC ), if the band bends downwards by an amount larger than the electron affinity (EA = EV AC − EC ), the band diagram is similar to that shown in Fig. 2.8c. Then, electrons in the conduction band can be emitted without any potential barrier. This situation is called negative electron affinity (NEA). A hydrogen-terminated diamond (111) surface is a well-known NEA surface [4]. One should note that an NEA does not mean a negative work function. Even if bands bend downwards, EV AC is still above the Fermi level. This means that one should excite electrons up to the conduction band in some way, and thus electron emission from an NEA surface is not a spontaneous phenomenon. Here, we discuss the image force. The concept of the image force was originally introduced for the method of image charges in electrostatics, where the surface electrostatic potential was not taken into account. Therefore, we start by considering the image force without a surface term, where the charge distribution induced by ion cores and that induced by valence electrons are uniform and overlap. The potential diagram without the image force taken into account is shown in Fig. 2.9a, where the potential changes abruptly at the surface. We consider adding the effect of the image potential to this. This image force in vacuum is expressed using the following equation. F=

1 e2 · 4π ε0 r 2

(2.6)

Here, e is the charge of electrons and is 1.602 × 10−19 [C], ε0 is the permittivity of vacuum and is 8.85 × 10−12 [F/m], and r [m] is the distance between an electron and the surface. By integrating Eq. (2.6), the image potential at distance z is expressed as [5] ∞

∫ z

e2 1 1 · dr = 14.42 · 10−10 · [eV ]. 4π ε0 r 2 z

(2.7)

The magnitude of the image potential at different z values is shown in Table 2.1. From the table, the image potential is of practical importance for z ≤ 100 nm. Therefore, when the work function is defined as in Fig. 2.1b with a  d  L, d should be large enough not to be influenced by the image potential, giving one more condition: d > 1000 nm (to avoid a minor influence, the distance should be one order of magnitude larger than the minimum distance of practical importance). When the image force is taken into account, the potential change near the surface becomes

2.2 Origin of the Work Function

(a)

(b)

surface

inside a solid

15

vacuum EVAC (im)

EF

VXC

EVAC(im) EF

VXC

Fig. 2.9 a Potential diagram without taking into account image force. b Potential diagram with image force taken into account. c Potential diagram with surface term and without taking image force into account. d Potential diagram with surface term and with image force taken into account. See text for explanation

gradual, as shown in Fig. 2.9b. Because the physical origin of the image potential in the bulk is exactly the same as that of VXC , the potentials in the bulk and at an infinite distance do not change upon introducing the image force. When the surface term is considered but not the image force, the bulk-related potential changes abruptly, as shown in Fig. 2.9a, but the potential related to the surface electrostatic potential changes smoothly near the surface. Thus, the resulting potential diagram is similar to that shown in Fig. 2.9c. Now, we consider the most realistic case in which both the surface potential and the image force are taken into account (Fig. 2.9d). Because the consideration of the image force changes the curve near the surface but not the potential in the bulk and vacuum, the potential curve in Fig. 2.9d is not so different from the potential without the image force (dotted curve in Fig. 2.9d) except for very near the surface.

16 Table 2.1 Magnitude of image potential at different z

2 What is the Work Function?: Definition and Factors … z (nm)

Image potential (eV)

z (nm)

Image potential (eV)

0.1

14.420

6

0.240

0.2

7.210

7

0.206

0.3

4.807

8

0.180

0.4

3.605

10

0.144

0.5

2.884

12

0.120

0.6

2.403

14

0.103

0.8

1.803

16

0.090

1

1.442

20

0.072

1.2

1.202

25

0.058

1.4

1.030

30

0.048

1.6

0.901

35

0.041

2

0.721

40

0.036

2.5

0.577

45

0.032

3

0.481

50

0.029

4

0.361

60

0.024

5

0.288

75

0.019

100

0.014

2.3 Factors Determining the Work Function The work function comprises a bulk term and surface term, as discussed in the previous section. The factors that determine the bulk term and surface term are separately discussed here. The bulk term represents how strongly valence electrons are bound inside the solid, and thus it is reasonable to assume that it has a strong correlation with the electronegativity since the electronegativity χ is “a chemical property that describes the tendency of an atom or a functional group to attract electrons (or electron density) towards itself” [6]. In Fig. 2.10, the correlation between Pauling’s electronegativity [7] and the work function of an elemental (polycrystalline) metal [8] is plotted. Values plotted as triangles are taken from Ref. [7] and those plotted as circles are re-examined values [9, 10]. The values are scattered along the straight line expressed by the following equation. W F (eV) = 2.27 × EN + 0.34

(2.8)

Here, EN represents Pauling’s electronegativity. Because Pauling’s electronegativity is a quantity belonging to each element, the above correlation implies how the work function is dependent on the element. However, Pauling’s electronegativity is determined on the basis of the experimental results of formation enthalpy and is defined only for elements. Therefore,

2.3 Factors Determining the Work Function

17

work function (WF, eV)

6.0 WF(eV) = 2.27 * EN + 0.34 5.5 5.0 4.5 4.0 3.5 3.0 EN [7] (JCP_1956) EN [9,10] (renewal)

2.5 2.0 0.5

1.0

1.5

2.0

2.5

3.0

Pauling’s electronega vity (EN) Fig. 2.10 Correlation between Pauling’s electronegativity [7, 9, 10] and work function of elemental (polycrystalline) metal [8]

to extend it to multielement systems, we need more general parameters. As shown in Fig. 2.7, the bulk term of the work function, φB , is φB = EV AC(bulk) − EF = 2 2 VXC − 2m kF . In DFT calculations for the jellium model, both VXC and kF2 are functions of the electron density in the bulk ρ, which is related to the Wigner–Seitz radius rs by the following equation. 4 3 1 πr = 3 s ρ

(2.9)

It was shown that both the bulk term and the surface term of the work function can be calculated as functions of the Wigner–Seitz radius in the jellium model (uniform background) [11], which is shown in Fig. 2.11. When the atomistic structure is neglected and the system is treated as a uniform “sea” of valence electrons, the surface term is also determined by the bulk quantity, the electron density in the bulk ρ, or the Wigner–Seitz radius rs , because the surface electron distribution is generated in order to achieve an equilibrium with the bulk. By using this relationship between the Wigner–Seitz radius and the work function, the work function of multielement systems can be estimated in the framework of the jellium model, which will be discussed in Chap. 3. In the framework of the jellium model, if r s increases, the bulk term increases but the surface term decreases, resulting in the work function, which is the sum of the bulk term and the surface term, decreasing with increasing r s . The figure gives an idea of the size of the surface term relative to the total work function. According to the above discussion, bulk properties such as the electronegativity and Wigner–Seitz radius exhibit a correlation with the work function when the atomistic structure can be neglected (the work function for polycrystals). The surface term originates from the surface electrostatic potential generated by the deviation of the electron distribution from the positive charge distribution.

18

2 What is the Work Function?: Definition and Factors … 7

work funcon bulk-term bulk term surface term surface-term

6

potenal (eV)

5 4 3 2 1 0 -1

Au

-2

Pt W Ta Hf

-3 2.0 Al Pb Zn

2.5 Mg

3.0

3.5 Li

Lanthanoides Lanthanoids

4.0

4.5

Na

5.0 K

Wigner-Seitz radius (Bohr unit)

Fig. 2.11 Calculated results of work function, showing both bulk term and surface term separately, plotted as a function of Wigner–Seitz radius

Within the framework of the jellium model, the electron distribution at the surface is determined only by rs , which is intrinsic to the bulk of a material. However, the work function is different among different crystal orientations of the same metal. Therefore, we discuss the electron distribution near the surface beyond the jellium model, i.e., with the atomic arrangement taken into account. Then, factors such as crystal orientations, surface roughness (steps and kinks), and adsorption are sources of the deviation in the electron distribution, which determines the surface term of the work function. First, the effect of the crystal orientation on the work function of metals is considered. In Fig. 2.12, a top view of the atomic packing at the surface of three low-index

Fig. 2.12 Atomic packing at the surface of three low-index orientations in fcc metal. The density of atoms increases in the order (110) < (100) < (111)

2.3 Factors Determining the Work Function

(a) Cross sec on of loosely packed (low-atomic-density) plane

vacuum

Electrons are a racted between nuclei

Electron cloud

19

(b) Cross sec on of closely packed (high-atomic-density) plane Almost no level out

vacuum

Atomic nuclei

Fig. 2.13 Schematic cross section of loosely packed and closely packed surfaces (see text for explanation)

orientations for a face-centered-cubic (fcc) metal is illustrated. At a glance, it is clear that the density of atoms increases in the order (110) < (100) < (111). Figure 2.13 illustrates schematic cross sections of loosely packed and closely packed surfaces. On the loosely packed surface, protruding electrons are attracted by the nearestneighbor ion cores; thus, the electron distribution outside the surface is less than that on the closely packed surface. Therefore, the electric dipole is smaller, resulting in a smaller surface term and a smaller work function. It is expected that a more closely packed surface will have a higher work function. Actually, this correlation can be found in many metals. The effect of the crystal orientation on the work function for some metals is listed in Table 2.2. Next, the effect of surface roughness is considered. A cross section of a stepped surface is schematically illustrated in Fig. 2.14. At step edges, the atomic density is reduced locally, and the cross section resembles the cross section of the low-atomicdensity surface in Fig. 2.13a. Therefore, the electrostatic potential of stepped surfaces is smaller than that of atomically flat surfaces. Hence, the work function of a stepped surface is considered to be lower than that of an atomically flat surface. This has been nicely demonstrated by experiments on a W(110) surface [12]. By cutting and polishing the surface of a single crystal with a small tilt angle from the (110) plane, the step density of the surface can be controlled. The obtained relationship between the step density and the work function is plotted in Fig. 2.15 [12]. As we discussed, the higher the step density is, the lower the work function is. In association with this, it is useful to point out that the reported work functions for metals with relatively high melting temperatures are sometimes very low compared with the values on surfaces

20

2 What is the Work Function?: Definition and Factors …

Table 2.2 Influence of crystal orientation on work function values for some metals Crystal orientation Metal

Crystal lattice

(110)

(100)

(111)

Cu

fcc

4.48

4.59

4.94

Ag

fcc

4.52

4.64

4.74

Ni

fcc

5.04

5.22

5.35

Ir

fcc

5.42

5.67

5.76

Au

fcc

5.37

5.47

5.31

Al

fcc

4.06

4.41

4.24

W

bcc

5.25

4.63

4.47

Mo

bcc

4.95

4.53

4.55

Ta

bcc

4.80

4.15

4.00

Nb

bcc

4.87

4.02

4.36

Level out of spreading electrons

Fig. 2.14 Schematic of cross section of a stepped surface (see text for explanation)

whose flatness is guaranteed. The reason is that after ion sputtering to remove the contaminant on the surface, which makes the surface rough, the heating to recover the surface smoothness by atomic diffusion is sometimes insufficient, especially for metals with high melting temperatures, resulting in a clean but rough surface. There are many steps on a rough surface, resulting in a lower work function than that on a flat surface. Some examples for Pt and Rh [13] are listed in Table 2.3. Concerning surface roughness, one more interesting phenomenon has been proposed. When a film is grown homoepitaxially, the surface roughness changes in a manner dependent on the growth mode. The possibility of distinguishing the growth mode from the change in the work function between the instantaneous nucleation mode and the progressive nucleation mode has been proposed [14]. The calculated changes in the work function during the growth for the two modes are shown in the left side of Fig. 2.16.

2.3 Factors Determining the Work Function

21

Fig. 2.15 Relationship between step density and work function values [12] (see text for explanation)

Table 2.3 Influence of geometric surface state on measured work function for Pt and Rh Element

Terrace plane {hkl}

Geometric surface state

Pt

{111}

Smooth

Measured terrace work function (eV)

Literature work function (eV) 6.22 , 6.0 5.99, 5.95 5.93

{111}

Roughened

5.53

(100}

Smooth

6.00

5.84, 5.81 5.8

Rh

(110}

Smooth

5.35

5.49, 5.4

(110}

Roughened

5.24



{111}

Smooth



5.62, 5.3

{111}

Roughened

4.95



{100}

Smooth

5.38

5.36

{110}

Smooth

4.80

4.89, 4.8

{110}

Roughened

4.70



See Ref. [13] for the references of the literature work function in the table

When an adsorbed atom species is different from the species of the substrate in the above growth situation (heteroepitaxy, not homoepitaxy), the initial step is regarded as the adsorption of heteroatoms. In practice, contaminant atoms are often adsorbed, which affects the work function to a large extent. The change in the work

22

2 What is the Work Function?: Definition and Factors …

Fig. 2.16 Calculated results of the change in work function during the growth for the two modes [14] (left) and the schematic illustration of the growth mode (right). The difference is caused by the difference in roughness

function owing to adsorption is described by the additional positive background in the jellium model using a uniform slab of background charge, as shown in Fig. 2.17 [15]. Modification of the work function by adsorption is discussed in more detail in Chap. 3.

Fig. 2.17 Schematic charge distribution perpendicular to the surface upon adsorption described by the additional positive background in jellium model using a uniform slab of background charge [15]

2.4 Effect of Temperature on the Work Function

23

2.4 Effect of Temperature on the Work Function One of the most common methods of measuring the work function, as well as one of the most common applications of electron emission, is to use thermionic electron emission, where a metal wire is heated at a high temperature. Therefore, the temperature dependence of the work function is important and described here. We saw that the work function is determined by the Wigner–Seitz radius in the jellium model in the previous section. Increasing the temperature of a material usually causes the expansion of the lattice, resulting in a decrease in the density of valence electrons and an increase in the Wigner–Seitz radius. According to Fig. 2.11, the bulk term increases whereas the surface term decreases with increasing Wigner–Seitz radius. The work function, which is the sum of the two terms, decreases with increasing Wigner–Seitz radius. Therefore, it is expected that the work function will decrease with increasing temperature. The temperature dependence of a metal work function based on the jellium model has been reported [16] and is reproduced in Table 2.4. The work function is expressed as a simple power function of the Wigner–Seitz radius in the jellium model, where the power factor is −0.5, but the numerical fitting to experiments gives a power factor of −0.674. The lattice expansion changes not only the average positive charge density but also the electron distribution at the surface, and these changes have opposite effects on the work function. However, we can see in Table 2.4 that the thermal coefficient of the work function is negative for all metals, which agrees with the above expectation based on the jellium model. Because the surface term is dependent on the crystal orientation, as discussed in Sect. 2.3, the effect of the crystal plane on the surface term (αhkl ) in the framework of the jellium model has also been examined [17]. In this reference, the effect of the temperature dependence on the ion core radius caused by atom vibration was taken into account in the calculation of the vib ). The result of this calculation is effect of the crystal plane on the surface term (αhkl reproduced in Table 2.5 and Fig. 2.18a–c for Na, Al, and Cu, respectively [17]. As shown in Table 2.5 and Fig. 2.18, above 300 K, results including the vibration effect show that a closely packed plane has a more positive temperature dependence for both bcc and fcc metals. However, the results without the vibration effect appear to have no general trend among the metals. Obtaining experimental results on the temperature dependence of the work function is not easy owing to possible contamination at elevated temperatures including the surface segregation of impurity elements and the difficulty of precise temperature control. Therefore, only a limited amount of data has been reported. In a report on Cu(111) and Cu(110) [18], the importance of cleaning the sample in the measurement of the temperature dependence on the work function is emphasized. Figure 2.19a shows that the temperature dependence of the work function on insufficiently cleaned Cu(111) is completely different from that for clean Cu(111) shown in Fig. 2.19b. The temperature coefficients in Fig. 2.19b are −(10 ± 6) × 10–5 eV/K for Cu(111) and −(20 ± 10) × 10–5 eV/K for Cu(110) [18], whereas they are −1.7 × 10–5 eV/K for Cu(111) and ~−17 × 10–5 eV/K for Cu(110) in the above calculations [17].

24

2 What is the Work Function?: Definition and Factors …

Table 2.4 Temperature dependence of a metal work function Metal

rs (293 K)

Volume thermal expansion coefficient (× 10–6 K−1 )

Temperature coefficient of work function based on the jellium model (× 10–5 eV/K)

Temperature coefficient of work function with fitting parameter obtained from experiments (× 10–5 eV/K)

Cs

5.64

291

−14.6

−13.1

Rb

5.23

270

−14.26

−12.77

K

4.96

249

−13.5

−12.2

Na

3.98

213

−13

−12.1

Li

3.25

168

−11.53

−10.94

Ag

3.02

56.7

−4.05

−3.88

Au

3.01

41.7

−2.98

−2.83

Cu

2.67

51

−3.86

−3.79

Ca

3.26

66

−4.52

−4.29

Mg

2.65

75

−5.69

−5.6

Cd

2.59

89.4

−6.92

−6.78

Zn

2.3

118.5

−9.9

−9.74

Be

1.88

39

−3.79

−3.67

La

2.71

14.7

−1.11

−1.08

Tl

2.49

50.4

−3.99

−3.92

In

2.41

99

−8.04

−7.88

Ga

2.2

54

−4.65

−4.57

Al

2.07

73.7

−6.58

−6.51

Sn

2.39

69

−5.6

−5.53

Pb

2.31

86.4

−7.17

−7.08

Ta

1.79

19.8

−2.04

−1.93

Nb

1.79

18.75

−1.92

−1.82

W

1.62

13.8

−1.58

−1.44

Mo

1.6

15.6

−1.84

−1.64

Re

1.5

20.1

−2.6

−2.2

Ir

1.41

19.5

−2.82

−2.23

For polycrystalline Ni, whose Curie point is 358 °C, a temperature coefficient of − (1.5 + 0.1) 10–4 eV/K has been reported for the temperature range of 230 °C < T < 450 °C [19]. Another report for Ni (100), (110), and (111) also showed that the thermal coefficient for 25 °C < T < 430 °C is −1.7 × 10–4 eV/K [20] (Fig. 2.20). The results suggest no difference in the temperature dependence below and above the Curie point. The order of the temperature coefficient for Ni is similar to that for Cu. For W, the temperature coefficient for the temperature range of 80–680 K has been

Ag (fcc)

Cu (fcc)

Pb (fcc)

Al (fcc)

Na (bcc)

(100)

0.25

−0.04

0.23

−0.33

(110)

(111)

0.07

(100)

(111)

−0.63

2.54

(110)

−0.27

−0.90

−1.41

(100)

0.09

−0.002

0.05

0.04

−0.15

1.78

−0.77

(111)

−1.38

−0.37

1.33

(110)

0.86

−0.38

−0.69

−11.52

−0.04

(100)

(111)

−2.45

−2.36

−2.09 −2.12

−1.78

−1.51

−1.78

0.06

−1.45

−0.73

−11.27

−10.90 0.33

−2.39

−2.02 −0.46

0.79

1.16

1.95

−0.46 3.67

−0.23 −3.44 2.32

0.19

0.42

1.65

−12.89

−12.25

−10.88

0.51 1.88

−9.30

−7.93

−0.10

1.38

−7.16

−0.10

−8.19

−7.80

1.07

−3.63

−6.77

αu + αhkl vib

−2.60

αhkl vib

0.22

0.78

αhkl

−0.62

(111)

−0.23

1.91

2.04

(100)

−1.37

0.70

(110)

(111)

−0.33

−1.03 0.93

(110)

Li (bcc)

αhkl (rc = C)

αu

Temperature coefficient of the work function

(100)

Plane

Metal (structure)

−2.36

−(2.32 ± 1.16)

−(1.16 ± 0.7)

9.23 (poly)

Exp

(continued)

100 ≤ T ≤ 1100

100 ≤ T ≤ 1300

100 ≤ T ≤ 1300

700 ≤ T ≤ 1300

100 ≤ T ≤ 700

100 ≤ T ≤ 600

200 ≤ T ≤ 600

100 ≤ T ≤ 200

100 ≤ T ≤ 600

100 ≤ T ≤ 900

500 ≤ T ≤ 900

100 ≤ T ≤ 500

100 ≤ T ≤ 900

100 ≤ T ≤ 500

100 ≤ T ≤ 500

Temperature range (K)

Table 2.5 Calculated temperature coefficient of work function with change in lattice parameter owing to vibration taken into account

2.4 Effect of Temperature on the Work Function 25

Sn (tetr.)

Metal (structure) −2.91

2.12 −6.38

−0.50 −0.04

−0.83 0.96

6.65

1.85

−1.72

−2.58 −1.45

αu + αhkl vib

αhkl vib

(111)

0.04

αhkl

(100)

0.31

αhkl (rc = C) 1.16

−0.27

αu

Temperature coefficient of the work function

0.92

(110)

(110)

Plane

Table 2.5 (continued)

33.1 ± 8.1 (poly)

Exp 300 ≤ T ≤ 500

Temperature range (K)

26 2 What is the Work Function?: Definition and Factors …

2.4 Effect of Temperature on the Work Function

27

Fig. 2.18 a Calculated temperature dependence of work function of Na. The full and dashed lines indicate the thermal expansion effect and the lattice vibration effect, respectively [17]. b Calculated temperature dependence of work function of Al. The full and dashed lines indicate the thermal expansion effect and the lattice vibration effect, respectively [17]. c Calculated temperature dependence of work function of Cu. The full and dashed lines indicate the thermal expansion effect and the lattice vibration effect, respectively [17]

28

2 What is the Work Function?: Definition and Factors …

Fig. 2.18 (continued)

Fig. 2.19 Temperature dependence of work function on Cu(111) and Cu(110) (replotted from the figure in Ref. [18])

obtained for many planes [21] and is shown in Fig. 2.21a. The sign of the temperature coefficient differs among the crystal orientations. For the (110) and (100) planes, the order of the coefficient is similar to that for Cu and Ni. For W(111), where the temperature coefficient is positive, the absolute value of the coefficient is one order of magnitude lower. A similar result has been reported in Ref. [22] for W(111) in the temperature range of 1500–2000 K (Fig. 2.21b), where the temperature coefficient is 1.5 × 10–4 eV/K. A positive temperature coefficient has also been reported for LaB6 [22]. In Fig. 2.22a, a comparison of the temperature dependence of the work function for LaB6 (100) from different references is presented. On the basis of some measurements, a change in the temperature dependence at around 1600 K has been

2.4 Effect of Temperature on the Work Function

29

Fig. 2.20 Temperature dependence of work function on Ni(100), (110), and (111) [20]

Fig. 2.21 a Temperature dependence of work function on various planes of W [21]. b Temperature dependence of work function on W(111) [22]

30

2 What is the Work Function?: Definition and Factors …

(a)

(b)

Fig. 2.22 a Temperature dependence of work function on LaB6 (100) [22]. b Temperature dependence of work function on different planes of LaB6 [23]

2.4 Effect of Temperature on the Work Function

31

reported. The temperature coefficient for straight line 3 is 1.75 × 10–4 eV/K. In Ref. [23], the temperature coefficient for many planes of LaB6 was reported (Fig. 2.22b), where the value for the initial LaB(100) was calculated to be about 2 × 10–4 eV/K, which is similar to the value reported in Ref. [22]. Another interesting example is the temperature dependence of the work function of Nb near the superconducting transition [24]; the measured results are shown in Fig. 2.23. In the superconducting range (T < 9.2 K), a temperature coefficient of 1.1 × 10–5 eV/K has been reported,

Fig. 2.23 Temperature dependence of work function on Nb [24]

32

2 What is the Work Function?: Definition and Factors …

whereas the temperature derivative of the work function increases approximately linearly with temperature for temperatures above 9.2 K.

2.5 Inhomogeneity of the Work Function Up to this point, we have discussed theoretical aspects or rather controlled surfaces. However, practical surfaces are inhomogeneous in many aspects such as polycrystallinity, irregular roughness, uneven bulk/surface composition, and uneven surface contamination. Here, we briefly discuss the work function of such inhomogeneous surfaces. Figure 2.24a shows a schematic potential diagram of a polycrystalline sample with three different crystal orientations in contact. In this figure, the potential of each crystal orientation is connected with the vacuum level reference. However, where grains with different crystal orientations are in contact, the electrons inside each grain try to maintain chemical equilibrium so that the Fermi level of each grain is aligned in the same energy level. As a result, the vacuum level outside the sample is similar to that shown in Fig. 2.24b. This means that the work function of a polycrystalline sample is inhomogeneous. When the size of one grain is sufficiently large to satisfy the definition of the work function in Sect. 2.2 and the work function measurement method with lateral resolution is applied, such inhomogeneity in the work function is actually observed. However, the work function obtained by usual methods is considered to be an averaged value obtained from surfaces with different

a) Vacuum level referenced

b) Fermi level referenced

Vacuum level

Fig. 2.24 Inhomogeneity with multiple grains having different crystal orientations. The vacuum level is position-dependent. See text for explanation

2.5 Inhomogeneity of the Work Function

33

work functions. The manner of averaging depends on the measurement method used, which will be discussed in Chap. 4. The inhomogeneity of the work function affects phenomena involving electron emission into both vacuum and solids, and hence the performance of electron devices. The manner by which the inhomogeneity affects the performance depends on the physical principles utilized for each device. This resembles the effect of inhomogeneity on the measurement of the work function.

References 1. Holzl J, Schulte FK (1979) Work function of metals in solid state physics. In: Springer tracts in modern physics, vol 85. Springer-Verlag, Berlin Heidelberg New York 2. Rademann K, Kaiser B, Even U, Hensel F (1987) Size dependence of the gradual transition to metallic properties in isolated mercury clusters. Phys Rev Lett 59:2319–2321 3. Sze SM, Ng KK (2007) Physics of semiconductor devices, 3rd edn. Wiley, New Jersey 4. Takeuchi D, Kato H, Ri GS, Yamada T, Vinod PR, Hwang D, Nebel CE, Okushi H, Yamasaki S (2005) Direct observation of negative electron affinity in hydrogen-terminated diamond surfaces. Appl Phys Lett 86:152103-1-152103–3 5. Lang ND, Kohn W (1973) Theory of metal surfaces: induced surface charge and image potential. Phys Rev B 7:3541–3550 6. IUPAC (1997) Compendium of chemical terminology, 2nd edn. (The “Gold Book”). Online corrected version: (2006–) Electronegativity 7. Gordy W, Thomas WJO (1956) Electronegativities of the elements. J Chem Phys 24:439–444 8. Michaelson HB (1950) Work functions of the elements. J Appl Phys 21:536–540 9. Yoshitake M (2001) Pauling’s electronegativity: Japan-U.S. & Europe double Standard!? J Surf Sci Soc Jpn 22:831–833 (in Japanese) 10. Huheey JE, Keiter EA, Keiter RL (1993) Inorganic chemistry—principles of structure and reactivity, 4th edn. Harper Collins, New York 11. Lang ND, Kohn W (1971) Theory of metal surfaces: work function. Phys Rev B 3:1215–1223 12. Krahl-Urban B, Niekisch EA, Wagner H (1977) Work function of stepped tungsten single crystal surfaces. Surf Sci 64:52–68 13. Vanselow R, Li XQD (1992) The work function of kinked areas on clean, thermally rounded Pt and Rh crystallites: its dependence on the structure of terraces and edges. Surf Sci 264:L200– L206 14. Kanter YO (1989) Theoretical analysis of work function oscillations during growth of thin epitaxial films. Surf Sci 219:437–444 15. Lang ND (1971) Theory of work-function changes induced by alkali adsorption. Phys Rev B 4:4234–4244 16. Kiejna A, Wojciechowski KF, Zebrowski J (1979) The temperature dependence of metal work functions. J Phys F: Met Phys 9:1361–1366 17. Kiejna A (1986) On the temperature dependence of the work function. Surf Sci 178:349–358 18. Gartland PO, Berge S, Slagsvold BJ (1973) Photoemission study of the anisotropic work function of a clean copper single crystal. Phys Norvegica 7:39–49 19. Holzl J, Porsch G (1975) Contact potential difference measurement on polycrystalline Ni during and after deposition with evaporated Ni in the temperature range 230° ≤ T ≤ 450°C. Thin Solid Films 28:93–106 20. Christmann K, Ertl G, Schober O (1974) Temperature dependence of the work function of nickel. Z Naturforsch 29a:1516–1517 21. Swanson LW, Crouser LC (1967) Total-energy distribution of field-emitted electrons and singleplane work functions for tungsten. Phys Rev 163:622–641

34

2 What is the Work Function?: Definition and Factors …

22. Bulyga AV, Solonovich VK (1989) The influence of temperature on the work function of W, LaB6 and Pseudo-alloys. Surf Sci 223:578–584 23. Swanson LW, Gesley MA, Davis PR (1981) Crystallographic dependence of the work function and volatility of LaB6 . Surf Sci 107:263–289 24. Darling DH, Pipes PB (1977) The effect of the superconducting transition on the electronic work function of niobium. Physica B 85:277–282

Chapter 3

Modification of the Work Function

In Sect. 2.3, we examined the factors that determine the work function. In this chapter, modification of the work function is described on the basis of the discussion in Sect. 2.3. There are three main strategies for modifying the work function (Fig. 3.1). Because the work function is primarily an atomic quantity, the first strategy is to mix an element with the mother element, which is often carried out by device material scientists. Mixing A (whose work function in the polycrystalline form is φ(A)) and B (whose work function in the polycrystalline form is φ(B)) at a 1:1 ratio does not necessarily result in an alloy with the work function of 21 (φ(A) + φ(B)). The effect of mixing elements on the work function is discussed in detail in Sect. 3.1. While the aim of mixing another element is to modify the bulk term of the work function (though the surface term is inevitably modified at the same time), there is a method of modifying only the surface term without changing the bulk. When another element exists only at the surface, the surface electrostatic potential φS is modified. This situation is experimentally realized by adsorbing another element, letting the impurity element in the bulk segregate on the surface, or making an underlayer element diffuse and segregate on the surface, as schematically shown in Fig. 3.1b. The mechanism and examples are given in Sect. 3.2. Because the work function modified by adsorption is dependent on not only the adsorbed species but also the number of adsorbed atoms, it is natural to consider multilayer adsorption as a work function modification method, which is called “deposition” (Fig. 3.1c). In Sect. 3.3, aspects of work function modification via the deposition method are discussed.

3.1 Mixing Elements It has been experimentally shown that the work function of a binary compound tends to be closer to that of the element with the lower work function of the two constituent elements [1]. There have been attempts to estimate the work functions © The Author(s), under exclusive license to Springer Japan KK, part of Springer Nature 2021 M. Yoshitake, Work Function and Band Alignment of Electrode Materials, NIMS Monographs, https://doi.org/10.1007/978-4-431-56898-8_3

35

36

3 Modification of the Work Function

Fig. 3.1 Schematic illustration of cross-sectional atomic arrangements for three main strategies of work function modification

of binary compounds using this trend, the relationship between the work function and Pauling’s electronegativity, and the representation of Pauling’s electronegativity using the effective radius and the number of valence electrons. As we saw in Sect. 2.3, the work function of a polycrystalline pure metal has a strong correlation with Pauling’s electronegativity χ . Pauling’s electronegativity has been found to also have a strong correlation with the number of electrons per atom that participate in the bonding, n, and the effective radius of the atom in the bonded state, r [2]. χ = 0.31

n+1 + 0.50 r

(3.1)

The relationship between n+1 and Pauling’s electronegativity is shown in Fig. 3.2, r which was prepared using data in Table 1 in Ref. [2]. Except for Ag, Au, and Cu, the points roughly lie on a straight line. The large deviation for Ag, Au, and Cu is explained in Ref. [2] as follows: “Ag, Au, and Cu are known to form compounds

(n+1)/r

Fig. 3.2 Relationship between (n + 1)/r and Pauling’s electronegativity for many elements (see text for explanation of n and r)

Ag Cu

Au

3.1 Mixing Elements

37

in which they contribute more than one electron to the formation of covalent bonds. Hence the most probable cause of their wide deviation is the assumption of screening constants of unity for all electrons except the one in the final shell.” The value of n in binary compounds, n∗ , is discussed on the basis of the estimation of the electronegativity of radical AB [3] and is expressed by the following equation (obtained by inserting p = s = 1 in Eq. (6) in Ref. [1]). n∗ = (nA − 1) + 3

χA χ A + χB

(3.2)

By substituting n∗ in Eq. (3.2) for n in Eq. (3.1), expressing the effective radius r in Eq. (3.1) using the bonding length d (= 2r), and substituting the value of d for that of element A, dA , the work function of a binary compound can be expressed using the following equation. χAB = χA +

  3χA 0.62 −1 dA χA + χB

(3.3)

Combining Eqs. (3.3) and (2.8) gives the work function of binary compound AB as φAB = φA +

  1.41 2φA − φB − 0.34 . dA φA + φB − 0.68

(3.4)

In Fig. 3.3, thus calculated values of φAB are shown with experimental values taken from Ref. [1]. Fig. 3.3 Calculated work function versus measured work function for various binary systems [1]

7.0

Mn-O

Ni-O W-N Pd-O W-H

6.0

Ф (eV) (measured)

Zr-O

W-O Ni-H Fe-H Ta-H Zr-Cl Ta-N W-Be Zr-Ce Ti-Cl Co-H Hf-Cs

5.0

Hf-O

4.0

Cu-Ba

3.0

Ni-Ba

W-Ca W-Sr W-Li Ni-Cs Ag-Ba C-Cs Mo-Cs Ta-Cs Ti-Cs

2.0 1.0

0

W-La W-Y

1.0

2.0

W-Zr Mo-Th Ta-Th

4.0 3.0 5.0 Ф (eV) (calculated)

6.0

7.0

38

3 Modification of the Work Function

Fig. 3.4 Typical phase diagrams for binary systems

In the above discussion, the composition of the binary compounds is not mentioned, but a 1:1 composition is implied from the forms of the equations. Because the work function is expected to be dependent on the composition of binary compounds, the composition is expected to be one of the important parameters for work function tuning. Then, we must consider the phase diagrams of mixtures. When two elements are mixed, the mixture can be divided into three types: alloy, intermetallic compound, and separated phase (Fig. 3.4). Owing to a characteristic difference in the effect of the composition on the work function, the alloy type is divided into two: substitutional alloys and interstitial alloys. The atomic arrangement in each type of mixture is schematically illustrated in Fig. 3.5. Note that we introduced the Wigner–Seitz radius in addition to Pauling’s electronegativity when the factors determining the work function were discussed in Chap. 2. The Wigner–Seitz radius can be calculated for multiple-element systems with different compositions. Therefore, it is expected that the work function of multiple-element systems can be estimated in the framework of the jellium model by calculating the Wigner–Seitz radius of multiple-element systems and by using the relationship between the Wigner–Seitz radius and the work function.

3.1.1 Substitutional Alloys Basically, a metal with a low melting point has a low work function. Because the melting point is a quantity that represents the strength of atomic bonding, which is a parameter that reflects the bulk term of the work function, a low-melting-point metal is expected to have a smaller work function. Similarly, weak atomic bonding results in a low surface free energy. A metal with a low surface free energy tends to segregate on the surface of an alloy. Therefore, the surface composition of an alloy is richer in the low-melting-point metal element than the bulk composition, resulting in the work

3.1 Mixing Elements

39

(b) inters

(a) subs tu onal alloy

al alloy

B,C,N

(d) separated phase (with miscibility gap)

(c) intermetallic (ordered alloy)

Fig. 3.5 Schematic illustrations of atomic arrangements in different types of binary mixtures

work func on

Fig. 3.6 Schematic representation of influence of chemical composition on work function in binary substitutional alloys and corresponding phase diagram

temperature

function of the alloy being closer to that of a low-melting-point metal. By taking this into account, a schematic representation of the effect of the chemical composition on the work function in binary substitutional alloys and the corresponding phase diagram are shown in Fig. 3.6. Some examples of the work function in alloys are demonstrated in Fig. 3.7a– e, together with their phase diagrams. For Nb–Mo, both metals are early transition metals (the number of d-electrons is less than 5) and have high melting temperatures; a nearly linear relationship between the composition and the work function has been reported, as shown in Fig. 3.7a [4]. For Ag–Au, where both metals are noble but have different atomic sizes, the work function smoothly changes with the composition

composi on

composi on

40

3 Modification of the Work Function

(a)

(b)

Fig. 3.7 a Phase diagram and work function in Nb–Mo system (the bottom figure is replotted from the figure in Ref. [4]). b Phase diagram and work function [5] in Ag–Au system. c Phase diagram and work function [6] in Ag–Pd system. d Phase diagram and work function [7] in Cu–Pd system. e Phase diagram and work function [8] in Cu–Ni system

but in a concave manner rather than linearly (Fig. 3.7b) [5]. The deviation from a straight line agrees with the trend that the work function of a binary compound tends to be closer to that of the element with the lower work function of the two constituent elements [1], as mentioned at the beginning of Sect. 3.1. For Ag–Pd, a similar composition dependence has been reported (Fig. 3.7c) [6]. For Cu–Pd [7] and Cu–Ni [8], where a solid solution is formed at a high temperature but a compound is formed at a low temperature, a slight concave deviation from a linear relationship has been reported (Fig. 3.7d, e, respectively).

3.1.2 Interstitials (Metal Carbides and Nitrides) When the second element mixed with the mother metal is a small nonmetal atom such as carbon or nitrogen, the second element is not substituted at the position of

3.1 Mixing Elements

(c)

41

(d)

Fig. 3.7 (continued)

the mother metal but occupies an interstitial position (Fig. 3.5b). For such materials, a vacancy of a nonmetal atom is easily introduced. Owing to this, it is difficult to obtain homogeneous stoichiometric materials, and reliable reports on work function measurements are very limited. Therefore, we first examine the results of first-principles calculations. The calculated work functions for 3d, 4d, and 5d transition metals and their carbides, together with some experimental values, are shown in Fig. 3.8 [9]. It is obvious that (1) the work functions of an elemental metal and its carbide are similar; (2) the work functions of both an elemental metal and its carbide increase with increasing number of d-electrons up to d8 then decrease in noble metals (Cu, Ag, and Au); (3) the work function increases with the number of d-electrons by a larger amount for heavier elements (5d > 4d > 3d). The general trends from (1) to (3) are explainable in terms of the Wigner–Seitz radius rs (Fig. 3.9 [9]): the larger the rs , the smaller the work function, as shown in Fig. 2.11. The values of rs are negligibly changed by the inclusion of either carbon or nitrogen atoms (1). The values of rs for both an elemental metal and its carbide decrease with increasing

42

3 Modification of the Work Function

(e)

Fig. 3.7 (continued)

number of d-electrons up to d6 or d8 then increase for noble metals (Cu, Ag, and Au) (2). rs decreases with increasing number of d-electrons by a larger amount for heavier elements (5d > 4d > 3d) (3). According to Fig. 2.11, the work function decreases with increasing rs . However, the bulk term of the work function increases with rs , which is opposite to the tendency of the (total) work function. In Fig. 3.10a, b, the calculated band structures of some transition metal carbides and nitrides are shown [10], respectively. From their calculated Fermi energy (indicated as red lines for carbides and as blue lines for nitrides), it is possible to qualitatively deduce the bulk term of the work function from these results, which is shown as arrows. From LaC to TaC, the bulk term decreases, which agrees with the decrease in rs from LaC to TaC. For nitrides, the same trend is observed. When the bulk term is compared between the carbide and the nitride of the same metal, smaller bulk term values are obtained for the nitride by first-principles calculations, as shown in Fig. 3.11a–d ([10] for (a)–(c), [11] for (d)). As discussed in the following paragraphs, the kind of atom found in interstitial positions, either carbon or nitrogen, has little effect on the surface term of the work function. As a result, it is expected that the work function of the nitride will be smaller than that of the carbide for the same metal. The work functions for several carbides and nitrides of the same metals, obtained by both calculation and experiments, are listed in Table 3.1 [11]. One can see that the work function of the nitride is smaller than that of the corresponding carbide for all metals.

3.1 Mixing Elements

43

Fig. 3.8 Calculated work function values for 3d, 4d, and 5d transition metals and their carbides, together with some experimental values

Now, we discuss the effect of defects (carbon and nitrogen atom vacancies) on the work function. In Table 3.2, both experimental [12] and theoretical [13] work functions of tantalum carbides (TaCx) and hafnium carbides (HfCx) (100) with and without carbon vacancies are listed. For TaCx, an increase in the work function is obtained by the introduction of vacancies both experimentally and in theory, whereas a decrease in the work function of HfCx is obtained by the introduction of vacancies both experimentally and in theory. These vacancies are formed both inside the bulk and at the surface. Because the work function is composed of the bulk term and the surface term, the location of vacancies, either in the bulk or at the surface, is significant. Figure 3.12 shows the densities of states (DOSs) near the Fermi level for TaCx without vacancies, with vacancies only at the surface, and with vacancies both in the bulk and at the surface [13]. In Fig. 3.13, the corresponding cross sections of the electron density of TaCx (a) without vacancies and (b) with vacancies both in the bulk and at the surface are displayed [13]. From Fig. 3.12, it can be seen that the introduction of surface vacancies causes almost no change in the position of the Fermi level or the DOS (Fig. 3.12 middle). However, the position of the Fermi level is shifted to the

44

3 Modification of the Work Function

Fig. 3.9 Values of Wigner–Seitz radius for 3d, 4d, and 5d transition metals and their carbides

left (deeper energy level) by the introduction of vacancies both in the bulk and at the surface (Fig. 3.12 bottom). Because vacancies at the surface cause almost no change (Fig. 3.12 middle), the cause of the above Fermi level shift is the vacancies in the bulk. Therefore, it is concluded that the introduction of vacancies in the bulk causes the Fermi level to shift, resulting in an increase in the bulk term of the work function. Regarding the surface term, Fig. 3.13 implies that the degree of electron distribution outside the surface is similar for TaC with and without vacancies, which is due to the fact that the DOS at the Fermi level is mostly composed of electrons from Ta, as shown in Fig. 3.14 [13]. As a result, there is almost no difference between the surface term of TaC with and without vacancies. Therefore, the work function of TaC is increased by the introduction of vacancies through the increase in the bulk term owing to the Fermi level shift, with the surface term nearly unchanged. This conclusion agrees with Table 3.2.

3.1 Mixing Elements

45

Fig. 3.10 a Calculated band structure of some transition metal carbides [10]. b Calculated band structure of some transition metal nitrides [10]. Red lines are the Fermi level and red arrows show the bulk term of the work function

A similar discussion is possible for HfCx but with the work function changing in the opposite direction. The position of the Fermi level is shifted toward the right (shallower energy level) by the introduction of vacancies both in the bulk and at the surface, resulting in a decrease in the bulk term of the work function, as shown in Fig. 3.15a [13]. Taking into account the origin of electrons composing the DOS near the Fermi level of HfC without vacancies (Fig. 3.15b [14]), which is Hf, we can deduce again that the vacancies at the surface should not affect the surface term of the work function of HfC. Hence, it is expected that the introduction of vacancies in HfC will result in a decrease in the work function through the decrease in the bulk

46

3 Modification of the Work Function

(a) LaC

LaN

(b) HfC

HfN

Fig. 3.11 Fermi level positions of carbide (red lines) and nitride (blue lines) for a La [10], b Hf [10], c Ta [10], and d Ti [11]

term owing to the Fermi level shift toward a shallower energy. This change in the work function agrees with Table 3.2. In the cases of TaCx and HfCx, the introduction of carbon vacancies does not affect the surface term of the work function, but it does affect the bulk term, where the effect is opposite for TaCx and HfCx. Here, we discuss a general procedure for estimating the effect of carbon/nitrogen vacancies on the surface and bulk terms of the work function. If the effect of vacancy introduction on the Fermi level is calculated for all carbides and nitrides, the change in the bulk term upon vacancy introduction can be estimated directly from the shift of the Fermi level. However, the effect of vacancy introduction has been calculated for a limited number of carbides and nitrides. Therefore, we search for experimental values that indicate the size of the bulk term. Experimental studies on transition metal carbides and nitrides are mostly conducted from the viewpoint of hard coatings. A very large number of results on

3.1 Mixing Elements

47

(c) TaC

TaN

(d) TiC

TiN

Fig. 3.11 (continued)

hardness and its systematic trends have been reported. Because hardness represents the bond strength in materials and is considered as a good measure of the bulk term of the work function for materials with a similar type of bonding, we adopt the change in hardness upon vacancy introduction to estimate the effect on the bulk term [9]. Figure 3.16a–c respectively show the hardness of various carbides, nitrides, and carbonitrides as a function of the valence electron concentration (VEC), which

48

3 Modification of the Work Function

Table 3.1 Calculated work functions (eV) for carbide and nitride surfaces Relaxed

Unrelaxed

Theory

Exp.

TiC

4.62

4.19

4.7 [14]

3.8 [16]

TiN

3.25

3.03

TaC

4.16

3.85

2.92 [13] 4.24 [15]

4.3 [17]

(3.86: unrelaxed) TaN

3.45

3.79

4.0 [13]

HfC

4.28

3.86

4.5 [17]

HfN

2.79

3.13

3.85–3.90 [13]

NbC

4.26

3.85

4.2 [17]

NbN

3.33

3.59

3.92 [13]

ZrC

4.30

3.94

4.0 [17]

ZrN

2.79

2.84

2.94 [13]

Table 3.2 Work functions of (100) plane of TaCx and HfCx Experiment x TaCx

1.0 0.5

Theory φ

φ 4.38

1

4.73

Vacancy in bulk and surface

(+0.35) HfCx

1.0 0.6

4.11 (+0.27)

4.63

1

3.87

Vacancy in bulk and surface

(−0.76)

3.84

4.31 3.35 (−0.96)

was defined in Ref. [15]. The method of obtaining the VEC for each material is as follows: the VECs of a dn metal, carbon, and nitrogen are equal to n + 2, 4, and 5, respectively. According to this definition, the VECs of TaC1.0 , HfC1.0 , and HfC0.5 are 9, 8, and 6 (4 + 4 × 0.5), respectively. The VECs of these stoichiometric carbides are decreased by introducing carbon vacancies. Therefore, as seen from Fig. 3.16a, the hardness of TaC increases with vacancy introduction, whereas that of HfC decreases; accordingly, the bulk term also decreases. The above results agree with the previously mentioned calculations. From Fig. 3.16c, the hardness as a measure of the bulk term may provide a way of estimating the effect of mixing metals or carbon/nitrogen on the work function. First-principles calculations on stoichiometric carbides and nitrides are useful for clarifying the effect of vacancy introduction on the surface term, as demonstrated for TaCx and HfCx. For carbides and nitrides whose DOS near the Fermi level is mainly composed of electrons from the metal, the surface term is unaffected by the introduction of vacancies. Calculation results in the case of vacancies are not necessary, and therefore, the results for a rather large variety of materials are available.

3.1 Mixing Elements

49

occupied ←

EF

No vacancies

Surface vacancies

Surface & bulk vacancies

Fig. 3.12 DOSs near the Fermi level for TaCx without vacancies, with vacancies only at the surface, and with vacancies both in the bulk and at the surface [13]

Figure 3.17a [9] schematically shows the DOS of metal- or carbon-derived electrons near the Fermi level for 4d transition metal carbides, where the position of the Fermi level is shown by broken lines for individual carbides. The intensity ratio among the peaks marked (a), (b), and (c) in the figure varies with the number of d-electrons; however, the figure indicates the position of the Fermi level relative to the electron density of metals and carbon in transition metals. Here, electrons from carbon are not involved in the DOS at the Fermi level of ZrC, NbC, MoC, TcC, and AgC. For RuC, RhC, and PdC, vacancy introduction is speculated to affect the surface term of the work function. A similar schematic DOS for 5d transition metal carbides is shown in Fig. 3.17b [9]. Because there is no carbon-derived DOS at the Fermi level for HfC and TaC, a vacancy will not affect the surface term, and the change in the work function is determined by the change in the Fermi level. On the other

50 Fig. 3.13 Cross sections of electron density of TaCx a without vacancies and b with vacancies both in the bulk and at the surface [13]

3 Modification of the Work Function

(a) No vacancies

Φ= 3.84eV

(b) Surface & bulk vacancies

Φ= 4.11eV (+0.27)

Fig. 3.14 DOS of each component at the Fermi level for TaC with vacancies [13]

Fermi level

Ta-derived

3.1 Mixing Elements Fig. 3.15 a DOS near the Fermi level for HfCx without vacancies and with vacancies both in the bulk and at the surface [13]. b Density of states of each component at the Fermi level for HfC [14]

51

Fermi level

(a)

Fermi level (b)

Hf-derived

hand, for WC and PtC, vacancy introduction will affect the surface term, and the change in the work function will be more complicated, although if the structure of WC is hexagonal, there is almost no involvement of carbon-derived electrons in the Fermi level and the surface term will not be affected by carbon vacancies. Although examples of calculations for nitrides are limited, similar schematic pictures of the DOS near the Fermi level can be deduced from previous studies and are shown in Fig. 3.18a [9] for 4d transition metal nitrides and Fig. 3.18b [9] for 5d transition metal nitrides. It is speculated that for 4d metal nitrides the surface terms of the

52

3 Modification of the Work Function

Fig. 3.16 a Hardness of various carbides as a function of valence electron concentration (VEC) (see text for explanation of VEC). b Hardness of various nitrides as a function of valence electron concentration (VEC) (see text for explanation of VEC). c Hardness of three carbonitrides as a function of valence electron concentration (VEC) (see text for explanation of VEC)

work functions of YN, ZrN, NbN, MoN, PdN, and AgN are unaffected by nitrogen vacancy introduction, but those of TcN, RuN, and RhN are. For TaN, the surface term of the work function will not be affected by vacancy introduction but that of WN will be affected, although if the structure of WN is hexagonal, the surface term will not be affected by nitrogen vacancies. Most of the transition metal carbides and nitrides in practical use are composed of low-d metals. Therefore, there is almost no effect of vacancy introduction on the surface term of the work function in most cases. In summary, we can estimate the effect of vacancy introduction on the work function in the following way. First, determine the direction in which the Fermi level is shifted by vacancy introduction (bulk term). Then, find whether the DOS is composed of electrons from carbon (surface term). When electrons from carbon are not involved in the Fermi level, there is no effect of vacancy introduction on the surface term of the work function; this appears to be the case for most practical transition metal carbides. Then, the change in the work function owing to vacancy introduction is determined by the bulk term. It may be possible to estimate the

3.1 Mixing Elements

53

Fig. 3.17 a Schematic DOS of metal- or carbon-derived electrons near the Fermi level for 4d transition metal carbides. b Schematic DOS of metal- or carbon-derived electrons near the Fermi level for 5d transition metal carbides

effect of vacancy introduction on the Fermi level shift from the change in hardness upon vacancy introduction. The Fermi level deepens with vacancy introduction for materials whose hardness increases with vacancy introduction, whereas it becomes shallow for materials whose hardness decreases with vacancy introduction.

3.1.3 Intermetallic Compounds (Ordered Alloys) Intermetallic compounds are substitutional alloys but the arrangement of substituting positions is ordered, meaning that the crystal structure is different from that without alloying. This changes many properties such as density, hardness, and electronic structure, and consequently, the work function. It is expected that the work function is

54

3 Modification of the Work Function

Fig. 3.18 a Schematic DOS of metal- or carbon-derived electrons near the Fermi level for 4d transition metal nitrides. b Schematic DOS of metal- or carbon-derived electrons near the Fermi level for 5d transition metal nitrides

not a smooth function of the composition in binary systems that form the intermetallic compounds in the phase diagram. One example of the composition dependence of the work function is shown in Fig. 3.19a for the Ni–Al system [16], together with its phase diagram. This experimental result was obtained by fabricating a sample by the successive evaporation of Al and Ni, followed by annealing at 618 K for 16 h to achieve the alloy equilibrium. The change in the composition dependence of the work function as a result of annealing clearly demonstrates the characteristic behavior of the work function in intermetallic compounds. Before annealing, the mixture of Ni and Al did not reach the equilibrium state and its work function showed a relatively smooth composition dependence. However, after annealing, specific features appeared at around Ni75 Al25 ,

3.1 Mixing Elements

(a)

55

(b)

Fig. 3.19 a Phase diagram and work function [16] for Ni–Al system. b Phase diagram and work function [17] for Sm–Au system

Ni50 Al50 , and Ni25 Al75 , where stable intermetallic compounds were formed. The appearance of such specific features in the composition dependence of the work function is reasonable because marked changes in atomic density and valence electron density are often accompanied by the formation of intermetallic compounds. Another example, the Sm-Au system, is shown in Fig. 3.19b [17], together with its phase diagram. The phase diagram is very complicated and the formation of many intermetallic compound phases are expected. Possibly owing to the low solubility of Au in Sm, the work function increases sharply with increasing Au content on the Sm side. Then, the work function of the mixture is reasonably constant up to ca. 60 Au at% but increases suddenly at a Au content of around 70 at%. The composition dependence of the work function appears to be difficult to predict because of the many different compound phases. However, for binary systems that form intermetallic compounds, the generic relationship between the phase diagram and the composition dependence of the work function can be schematically represented as in Fig. 3.20.

56

3 Modification of the Work Function

Fig. 3.20 Schematic phase diagram and relationship between work function and bulk content for binary systems forming intermetallic compounds

3.1.4 Two Elements with Miscibility Gap There are combinations where two metals do not mix but separate, forming a miscibility gap in the phase diagram. The composition dependence of the work function exhibits specific features in accordance with the miscibility gap. The characteristic feature of this type of binary system is that the work function is insensitive to the composition in the range of the gap. The reason for this feature is explained as follows. When a small amount of element B is added to element A, B dissolves in A until the concentration of B reaches the miscibility gap. Up to this concentration, the composition dependence of the work function is the same as that of alloys because the mixture is actually an alloy. When the concentration of B exceeds the solubility limit, the mixture separates into two phases, B-dissolved A and A-dissolved B. Phase separation occurs until the concentration of B reaches the opposite side of the limit, where A is dissolved in B. For the entire composition range where the mixture separates into the two phases, the surface is covered by either B-dissolved A or A-dissolved B, because the one with the lower surface energy preferentially exists at the surface regardless of the mixing ratio. In this way, the work function of the mixture remains as that of one of the two phases at the solubility limit in the phase diagram with the lower surface energy. Beyond the gap, A is dissolved into B, so the composition dependence of the work function is that of an alloy. Therefore, the composition dependence of the work function is similar to that schematically shown in Fig. 3.21, which also shows the phase diagram.

Fig. 3.21 Schematic phase diagram and relationship between work function and bulk composition for binary systems having miscibility gap

3.1 Mixing Elements

57

Some examples of composition dependence are shown in Fig. 3.22a–c for Ni–Au [18], Au–Pt [19], and Pt–Ru [20], respectively, together with their phase diagrams. For Ni–Au, it is clear that the work function gradually changes near 100% Au, becomes constant regardless of the Ni content, and then suddenly decreases at 100% Ni. A very similar composition dependence has been reported for Au–Pt; on the side with higher solubility, the work function changes moderately but it sharply increases on the other side (near 100% Pt in this case). In contrast, the Pt–Ru system shows a very smooth composition dependence similar to that for an alloy, because it actually

(a) 1500

1455

Temperature, q C

1300

L

1100 1064

955

900

(Au,Ni)

810

700 500 300 100

(b)

0 Au

20

40 60 at. Percent Ni

80

1800

5.7

1400 1200

work func on (eV)

Temperature, q C

5.8

1769

L

1600

100 Ni

1260

(Au,Pt)

1000 1064

800 600 400

0 Au

20

40 60 at. Percent Pt

80

5.6 5.5 5.4 5.3

100

0

20

1800

2334 L

(Pt)

(Ru)

800 600 400

100

40 60 Ru (at%)

80

100

5.7

work func on (eV)

Temperature, q C

1769

1000

80

5.8

2130

1400 1200

60 Pt at%

(c) 1600

40

5.6 5.5 5.4 5.3 5.2 5.1

0 Pt

20

40 60 at. Percent Pt

80

100 Ru

0

20

Fig. 3.22 a Phase diagram and work function [18] for Au–Ni system. b Phase diagram and work function [19] for Au–Pt system. c Phase diagram and work function [20] for Pt–Ru system

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3 Modification of the Work Function

forms an alloy in a wide composition range and undergoes phase separation only in a very limited composition range (65–80% Ru), and the work function is similar on both sides of the gap.

3.2 Surface Termination Materials composed of more than one component, such as intermetallic compounds, compound semiconductors, and oxides, can have different terminations, as schematically shown in Fig. 3.23. A surface with a different termination has a different electron distribution at the surface, and hence a different value of the surface term of the work function. Since the bulk term of the work function is the same among differently terminated surfaces with the same bulk composition, the differently terminated surfaces have different work functions. For example, the intermetallic compound NiAl, whose crystal structure is schematically shown in Fig. 3.24a, has a different termination on the NiAl(100) surface, where either only Al (Al-term) or only Ni (Ni-term) exists at the surface. A work function of 4.6 eV has been obtained experimentally for the Al-term surface [21]. For the Ni-term surface, a first-principles calculation gave a work function of (a) Terminated by red atoms

(b) Terminated by green atoms

(c) Terminated by both red and green atoms

Fig. 3.23 Schematics of cross-sectional atom arrangements for typical types of surface termination

(a)

(b)

Fig. 3.24 Crystal structures of a NiAl, b ZnO, and c GaN

(c)

3.2 Surface Termination

59

5.17 eV, although an experimental value has not been obtained, whereas the calculated value for Ni(100) is 5.47 eV [22]. Because the experimentally reported work functions of Ni(100) are 5.22 eV [23], 5.53 eV [24], and 5.20 eV [25], the expected experimental work functions of the Ni-term NiAl(100) are 4.92, 5.23, and 4.90 eV, respectively (0.3 eV lower than the values for Ni(100)). In any case, it appears that the work function of the Ni-term NiAl(100) is higher than that of the Al-term NiAl(100). Although a differently terminated surface is structurally possible, in most cases, only one of the possible terminations or reconstructed surface structures is stable for intermetallic compounds. Often, only the work function for the most stable surface is experimentally available. The situation is different for compound semiconductors. It is possible to obtain a differently terminated surface for many compound semiconductors such as ZnO, GaAs, and GaN. Figure 3.24b shows the schematic crystal structure of ZnO. In Table 3.3, the reported work functions for ZnO(0001) (Zn-term) and ZnO(000-1) (Oterm) are summarized [26]. For GaN, whose crystal structure is shown in Fig. 3.24c, work functions of 4.2 eV for GaN(0001) (Ga-term) and 4.5 eV for GaN(000-1) (Nterm) have been reported, where the Ge-terminated GaN(0001) surface undergoes a 2 × 2 surface reconstruction [27]. Surface reconstruction often occurs on a clean surface of compound semiconductors and exhibits various work functions in accordance with the reconstruction. One example is the change in the work function during the molecular beam epitaxy (MBE) growth of GaAs [28], as shown in Fig. 3.25. Depending on the coverage of arsenic on the surface, the surface exhibits various types of reconstruction and the work function changes accordingly. Table 3.3 Work functions for different crystal orientations, terminations, and surface preparations of ZnO Face

Surface preparation

Work function

(0001) Zn-term

Ion-bombarded and 700 K anneal

6.0

(000-1) O-term

(10-10)

Cleaved at 300 K

4.95

Cleaved and annealed to 800 K

4.64

Ion-bombarded and 700 K anneal

3.7

Cleaved at 300 K

4.25

Cleaved at 200 K

4.4

Cleaved at 200 K and annealed to 400–700 K

3.9

Ion-bombarded and 825 K anneal

5.05

Cleaved at 300 K

4.64

Cleaved at 290 K

4.7

Cleaved at 290 K and annealed to 750 K

4.5

60

3 Modification of the Work Function

Fig. 3.25 Change in work function during MBE growth of GaAs [28] (see text for explanation)

3.3 Adsorption or Segregation One of most frequently applied techniques for modifying the work function is to adsorb a second metal on the mother surface. Adsorbates on the surface change the electron distribution at the surface and modify the surface term of the work function while maintaining the bulk term of the material. “Adsorption” is the term used when the adsorbate atoms originate from outside the material. As we mentioned briefly in the section on alloys, there is a possibility that one of the alloy components is concentrated on the surface, resulting in a surface composition different from that of the bulk; this is called “segregation”. When the alloy is a very dilute alloy (impurity level), the second element practically exists only on the surface, resulting in a similar surface structure to that formed by adsorbing the second element on the mother surface (Fig. 3.26). In both cases, only the surface term of the work function is modified. In many cases, a surface with adsorption cannot be distinguished from Fig. 3.26 Schematic cross section of atoms near the surface with a segregation and b adsorption

(a)

(b)

3.3 Adsorption or Segregation

61

one with segregation, but they are often different from the viewpoint of thermodynamic equilibrium. Usually, the surface composition realized by segregation is at thermodynamic equilibrium, whereas a surface with adsorption is not in many cases. Because a surface with adsorption is realized when an adsorbate is supplied from the outside, it cannot be reproduced when the adsorbate is removed for some reason. On the other hand, a surface with segregation can, in many cases, be reproduced by heating because an adsorbate can be supplied from inside to achieve thermodynamic equilibrium. When the work function is modified by adsorption or segregation, the position of the adsorbate on the surface is strongly dependent on the method of modification. Figure 3.27a, b demonstrate an example of Al segregation in Cu-9 at% Al(111) obtained by first-principles calculations [29]. The work functions are different when Al is on the surface (adatom), inside the top layer (replace), and in the bulk. The position of the adsorbate affects the surface electron distribution decisively and thus the surface term of the work function. In practice, only one state is thermodynamically stable and realized under equilibrium. Furthermore, the distance between an adsorbate and the top surface of the substrate also affects the work function. The effect of the distance on the work function of N-adsorbed W determined by firstprinciples calculations is shown in Fig. 3.28 [30]. It can be seen that the direction of the change in the work function, either an increase or decrease, upon nitrogen adsorption varies with the distance. In reality, the distance is determined by nature, and the work function is accordingly determined by the stable distance. Note that the work function does not necessarily increase when an element with a larger work function (than the substrate) is adsorbed. Not only the electron transfer between the adsorbate and the substrate but also the surface roughness at the atomic level affects the work function. Figure 3.29 shows experimentally obtained changes in the work function upon the adsorption of various elements on W(110) as a function of coverage [31]. At the first stage of adsorption up to a coverage of one monolayer, the work function decreases upon adsorption for most elements. There is one more type of surface segregation that is not under equilibrium, as schematically shown in Fig. 3.30. When a thin film is deposited and annealed, rapid diffusion and surface segregation of an underlayer element are often observed [32– 34]. The mechanism of this type of segregation [35] and the method of generally predicting whether this type of segregation occurs for a specific combination of an underlayer element and overlayer film element [36, 37] have been reported. Underlayer elements reach the surface through grain boundary diffusion, and segregation is achieved under a quasi-stable state. Although it is not under thermodynamic equilibrium, a surface with this type of segregation can also be reproduced by heating, as in the case of equilibrium surface segregation. Therefore, a change in the work function occurs with this type of segregation. Some examples are given in Fig. 3.31 [38, 39]. Adsorption or segregation has been utilized to modify the work function in practical applications. So-called thoria-coated tungsten or iridium (tungsten or iridium coated with thorium dioxide, ThO2 ) shows a stable low work function and has been used as an electron emitter for vacuum gauges and other electron sources. A zirconia

62

3 Modification of the Work Function

(a)

replace

adatom

Top view

C B A C B

side view

A C B A

A

(b)

adatom

replace

Calc.WF Exp. WF

replace 4.45 4.39

adatom 4.15 -

bulk

bulk 4.41 4.33

Fig. 3.27 a Different atomic models for Al surface segregation on Cu-9 at% Al(111). b Calculated and experimental work functions for different atomic models

3.3 Adsorption or Segregation

63

N

Fig. 3.28 Influence of the distance on the work function of N-adsorbed W(100) [30]. The left figures show top (a) and side (b) views of the atomic arrangement, the upper right figure (right (a)) shows the charge distribution as a function of vertical distance, and the bottom right figure (right (b)) shows the change in the work function as a function of distance

Atomic density of W(110)

Fig. 3.29 Change in work function upon adsorption of various elements on W(110) [31], whose work function is 5.25 eV

64

3 Modification of the Work Function

Higher or longer hea ng

Grain boundary diffusion is dominant film Sub.

a)

film Sub.

alloy, intermetallics

b)

film Sub.

c)

Sub.

Fig. 3.30 Schematic illustrations of nonequilibrium surface segregation, where diffusion stops at (a) and no further interface reaction occurs. With annealing at higher temperature or much longer time, interface reaction starts (b) and finally film element is consumed to form an alloy or intermetallic (c). (see text for explanation)

(ZrO2 ) coating instead of a thoria coating has been developed for the same application to avoid the use of radioactive thorium. The adsorption of alkali metals on various materials is also a popular method of decreasing the work function. To generate heavy ions for implantation, a Cs coating is used to promote the ionization of heavy ions. Hydrogen termination on semiconductors, such as silicon, diamond, and GaAs, is a frequently used technique for modifying surface band bending and sometimes results in the formation of a surface with a negative electron affinity (NEA), which is utilized in photodetectors.

3.4 Deposition To form a surface with adsorbate atoms, as mentioned in Sect. 3.3, adsorbate atoms are deposited on the mother surface. If the amount of deposited atoms increases so that the coverage of the deposited atoms exceeds one layer, we call this process “deposition” instead of “adsorption”. Here the surface is completely covered by the deposited atoms, whereas the surface is partially covered in the case of adsorption. The work function decreases with adsorption for most elements, as shown in Fig. 3.29. When the thickness of the adsorbed layer exceeds one atomic layer, we can see that the work function gradually approaches that of the deposited element and reaches that of the deposited element at around 3–4 atomic layers. This situation is realized when the deposited layer grows in a layer-by-layer mode, as schematically illustrated in Fig. 3.32. If a deposited layer does not grow in a layer-by-layer mode, islands are formed, and the work function reaches that of the layer of metal with a rough surface (lower than that with a flat surface, as discussed in Sect. 2.3) when more than 3–4 layers of the surface are completely covered by the overlayer metal. An exception to the above case of layer-by-layer growth occurs in mismatched lattice epitaxy, where a film with a crystal structure not in the bulk phase diagram grows to a certain thickness and has a different work function from that of a film with a crystal structure in the bulk diagram.

3.4 Deposition

65

(a) Segregated Cu

Ti film Cu

Decrease in work function (eV)

(b) i)

Decrease in work function (eV)

ii)

0.00

Segregated Cu

-0.05 -0.10

Segregated Ti

-0.15 -0.20 -0.25

Nb film 0

1

2 3 4 5 Cu concentration (at.%)

6

Ti film Cu subst.

0.00 -0.05 -0.10 -0.15 -0.20 -0.25 -0.30 0

5

10

15

20

25

30

Ti concentration (at.%)

Fig. 3.31 a Change in work function upon nonequilibrium surface segregation of substrate atoms for Ti film/Cu substrate (see text for explanation). b Change in work function upon nonequilibrium surface segregation for Nb film/Ti film/Cu substrate: (i) as a function of segregated Cu concentration; (ii) as a function of segregated Ti concentration

66

3 Modification of the Work Function

Fig. 3.32 Schematic plot of change in work function upon film deposition grown in layer-by-layer mode

A system comprising an overlayer film on an underlayer is often not under thermodynamic equilibrium and undergoes changes in its chemical composition upon heat treatment via diffusion and segregation, for example, as schematically illustrated in Fig. 3.33. As a result, the desired work function is often not obtained by deposition or the work function changes with time. Figure 3.34 shows an example of a change in the C–V curve (characteristic of band alignment at the interface, which is governed by the work function) [40]; this will be discussed in detail in Chap. 5. When the work function is to be modified by deposition, a system should be designed by taking the diffusion/reaction into account.

(a) Metal-A

(b)

(c)

Metal-B

Fig. 3.33 Schematic of cross-sectional atomic arrangement for interface modification: a ideal interface insertion, b mixing at the interface, c reaction at the interface to form a new compound

3.4 Deposition

67

Fig. 3.34 Example of change in electric property caused by interface reaction [40]. The states of the specimens are schematically shown in the upper figures and their C–V characteristics are shown in the lower ones

References 1. Yamamoto S, Susa K, Kawabe U (1974) Work functions of binary compounds. J Chem Phys 60:4076–4080 2. Gordy W (1946) A new method of determining electronegativity from other atomic properties. Phys Rev 69:604–607 3. Wilmshurst JK (1957) Electronegativity of radicals. A method of calculation. J Chem Phys 27:1129–1131 4. Savitskiy EM, Litvak LN, Burov IV (1971) Work function of alloy single crystals in the system molybdenum-niobium. Zh Tekh Fiz 41:2431–2432 (in Russian) 5. Fain SC Jr, McDavid JM (1974) Work-function variation with alloy composition: Ag-Au. Phys Rev B 9:5099–5107 6. Crampin S (1993) Segregation and the work function of a random alloy: PdAg(111). J Phys Condens Matter 5:L443–L448 7. van Langeeld AD, Hendrickx HACM, Nieuwenhuys BE (1983) The surface composition of PdCu alloys: a comparative investigation of photoelectric work function measurements, Auger electron spectroscopy and calculations based on a broken bond approximation. Thin Solid Films 109:179–192 8. Takasu Y, Konno H, Yamashina T (1974) Work function of well-defined surface of coppernickel alloy plates. Surf Sci 45:321–324 9. Yoshitake M (2014) Generic trend of work functions in transition-metal carbides and nitrides. J Vac Sci Technol a 32:061403-1–61406 (and references therein) 10. Fernández Guillermet A, Häglund J, Grimvall G (1993) Cohesive properties and electronic structure of 5d-transition-metal carbides and nitrides in the NaCl structure. Phys Rev B 48:11673–11684 11. Kobayashi K (2001) First-principles study of the electronic properties of transition metal nitride surfaces. Surf Sci 493:665–670 12. Gruzalski GR, Lui SC, Zehner DM (1990) Work-function changes accompanying changes in composition surfaces of HfCx , and TaCx . Surf Sci Lett 239:L517–L520 13. Price DL, Cooper BR, Wills JM (1993) Effect of carbon vacancies on carbide work functions. Phys Rev B 48:15311–15315

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14. Chauhan M, Gupta DC (2013) Electronic, mechanical, phase transition and thermo-physical properties of TiC, ZrC and HfC: high pressure computational study. Diam Relat Mater 40:96– 106 15. Delgado JM (1998) Ternary and multinary compounds. In: Tomlinson RD, Hill AE, Pilkington RD (eds) Institute of physics conference series, vol 152. CRC, Boca Raton 16. Franken PEC, Ponec V (1974) Photoelectric work functions of Ni-Al alloys: clean surfaces and adsorption of CO. J Catal 35:417–426 17. Kiwa N, Gotoh Y, Tsuji H, Ishikawa J (2002) Relationship between composition and work function of gold–samarium alloy thin films. Vacuum 66:517–521 18. Franken PEC, Ponec V (1976) Photoelectric work function measurements on nickel-copper and nickel-gold alloy films: clean surfaces and adsorption of ethylene and carbon monoxide. J Catal 42:398–407 19. Bouwman R, Sachtler WMH (1970) Photoelectric determination of the work function of goldplatinum alloys. J Catal 19:127–139 20. Bouwman R, Sachtler WMH (1972) Photoelectric investigation of the surface composition of equilibrated Pt-Ru alloy films in ultrahigh vacuum and in the presence of CO. J Catal 26:63–69 21. Chaturvedi S, Strongin DR (1997) A trend in the C-O bond strength of CH3 O(ad) on NiAl(100), FeAl(100) and TiAl(010). Effect of the alloy Fermi level. Catal Lett 47:105–109 22. Ostroukhov AA, Floka VM, Cherepin VT (1996) Electronic structure and magnetic ordering on the (001) surfaces of FeA1, CoAl and NiA1 alloys with bulk B2-structure. Surf Sci 352– 354:919–922 23. Baker BG, Johnson BB, Maire GLC (1971) Photoelectric work function measurements on nickel crystals and films. Surf Sci 24:572–586 24. Strayer RW, Mackie W, Swanson LW (1973) Work function measurements by the field emission retarding potential method. Surf Sci 34:225–248 25. Eib W, Alvarado SF (1976) Spin-polarized photoelectrons from nickel single crystals. Phys Rev Lett 37:444–446 26. Jacobi K, Zwicker G, Gutmann A (1984) Work function, electron affinity and band bending of zinc oxide surfaces. Surf Sci 141:109–125 27. Lorenz P, Haensel T, Gutt R, Koch RJ, Schaefer JA, Krischok S (2010) Analysis of polar GaN surfaces with photoelectron and high resolution electron energy loss spectroscopy. Phys Status Solidi B 247:1658–1661 28. Massies J, Devoldere P, Linh NT (1979) Work function measurements on MBE GaAs(001) layers. J Vac Sci Technol 16:1244–1247 29. Yoshitake M, Karas I, Houfek J, Madeswaran S, Song W, Matolín V (2010) Position of segregated Al atoms and the work function: experimental low energy electron diffraction intensity √ √ analysis and first-principles calculation of the ( 3× 3)R30° superlattice phase on the (111) surface of a Cu–9at.%Al alloy. J Vac Sci Technol A 28:152–158 30. Michaelides A, Hu P, Lee MH, Alavi A, King DA (2003) Resolution of an ancient surface science anomaly: work function change induced by N adsorption on W{100}. Phys Rev Lett 90:246103-1-246103–4 31. Kolaczkiewicz J, Bauer E (1985) The dipole moments of noble and transition metal atoms adsorbed on W(110) and W(211) surfaces. Surf Sci 160:1–11 32. Oura K, Hanawa T (1979) LEED-AES study of the Au-Si(100) system. Surf Sci 82:202–214 33. Tsukimoto S, Morita T, Moriyama M, Ito K, Murakami M (2005) Formation of Ti diffusion barrier layers in thin Cu(Ti) alloy films. J Electron Mater 34:592–599 34. Holloway K, Fryer PM, Cabral C Jr, Harper JME, Bailey PJ, Kelleher KH (1992) Tantalum as a diffusion barrier between copper and silicon: failure mechanism and effect of nitrogen additions. J Appl Phys 71:5433–5444 35. Yoshitake M, Yoshihara K (1992) Surface segregation of substrate element on metal films in film/substrate combinations with Nb, Ti and Cu. Surf Interface Anal 18:509–513 36. Yoshitake M, Aparna Y, Yoshihara K (2001a) General rule for predicting surface segregation of substrate metal on film surface. J Vac Sci Technol A 19:1432–1437 37. https://surfseg.nims.go.jp/

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38. Yoshitake M, Aparna Y, Yoshihara K (2001b) Tailoring of work function by surface segregation. Appl Surf Sci 169–170:666–670 39. Aparna Y, Yoshitake M, Yoshihara K (2000) Work function and surface segregation study on Nb/Ti/Cu multilayer films. Jpn J Appl Phys 39:4447–4450 40. Lu CH, Wong GMT, Deal MD, Tsai W, Majhi P, Chui CO, Visokay MR, Chambers JJ, Colombo L, Clemens BM, Nishi Y (2005) Characteristics and mechanism of tunable work function gate electrodes using a bilayer metal structure on SiO2 /and HfO2 . IEEE Electron Device Lett 26:445–447

Chapter 4

Measurement of Work Function

The principle of work function measurement is primarily divided into two concepts in accordance with the electron density of states (DOS) at the Fermi level. As we saw in Sect. 2.1, if there are electrons at the Fermi level, it is possible to excite these electrons and observe the minimum energy needed for excitation, which is the work function as defined previously. In this case, the absolute values of the work function are obtainable. There are different methods of electron excitation, as shown in Fig. 4.1. Measurement techniques can also be divided in accordance with the method of measuring emitted electrons, namely, current measurement or spectroscopic methods. In the case of semiconductors or insulators, there are almost no electrons at the Fermi level. In this case, the minimum energy necessary for the emission of electrons is not the work function but the ionization energy. Therefore, a less direct method, utilizing the contact potential difference, is applied for work function measurement, wherein only relative values can be obtained. The method utilizing the contact potential difference is also applicable when electrons exist at the Fermi level, and is often used for measurements of, for example, the change in the work function with time upon chemisorption on metals. In a special case, an absolute work function can be measured for semiconductors or insulators, which will be discussed in Sect. 4.2.2.

4.1 Utilizing Electron Emission Current Measurement The measurement of the electric current of emitted electrons either by thermal excitation (heating a specimen) or by the application of a high electric field is rather simple from an instrumental viewpoint. No sophisticated, expensive equipment is necessary. Therefore, work function values were mostly obtained by these measurement methods until the 1970s. Thermal and field emissions are still widely used

© The Author(s), under exclusive license to Springer Japan KK, part of Springer Nature 2021 M. Yoshitake, Work Function and Band Alignment of Electrode Materials, NIMS Monographs, https://doi.org/10.1007/978-4-431-56898-8_4

71

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4 Measurement of Work Function

metal Photon excitaon

vacuum Thermal excitaon Electric field = 0

Work funcon

Extract electrons via strong field

Tunneling electrons Valence band

Strong electric field

Fig. 4.1 Schematic illustration of different methods of electron excitation (see text for detailed explanation)

for work function measurement because these are the main techniques of generating electron beams. Care should be taken for photoelectron emission. Work function values measured before the 1980s “by photoelectron emission” were obtained by measuring photoelectron emission current as described in Sect. 4.1.3, whereas nowadays, “measured by photoelectron emission” mostly refers to the spectroscopic technique described in Sect. 4.2. For all methods in this section, equations relating the electric current and work function are derived with the free electron approximation. The complicated shape of the DOS near the Fermi level is not taken into account. Therefore, the deviation of the DOS from that for free electrons is a source of error in the obtained work function. In addition, many effects are neglected when the equations are applied. For example, the effects of the electric field and the inhomogeneity of the temperature on thermal emission, that of the electric field on the electron emission area in field emission, and that of the inhomogeneity of the electron emission area on photoelectron emission are neglected in most cases.

4.1.1 Thermal Emission The electrons near the Fermi level are distributed energetically in a stepwise manner at zero Kelvin (curve a), as shown in Fig. 4.2. The distribution changes with the temperature, as shown in Fig. 4.2 and described by Eq. (4.1), which is called the Fermi–Dirac distribution function. Among the thermally excited electrons, a certain proportion of them have a momentum toward the outside of the surface in accordance with their statistical distribution. When the kinetic energy of such electrons exceeds the work function, these electrons are emitted, producing electric current. f (E) =

exp

1  ε−1  τ

+1

ε=

E EF

τ=

kB T EF

(4.1)

4.1 Utilizing Electron Emission Current Measurement Fig. 4.2 Fermi distribution function as a function of energy with the scale E/E F at different temperatures, where E F is the Fermi level

73

Fermi distribution function

1 −1

= (a)

+1

1.0 =

0.5

0.0 0.0

=

τ= 0 0.02 0.05 0.1 0.2 0.4

0.5

1.0

1.5

2.0

The electron current density JS is described by the Richardson–Dushman equation (Eq. 4.2) [1], where φ is the work function, T is the temperature in Kelvin, kB is the Boltzmann constant, m and e are the mass and charge of an electron, respectively, and h is Planck’s constant.   4π mekB2 φ A= (4.2) JS = AT 2 exp − kB T h3

log(current density/(temperature2)

By transforming Eq. (4.2) into Eq. (4.3), it is clear that plotting the inverse of the temperature as the ordinate and the logarithm of ( TJS2 ) as the abscissa reveals a linear relation, as schematically shown in Fig. 4.3. The gradient of the straight line corresponds to − kφB .

Inverse of temperature Fig. 4.3 Schematic plot of the relationship between temperature and emitted electron current density for thermal emission, expressed by Richardson–Dushman equation

74

4 Measurement of Work Function

Fig. 4.4 Current density versus temperature for ϕ = 4.5 eV during thermal emission

20

Js [mA/m2 ]

15

10

5

0 500

log

JS φ 1 − logA = − × 2 T kB T

1000 1500 Temperature [K]

2000

  JX φ = exp − AT 2 kB T

(4.3)

Therefore, from a plot such as that shown in Fig. 4.3, the work function is obtained. In order to apply this thermal emission method, a material should be able to withstand a relatively high temperature because the electron current obtained at a temperature of, for example, 1000 K is insufficient. Because of this fact, materials measured by this method are high-melting-point metals such as W, Mo, and Ta or compounds such as LaB6 and BaO. In Fig. 4.4, current density versus temperature for φ = 4.5 eV is plotted as an example (A = 1.2 × 106 [A/m2 K2 ]). For the measurement, the temperature dependence of the work function discussed in Chap. 2 and the effect of the electric field applied in order to guide emitted electrons to the anode should be taken into account.

4.1.2 Field Emission In this measurement, electrons are emitted not by being excited to overcome the potential barrier, but by tunneling through the potential barrier, whose thickness becomes 1 nm upon the application of a strong electric field, as shown in Fig. 4.1. The electron current density J0 is described using Eq. (4.4), which is called the Fowler–Nordheim equation [2], where F is the strength of the electric field at the emitter surface, y is the Schottky lowering of the work function barrier, and t(y) and ν(y) are correction terms for the image force barrier.   3 Bφ 2 AF 2 exp − J0 = φ F

e2 , A= 8π ht 2 (y)

√ 4 2mν(y) , B= 3e

√ y=

e3 F φ (4.4)

4.1 Utilizing Electron Emission Current Measurement

75

When J0 [A/cm2 ], F [V/cm], and φ [eV] are used, A = 1.54 × 10−6 (for t 2 (y) = 1), √ B = 6.83 × 107 (for ν(y) = 1), and y = 3.78 × 10−4 × φF . Because y represents the effect of the field on the barrier height, when F → 0 (zero-field limit), t 2 (y) and ν(y) are equal to 1. Approximations of t 2 (y) = 1.1 and ν(y) = 0.95 − y2 have been proposed [3]. In practice, the field emission current I and the applied voltage V are experimentally obtained. Therefore, J0 and F in Eq. (4.4) are respectively replaced by I and V using the emission area α and the local field conversion factor β as follows. I = J0 × α, F = β × V Then Eq. (4.4) can be rewritten as Eq. (4.5) using I and V instead of J0 and F, respectively [4].   3 2 9.8 (βV )2 7 φ exp −6.49 × 10 +√ I = 1.4 × 10 α φ βV φ −6

(4.5)

Here, it should be noted that β has a unit of cm−1 . When both the emitter and the collector of emitted electrons are flat parallel plates, F = E (the strength of a macroscopic electric field) = Vd , where d is the distance between the emitter and the collector. In this case, β = d1 . However, in some studies the local field conversion factor has been defined as F = β − Vd for nonflat emitters, and one should be careful when using a local field conversion factor. Equation (4.5) can be transformed into Eq. (4.6). 

I log V2

 =a+

b V

(4.6)

Upon plotting the relationship in Eq. (4.6) with VI as the abscissa and the logarithm of VI 2 as the ordinate, a graph such as Fig. 4.5 is obtained. If the work function, emission area, and local field conversion factor are constant for the entire range of the applied voltage, then the slope is constant, meaning that the graph is a straight line. Here, base of a logarithm is taken as 10 instead of e (Napier’s constant) for convenience in later discussion. Then, the slope b is represented by Eq. (4.7) and the intercept a is represented by Eq. (4.8). b = −2.82 × 10



3 2

β 2

 β a = log 1.4 × 10−6 α φ

(4.7) 4.26 + √ φ

(4.8)

Fig. 4.5 Schematic plot of the relationship between field strength and field emission current expressed by Eq. (4.6)

4 Measurement of Work Function

log(I/V2)

76

Inverse of applied voltage V

It is well known that the slope deviates slightly for the same specimen, as shown in Fig. 4.6a [5]. Usually, work functions are obtained using Eq. (4.7) (the slope of a plot such as that in Fig. 4.6a). However, the slight deviation in the gradient of the slope ends up as a relatively large deviation in the obtained work function. On the basis of numerous experiments and Fowler–Nordheim plots of the results, the utilization of the so-called S–K chart, a plot with the intercept as the abscissa and the slope as the ordinate, has been proposed [4]. It has been revealed that when the slopes of the plot deviate for the same specimen, there is a linear relationship between the slope and the intercept, as shown in Fig. 4.6b [5]. The reasons for the deviation have been analyzed, and it has been proposed that the work function of a specimen having a similar (macroscopic) shape to a reference with a known work function can be obtained from the slope of the S–K chart (Fig. 4.7) [6], even if a plot such as Fig. 4.5 deviates from a straight line.

Fig. 4.6 a Example of experimental results illustrating the relationship of Eq. (4.6) for W emitter with (011) facet [5]. b Example of experimental results illustrating the relationship of Eq. (4.6) for W emitter with (011) facet [5]

4.1 Utilizing Electron Emission Current Measurement

77

Fig. 4.7 a Influence of work function and apex radius of an emitter in S–K chart [6] (see text for explanation). b F-N characteristics of Spindt-type virgin Pt cathode (circles), after the first CO treatment (squares), and after the second CO treatment (diamonds) in S–K chart [6]. The solid and broken lines show the equi-work function line and the equi-apex radius line, respectively

4.1.3 Photoelectron Emission In this method, light with a fixed energy is irradiated to the specimen and photocurrent is measured as a function of the specimen temperature [7]. This resembles the method of thermal emission, because the change in the current density is a result of the change in temperature. The current density J is expressed by Eq. (4.9), where α is the probability that an electron adsorbs a photon and f (μ) is the Fowler function.  J = αAT 2 f

hν − eφ kB T

 A=

4π mekB2 h3

(4.9)

  A plot with khν as the abscissa and ln TJ2 as the ordinate is similar to the graph BT shown in Fig. 4.8. The dots represent experimental results, where the photocurrent under a fixed photon energy is measured as a function of the specimen temperature. The solid line represents Eq. (4.9) with φ = 0. Therefore, by shifting the line given by Eq. (4.9) so that it overlaps with the measured plot, i.e., the broken line in Fig. 4.8, the work function of the specimen φ is obtained from the shift in the lateral direction (2.6 eV in this case).

4.2 Utilizing Electron Emission Spectroscopy Because the work function is a potential barrier for electrons, and the excitation of electrons by providing energy from the outside causes this barrier to be overcome, resulting in electron emission, measuring either the minimum excitation energy or

4 Measurement of Work Function

ln(J/T2)

78

5 4 3 2 1 0 -1 -2 -3 -4 -5

-100

0

100

200

300

400

500

600

(hν-e )/kBT Fig. 4.8 Example of a plot represented by Eq. (4.9) when photoelectron emission current density is measured as a function of temperature (closed circles), the solid line represents Eq. (4.9) with φ = 0, and the broken line represents Eq. (4.9) shifted to fit the closed circles, giving φ = 2.6 eV

the energy of emitted electrons having zero kinetic energy with respect to the Fermi level should give the work function. Work function measurement by photoelectron emission yield spectroscopy (PYS), where the photoemission current is measured as a function of the excited photon energy, is based on the former principle. To use the latter principle, the measurement of the electron energy is essential, where the electrons can be excited in many ways. Because the threshold energy of emitted electrons having zero kinetic energy is called the secondary electron cutoff, this type of method is called “secondary electron cutoff spectroscopy” in this chapter. Usually, different names are given for different methods of electron excitation, such as UPS (ultraviolet photoelectron spectroscopy), XPS (X-ray photoelectron spectroscopy), and AES (Auger electron spectroscopy), where the primary aim of these techniques is not the measurement of the work function. In order to obtain the absolute value of the work function, the energy of emitted electrons with respect to the Fermi level must be known. In Fig. 4.9, the principles of the above two types of electron emission spectroscopy are schematically illustrated.

4.2.1 Photoelectron Emission Yield Spectroscopy (PYS) The principle of photoelectron emission yield spectroscopy is schematically illustrated in Fig. 4.10. In this method, the photoelectron emission yield is measured as a function of the photon energy. Let us assume a specimen having the DOS of an electron as shown in Fig. 4.10. Electrons having energy above EV AC − hν are excited by photons, making the photoelectron yield proportional to the area of the DOS above EV AC − hν. Because no electrons are excited by photons having energy below φ,

4.2 Utilizing Electron Emission Spectroscopy

79

Emied electrons

Photoelectron emission yield spectroscopy (PYS)

Electrons from EF level

Photoelectron spectroscopy

EMAX

hν Core level



EMIN EF Posion of EMIN → Posion of EMAX → ΔEVB metal

Fig. 4.9 Schematic illustration of the principles of two types of electron emission spectroscopy, photoelectron emission yield spectroscopy and photoelectron spectroscopy (see text for explanation)

Fig. 4.10 Schematic illustration of principle of photoelectron emission yield spectroscopy (see text for explanation)

80

4 Measurement of Work Function

the threshold of the photoelectron emission yield is equal to φ. If the free electron approximation is employed, the shape of the DOS near the Fermi level is represented by a quadratic function. Therefore, the photoelectron emission yield is proportional to (hν − φ)2 . In practice, the photoemission current should be divided by the photon intensity at each photon energy to obtain the photoelectron emission yield. By plotting the square root of the photoelectron emission yield as a function of the photon energy, as schematically shown in Fig. 4.11, the threshold photon energy, which is equal to the work function, is obtained. In Fig. 4.12, plots for polycrystalline Pt and Al measured in air are shown as examples. Because measurements are performed Fig. 4.11 Schematic illustration of plot of square root of photoelectron emission yield versus photon energy to obtain work function (see text for explanation)

Fig. 4.12 Plots obtained by photoelectron emission yield spectroscopy for polycrystalline Pt and Al measured in air

4.2 Utilizing Electron Emission Spectroscopy

81

in air, the surfaces of Pt and Al are not clean, meaning that the obtained values are different from those in the references. As expected from the principle in Fig. 4.10, the electrons emitted at the threshold photon energy (Eth ) are those at the lowest binding energy, not those at the Fermi level, since the electrons are thermally excited near the Fermi level. Therefore, at high temperatures, the apparent work function obtained from Eth in a plot such as Fig. 4.12 becomes lower. Moreover, from Fig. 4.10, Eth corresponds to the ionization energy (IE) for semiconductors and insulators since the electrons emitted at Eth are those at the lowest binding energy. No electrons are emitted until the photon energy reaches Eth , resulting in much less difficulty in charging with this technique than with measurement techniques using secondary electron cutoff spectroscopy, as described in Sect. 4.2.2. The IE of insulators and semiconductors with low carrier density, such as organic semiconductors, can be measured by PYS. In the case of insulators and semiconductors, a plot is usually made with the cube root, not the square root, of the photoelectron emission yield as the ordinate [8, 9], but the assumption of the cube root is not necessarily realistic. The order of the photoelectron emission yield to be used is still an open question. Although Eth obtained for insulators and semiconductors is the IE, it is also possible to obtain the work function in a special case. When an insulator or semiconductor is a thin film on a metallic substrate and electrons from the metal substrate can penetrate the film so that they contribute to photoelectron emission spectra, the work function of the insulator or semiconductor can be obtained as follows. First, the photoelectron emission spectrum of the metallic substrate should be measured to obtain the work function of the substrate. Then the substrate is covered by the insulator or semiconductor, causing a lateral shift of φ in the photoelectron emission spectrum of the substrate, as illustrated in Fig. 4.13a. Upon covering the substrate with the film, a new feature from the film appears, the threshold energy of which

Fig. 4.13 a Schematic illustration of photoelectron emission yield spectrum for thin insulator or semiconductor (B) on metal (A). b Relationships between measured quantities in (a)

82 Fig. 4.14 Schematic illustration of applying bias to either specimen (black) or collector electrode (blue) (see text for explanation)

4 Measurement of Work Function

V



A

photoelectron

V A

I

corresponds to the IE of the film. As seen in Fig. 4.13b, the work function of the film φB is equal to (φA − φ), where IE = φA − φ + (EF − EV ) and ε ≡ (EF − EV ) in the figure. By this method, both the work function of the film and the band offset or p-type Schottky barrier (EF − EV ) are obtained. This means that the band alignment between the substrate metal and the insulator or semiconductor on the substrate can be determined. For practical measurements of the photoelectron emission current, bias voltage must be applied to either the electron collector (blue in Fig. 4.14) or the sample (black in Fig. 4.14), so that all the emitted electrons with nearly zero kinetic energy reach the collector. The current is usually very small, of picoampere or sub-picoampere order. Therefore, a good noise shield is also necessary. To find an appropriate bias voltage, a suitable shape and arrangement of the collector are essential for reliable measurement.

4.2.2 Secondary Electron Cutoff Spectroscopy (UPS, XPS, AES …) The principle of secondary electron cutoff spectroscopy is schematically illustrated in Fig. 4.15a. In this method, monochromatic photons with an energy of hν are used to excite electrons in a specimen, and the kinetic energy distribution of the emitted electrons is analyzed. The kinetic energy of an electron is equal to hν−(EF − EB )−φ, where EF , EB , and φ are the Fermi level, the binding energy in the specimen referring to the Fermi level, and the work function of the specimen, respectively. When the kinetic energy distribution is plotted as the spectrum shown on the right side in Fig. 4.15a, electrons with energy EMIN are emitted with zero kinetic energy, whereas those with energy EMAX are emitted with kinetic energy hν − φ. In practice, negative bias voltage is applied to the specimen to accelerate electrons with zero kinetic energy

4.2 Utilizing Electron Emission Spectroscopy

83

Fig. 4.15 a Principle of measuring work function difference between two materials by secondary electron cutoff spectroscopy; b secondary electron cutoff spectra for Cu and Pt with X-ray excitation under −4 V bias [10], where the work function of Pt is larger than that of Cu (see text for explanation)

toward the energy analyzer, making the spectrum shift uniformly upward. Because the bias voltage only shifts the spectrum, the energy difference between EMAX and EMIN is equal to hν − φ. By measuring EMAX and EMIN , the work function of the specimen φ is obtained from the following equation. φ = hν − (EMAX − EMIN )

(4.10)

The precision of the measurement strongly depends on the calibration of the energy scale of the electron analyzer. Therefore, the larger the value of hν, the less precise the value of φ. The spread of the photon energy affects the precision with which the position of EMIN is determined. As a result, a He-discharged ultraviolet lamp or synchrotron radiation with absolute photon energy calibration is usually used for the measurement of absolute work functions. If the work function is φ  instead  , whereas the position of of φ, the position of EMIN in the spectra changes to EMIN EMAX is maintained.    φ  = hν − EMAX − EMIN

(4.11)

From the above, it is clear that the difference in the work function can be measured by monitoring the position of EMIN , the secondary electron cutoff, with any type of electron excitation. The source of electron emission can be an X-ray, hard-X-ray,

84

4 Measurement of Work Function

electron beam, or ion beam. Examples of the secondary electron cutoff region of XPS spectra for polycrystalline Cu and Pt are shown in Fig. 4.15b [10]. The position of the secondary electron cutoff for Cu is located at a lower kinetic energy (a higher binding energy) than that for Pt, meaning that the work function of Cu is smaller than that of Pt. Because the energy difference of the secondary electron cutoff position indicates the absolute difference in the work function, the relative work function can be obtained from any secondary electron cutoff spectrum. Note that a low work function does not mean a higher secondary electron emission current, as demonstrated in Fig. 4.16. In the figure, inner-shell photoelectron intensity images, a secondary electron image, and an emission image at the low electron kinetic energy (work function image, taken at the energy marked at the bottom left spectrum in Fig. 4.16) measured on mesh-shaped patterns of Cu and Pt are shown. The patterns of the secondary electron image and the work function image are opposite, i.e., higher secondary electron emission from Pt, but a higher intensity for electron with low kinetic energy from Cu [10]. This technique is also applicable to the work function measurement of semiconductors that do not charge up (i.e., they have relatively high electric conductivity). The principle of the measurement is illustrated in Fig. 4.17. Because there are no electrons in the Fermi level in this case, the energy difference (EMAX − EMIN ) is equal not to hν − φ but to hν − φ − (EF − EV ), where (EF − EV )(≡ EV B ) can be obtained from the binding energy of electrons with the highest kinetic energy. From experimentally obtained values for (EMAX − EMIN ) and EV B , the work function of semiconductors is obtained as follows. φ = hν − (EMAX − EMIN ) − EV B

(4.12)

Figure 4.18 demonstrates an example of the work function measurement of ZnO. In this example, hν = 21.22 eV, (EMAX − EMIN ) = 14.39, and EV B = 2.75, which give φ = 4.08 eV. The above method cannot be applied to bulk insulators, which charge up. However, in the special case that a very thin insulator film is on a metallic substrate and does not charge up, the work function of the insulator film can be measured by the same principle as that discussed for a semiconductor. The example of an ultrathin epitaxial alumina film on an NiAl(110) single crystal is shown in Fig. 4.19. The bottom spectrum is for clean NiAl(110), and the change in the spectrum upon the oxidation of NiAl(110) with the growth of an epitaxial alumina film can be seen, where unit of oxygen dosage is L (Langmuir, 1 [L] = 1.3 × 10−4 [Pa] × 1 [s]). The secondary electron cutoff position shifts towards a higher binding energy, indicating a decrease in the work function. This type of measurement is possible when an insulator film is sufficiently thin for electrons generated inside the insulator to be able to tunnel either to the vacuum or to the substrate. Here are some tips for the measurement of the secondary electron cutoff position. Because secondary electrons have very low kinetic energy, they are easily affected by weak electric and magnetic fields. For most commercially available equipment for electron spectroscopy, the magnetic field is shielded, which is not usually a problem.

4.2 Utilizing Electron Emission Spectroscopy

85

Pt

Cu

Pt 4f

Cu 2p

Imaging with intensity at this energy

Secondary electron (-4 V bias) 4

Secondary electron image

Secondary electron (zero bias)

X 104

4

-4V

2

1

0V intensity for mapping

Cu > Pt

3

Pt c/s

c/s

3

X 104

2 1

Cu Pt

0 1482 1482 1478 1476 1474 1472 Binding Energy (eV)

0

Cu

Pt > Cu 1480 1475 1470 1465 Binding Energy (eV)

Fig. 4.16 Photoelectron images and secondary electron images with/without bias on specimens patterned with Pt and Cu [10] (see text for explanation)

86

4 Measurement of Work Function

Fig. 4.17 Principle of measuring work function of semiconductors by secondary electron cutoff spectroscopy with photons (see text for explanation)

Fig. 4.18 Example of work function measurement of ZnO by secondary electron cutoff spectroscopy using UV light with bias voltage of −3 V (see text for explanation)

Regarding the electric field, caution is advised because the voltage applied to the specimen for the measurement generates an electric field, which might affect the measurement. In order to extract electrons with nearly zero kinetic energy towards the energy analyzer, a negative bias of 5–20 eV is applied to the specimen while the electric potential of both the outer shield of the energy analyzer and the chamber is

4.2 Utilizing Electron Emission Spectroscopy

87

He I

11.00

-10 V bias 9.45

26.79

-9.45 He II

Normalized intensity

26.73 Shift in O 2p 26.61

26.50

26.28

26.17

26.07 25

20

15

10

-5

-10

Binding energy (eV) Fig. 4.19 Example of work function measurement of an insulator film, where the change in the work function during the growth of an ultrathin epitaxial alumina film on NiAl(110) single crystal has been measured by secondary electron cutoff spectroscopy with He lamp excitation under − 10 V bias (see text for explanation)

grounded, as shown in Fig. 4.20a. Because there is a potential difference between the specimen and the surrounding area, if there is a bump around the specimen, the electric field converges to the bump, disturbing the line of electric force. If the line of electric force is disturbed, low-energy electrons emitted from the specimen cannot reach the analyzer, resulting in an error in the secondary electron cutoff position. Therefore, one should avoid bumpy structures around the specimen as much as possible, as shown in Fig. 4.20b.

88

4 Measurement of Work Function

(a)

Energy analyzer

(b)

good

poor

specimen Fig. 4.20 a Schematic illustration of electric potential for the measurement setup in secondary electron cutoff spectroscopy; b examples of good and poor sample mounting for measurements to avoid disturbing the electric field

4.3 Utilizing Contact Potential Difference Measurement The methods described in Sects. 4.1 and 4.2 enable the measurement of the absolute value of the work function in principle. However, there are many cases where only relative values or changes in the work function are important and absolute values are not necessary in experiments. In particular, when the change in the work function with time is measured, quick measurements are important rather than obtaining absolute values. For such cases, the contact potential difference (CPD) between two materials, a reference material (reference) and a specimen, is measured. In Fig. 4.21, the energy diagram for the generation of a CPD is schematically illustrated. It can be seen from the figure that the CPD is the difference in the work function between two materials. Either the Kelvin probe method or the diode method is used to measure the CPD.

4.3.1 Kelvin Probe Method When there is a CPD between two metals, as in Fig. 4.21, a capacitor is formed. When the reference side of one of the metals vibrates so that the distance (x) between the two metals changes with time, a current (i) is induced in the circuit (Fig. 4.22). The induced current is expressed by the following equation: i=

d εε0 A dQ = V × , dt dt x

(4.13)

4.3 Utilizing Contact Potential Difference Measurement

89

Electrically connect two materials and move them closer Contact potenal difference = work funcon difference EVAC

EVAC

EF

EF

Fig. 4.21 Schematic illustration of the energy diagram for the generation of contact potential difference (see text for explanation)

Fig. 4.22 Principle of Kelvin probe method (see text for explanation)

x = x0 + x1 sin(ωt + α)

x1  x0 ,

(4.14)

where V is the potential difference between the reference and the specimen under a backing potential (BP), i.e., V = CPD + BP, ε is the dielectric constant of the

90

4 Measurement of Work Function

space between the reference and the specimen, ε0 is the vacuum permittivity, and A is the area of the capacitor. i = −εε0 A ·

x1 ω cos(ωt + α) · V x02

(4.15)

If a bias voltage, sometimes called a backing potential, is applied to the reference so that the potential of the reference is equal to that of the specimen, V = 0 and no induced current flows. This is the principle of the Kelvin probe method. In other words, the Kelvin probe method detects a CPD by detecting the current induced by changing the distance between the reference and the specimen. In practice, the induced current is measured as a function of the backing potential (Fig. 4.23). When no current is induced, V should be zero. From the equation V = CPD + BP, the backing potential for the zero-induced current corresponds to the CPD value but with the opposite sign. The typical distance x used in the measurement is about 0.5 mm. In principle, the distance between the reference and the sample does not affect the measured CPD. However, it often does in experiments, possibly owing to a nonideal capacitor arrangement. Therefore, once the absolute work function of the reference is determined using a sample whose absolute work function is known, a series of work function measurements should be conducted with the same distance. However, it

Fig. 4.23 Schematic illustration of measuring contact potential difference by Kelvin method (see text for explanation)

4.3 Utilizing Contact Potential Difference Measurement

Δ

EVAC EC EF

91

IP BP

EV Nonmetallic specimen

Reference probe (metal)

Nonmetallic specimen

Reference probe (metal)

Fig. 4.24 Schematic illustration of contact potential difference measurement for a nonmetallic specimen (see text for explanation)

is not easy to maintain the same distance when the specimen must be removed for treatment in another chamber or when the specimen is exchanged. From Eq. (4.15), it can be seen that when the amplitude of the induced current is plotted as a function of BP, the gradient of the plot is inversely proportional to x02 . Therefore, by adjusting the distance so that the gradient in Fig. 4.23 is kept constant throughout the whole set of measurements, the effect of the distance on CPD measurements is minimized. In this method, no direct current flows between the reference and the specimen; therefore, the CPD value of semiconducting or insulating specimens can be measured. In Fig. 4.24, a potential diagram of the capacitor, where the specimen is either a semiconductor or insulator (nonmetallic), is shown. Because CPD values are determined by the position of the Fermi level regardless of the electron density, the principle of the measurement is exactly the same as that described above for metal specimens.

4.3.2 Diode Method This method is less commonly used these days since many sophisticated methods have been developed. However, this method used to be popular owing to its concise experimental setup [11, 12]. Figure 4.25 illustrates the measurement principle. One must prepare a cathode that emits electrons. E is the electric field applied to induce electron emission from the cathode. When the work function of the cathode (φB ) is lower than that of the specimen (φA ), the emitted electrons cannot reach the specimen owing to the potential barrier under zero BP. Therefore, no current flows between the cathode and the specimen. While applying a BP to the specimen, a current (i) starts flowing when the potential barrier disappears. The BP at this time is equal to the work function difference between the cathode and the specimen. A plot of current versus BP is schematically illustrated in Fig. 4.26. In practice, the current– BP curve for the reference specimen is first measured and then the BP(V0 ) required

92

4 Measurement of Work Function

(a)

(b)

(c)

Fig. 4.25 Schematic illustration of principle of work function difference measurement by diode method: a setup of measurement system, b band diagram under zero bias; c band diagram under BP bias, where there is no contact potential difference (see text for explanation)

Fig. 4.26 Schematic illustration of the relationship between BP bias voltage and diode current in the diode method (see text for explanation)

for a certain current to flow is obtained. Then, the BP bias (V ) required to obtain the same current for the specimen is measured. The difference, V − V0 , is the contact potential difference between the reference and the specimen.

4.4 Other Methods

93

4.4 Other Methods There are many other methods of measuring the work function, both old and new. Here, a distinctive indirect method called the photoemission of adsorbed xenon (PAX) is described because its measurement principle is considerably different from those of the above methods and it is still utilized for some specific measurements.

4.4.1 Photoemission of Adsorbed Xenon (PAX) The work function is measured indirectly in this method, where the inner-shell binding energy of xenon adsorbed on the surface of a specimen is measured. Originally, the method was developed to measure the local work function on patched surfaces (patches with different work functions exist on the surface) at the time when there were no scanning probe microscopy techniques. The principle of the method is that the inner-shell binding energy (usually the Xe 5p1/2 peak is used) of xenon on the surface having a work function of φ is constant when the vacuum level is used as the reference but becomes variable when the Fermi level is used as the energy reference, as in Eq. (4.16).   EBV Xe 5p 12 = EBF Xe 5p 12 + φ

(4.16)

 Here, EBV Xe 5p 12 is the binding energy of Xe 5p1/2 with respect to the vacuum  level, EBF Xe 5p 21 is that with respect to the Fermi level, and φ is the work function of the specimen. This method is based on the fact that Xe adsorbs on the specimen without chemical interaction and only with van der Waals interaction, meaning that there is no chemical shift in the Xe binding energy upon adsorption. A schematic energy diagram of this relation for two patches with different work functions is shown in Fig.4.27. The relationship described by Eq. (4.16) has been verified by measuring EBE Xe 5p 12 on various samples whose work functions are already known  (Table 4.1), and the value of EBV Xe 5p 21 is given as 12.3 ± 0.1 eV [13]. As an extension of this method, the use of Kr and Ar as adsorbates instead of Xe has also been proposed [14]. The work function obtained with Kr and Ar adsorption is in agreement with those obtained with Xe adsorption. However, Wandelt [13], who examined the work function of NiAl(110) with various compositions, cautioned that there could be preferential adsorption sites on the surface and that work functions obtained by inert gas adsorption do not necessarily agree with those obtained by secondary electron cutoff spectroscopy (compared using values measured by UPS).

94

4 Measurement of Work Function

Fig. 4.27 Schematic energy diagram of the relationships among the Xe core level, Fermi level, and vacuum level for two metal patches with different work functions Table 4.1 Binding energy of Xe 5p1/2 peak with respect to the Fermi level (EB F (5p(1/2 ))) and calculated with respect to the vacuum level (EB V ) by EB V = EB F (5p(1/2 )) + φ: φ = clean metal work function [13] Sample

ϕ

Pd(110)

5.20

7.03

12.23

Pd(100)

5.65

6.75

12.40

Pd(111)

5.95

6.47

12.42

Pt(111)

6.40

5.90

12.30

Ir(100)(1 × 1)

6.15

6.24

12.39

Ir(100)(5 × 1)

6.00

6.38

12.38

Ru(0001)

5.52

6.60

12.12

W(100)

4.50

7.90

12.40

W(110)

5.10

7.13

12.23

Ni(110)

4.65

7.75

12.40

Ni(100)

5.30

6.90

12.20

Ni(111)

5.40

6.80

12.20

Cu(110)

4.48

7.80

12.28

EB F (5p1/2 )

EB V = E B F + ϕ

Al(111)

4.53

Ag(111)

4.75

7.45

12.20

Cs(poly)

1.80

10.50

12.30

Xe gas

12.15

13.4

4.4 Other Methods

95

Experimentally, the inert gas must be introduced at a low temperature in an XPS instrument. As pointed out in Ref. [11], the possibility of inert gas atoms migrating inside the specimen, not merely remaining at the surface, should be taken into account.

References 1. Richardson OW (1912) Some applications of the electron theory of matter. Lond Edinb Dubl Phil Mag Ser 6(23):594–627 2. Fowler RH, Nordheim LW (1928) Electron emission in intense electric fields. Proc R Soc London A 119:173–181 3. Spindt CA, Brodie I, Humphrey L, Westerberg ER (1976) Physical properties of thin-film field emission cathodes with molybdenum cones. J Appl Phys 47:5248–5263 4. Ishikawa J, Tsuji H, Inoue K, Nagao M, Sasaki T, Kaneko T, Gotoh Y (1993) Estimation of metal-deposited field emitters for the micro vacuum tube. Jpn J Appl Phys 32:L342–L345 5. Gotoh Y, Mukai K, Kawamura Y, Tsuji H, Ishikawa J (2007) Work function of low index crystal facet of tungsten evaluated by the Seppen-Katamuki analysis. J Vac Sci Technol B 25:508–512 6. Gotoh Y, Nagao M, Nozaki D, Utsumi K, Nakatani K, Sakashita K, Betsui K, Tsuji H, Ishikawa J (2004) Electron emission properties of Spindt-type platinum field emission cathodes. J Appl Phys 95:1537–1549 7. Fowler RH (1931) The analysis of photoelectric sensitivity curves for clean metals at various temperatures. Phys Rev 38:45–56 8. Kane EO (1962) Theory of photoelectric emission from semiconductors. Phys Rev 127:131– 141 9. Gobeli GW, Allen FG (1962) Direct and indirect excitation processes in photoelectric emission from silicon. Phys Rev 127:141–149 10. Yoshitake M (2006) Evaluation of electric potential at metal-insulator interface using electron spectroscopy and Kelvin probe techniques. Mater Res Soc Proc 894:45–53 11. Holzl J, Schulte FK (1979) Work function of metals. In: Solid state physics. Springer tracts in modern physics, vol 85. Springer-Verlag, Berlin Heidelberg New York 12. Anderson PA (1941) A new technique for preparing monocrystalline metal surfaces for work function study. The work function of Ag(100). Phys Rev 59:1034–1041 13. Wandelt K (1984) Surface characterization by photoemission of adsorbed xenon (PAX). J Vac Sci Technol A 2:802–807 14. Onellion M, Erskine L (1987) Experimental test of the photoemission of adsorbed xenon model. Phys Rev B 36:4495–4498

Chapter 5

Modification of Band Alignment via Work Function Control

In this chapter, the band alignment in an ideal case will be discussed. Ideally, the band alignment is solely determined by the work functions of the materials in contact. In many cases, however, the interface band alignment deviates from the ideal condition for many intrinsic and extrinsic reasons. Even in such nonideal cases, an ideal contact is considered as a starting point. Therefore, ways of modifying the band alignment through work function control in an ideal case are of great importance.

5.1 Ideal Band Alignment The band alignment between a metal (work function of φm ) and an n-type semiconductor (work function of φs ) in an ideal case is shown in Fig. 5.1. Similarly to the surface discussed in Chap. 2 (Fig. 2.8a), the electron distribution at an edge where the surrounding electric condition changes sharply deviates from that in a uniform region, forming an interface dipole and an interface potential due to the dipole. In the case of an interface, electron redistribution occurs so that the Fermi level of the metal aligns with that of the semiconductor (or insulator) in order to realize thermodynamic equilibrium in the electronic system. The Fermi level is aligned by introducing an interface potential so that the vacuum level at the contact is continuous. This electron redistribution or the interface potential causes band bending at the interface. Therefore, the amount of band bending E is equal to the difference in the work function between the metal and semiconductor (φm − φs ). As a result, the Schottky barrier height (SBH), which is the activation energy needed to excite an electron in the Fermi level of the metal to the conduction band of the semiconductor (EC ), is equal to {(EC − EF ) + E}. Using the relationships EA = φs − (EC − EF ) and E = (φm − φs ), the SBH is expressed as (φm − EA), where EA is the electron affinity of the semiconductor.

© The Author(s), under exclusive license to Springer Japan KK, part of Springer Nature 2021 M. Yoshitake, Work Function and Band Alignment of Electrode Materials, NIMS Monographs, https://doi.org/10.1007/978-4-431-56898-8_5

97

98

5 Modification of Band Alignment via Work Function Control

Fig. 5.1 Band alignment between a metal (work function of φm ) and an n-type semiconductor (work function of φs ) in an ideal case (see text for explanation)

n-semiconductor EVAC

metal EVAC

IP EC EF

EA EF

EV

EVAC

SBH

EVAC

EA ΔE

- EA

Band bending ΔE =

EC EF EV -

Although the Schottky contact condition is illustrated in Fig. 5.1, an ohmic contact (SBH = 0 or negative) is also possible for a contact between a metal and semiconductor (Fig. 5.2). Whether the contact is the Schottky type or ohmic is determined by the work functions of the metal and semiconductor. This suggests that when utilizing a metal–semiconductor interface as a switch, a metal with a larger work function is preferred, whereas a metal with a low work function is preferred when the metal acts as a simple conductor of excited electrons in semiconductors such as in solar cell applications. When a Schottky contact is formed, SBH = (φm − EA). Therefore, a plot of SBH for various metals against their work function should be a straight line with a slope of 1, as illustrated in Fig. 5.3. An example of the relationship between SBH and the work function of a metal in contact with HfO2 is presented in Fig. 5.4 [1]. In this experiment, SBH was determined by internal photoemission spectroscopy. In

(a) Schoky metal n-semiconductor

EVAC

EVAC ΔE

EF

SBH =

- EA

EC EF EV

(b) ohmic metal n-semiconductor

EVAC

EVAC

EA ΔE

EF

EC EF

EV SBH = 0 → ohmic

Fig. 5.2 Energy diagrams of a Schottky contact and b ohmic contact (see text for notation)

5.1 Ideal Band Alignment

99

Fig. 5.3 Schematic plot of SBH against work function of metal in contact (see text for explanation)

→SBH

ideal → slope = 1 reality

S

Fig. 5.4 Relationship between Schottky barrier height and metal work function in contact with HfO2 [1]

d (SBH ) dF m EA of metal



Schottky barrier height (V)

S

d (SBH ) dIm

Metal work function (eV) this example, a nearly ideal Schottky relation can be observed. However, in practical systems it is often observed that the slope of the plot of SBH vs the work function of the metal is less than 1. The slope of such plots is called the ‘S factor’, which will be discussed in Chap. 6. When the equation SBH = (φm − EA) is not satisfied, an “effective work function” φm,eff that satisfies the equation SBH = φm,eff − EA is often used. In such cases, the work function (defined for a surface) is sometimes called the “vacuum work function”. Using φm,eff , the effective work function is plotted against the work function instead of SBH against the work function of the metal. In an ideal case, the effective work function is linearly dependent on the work function of the metal with a slope of 1. A nearly ideal band alignment has also been reported for a metal–SiO2 contact, whereas a nonideal alignment has been reported for a metal–ZrO2 contact, as shown in Fig. 5.5 [2]. When semiconductor devices are used as field-effect transistors (FETs), electrons flow from a source to a drain, where the flow is controlled by the voltage applied to the gate (Fig. 5.6a). Among the most commonly used FETs are the so-called MOSFETs,

100

5 Modification of Band Alignment via Work Function Control

Fig. 5.5 Relationship between effective work function and metal work function for contacts with SiO2 and ZrO2 [2] (see text for explanation)

(a)

(b)

metal

source

insulator

drain

n-semiconductor



EVAC EF

insulator

gate

n-semiconductor

EVAC EA ΔE EC EF EV

ΔE =

-

Fig. 5.6 a Schematic illustration of MOS and b energy level diagram across the red broken line in (a)

5.1 Ideal Band Alignment

101

Fig. 5.7 Change in band bending under bias for ideal MOS (see text for explanation)

metal

n-semiconductor

insulator

EVAC EF

ΔE =

insulator

EVAC

Flat band V FB =

-

EF VFB

EVAC

EA ΔE

EC EF EV

-

EVAC EA

EC EF EV

metal-oxide-silicon field-effect transistors. The energy and alignment across a gateinsulator–semiconductor interface in a MOSFET are schematically illustrated in Fig. 5.6b. The band aligns so that the Fermi levels of the gate, insulator, and semiconductor all coincide, usually resulting in band bending in the semiconductor at the insulator–semiconductor interface. This interface acts as a channel between the source and drain. Changing the direction and amount of band bending by applying a voltage to the gate generates carriers at the channel or causes them to vanish, which is the principle of MOSFET operation. In Fig. 5.7, the change in band bending with gate bias application for an ideal MOSFET is illustrated. The bias voltage needed to make a band flat (zero band bending) is called the flat-band voltage VFB and is often used as a characteristic of a MOSFET. If a MOSFET is ideal, VFB is equal to the work function difference between the gate metal and the semiconductor, VFB = φm − φs . Similar to the case of metal–semiconductor interfaces, the above equation is not satisfied in many practical systems. Therefore, the effective work function in this case is determined by the equation VFB = φm,eff − φs . A plot of the effective work function against the (vacuum) work function is often used instead of a plot of the flat-band voltage against the work function. If the slope of the plot is 1, the system is an ideal MOSFET. Figure 5.8 shows an example of the

102

5 Modification of Band Alignment via Work Function Control

metal HfO2 Si

Fig. 5.8 Relationship between effective work function and vacuum work function for metal/HfO2 /Si MOSFET [3], where the slope of the red broken line is nearly 1, indicating that the system is almost under the ideal condition

relationship between the effective work function and the (vacuum) work function for a metal/HfO2 /Si MOSFET obtained from C–V measurements [3]; it shows a nearly ideal situation. It is useful to mention the interface between two metals, metal A and metal B, with different work functions. The Fermi level is aligned with the contact of metal A with metal B. Because the electron affinity (equal to the work function for metals) is different for the two metals, electron transfer occurs at the contact, forming an electric dipole layer at the interface. As in the case of metal–semiconductor interfaces, the band bends at the interface but in a very thin region owing to the large carrier density in metals (Fig. 5.9a). The change in the vacuum level with the lateral position on the surface at the interface between two metals, which is suggested to occur from Fig. 5.9a, has actually been demonstrated using a specimen with a mesh pattern of Pt and Cu (Fig. 5.9b) [4]. The right side of Fig. 5.9b shows the work function mapping of the mesh pattern, obtained from the secondary electron cutoff, together with a schematic illustration of the specimen on the left side. Because the thickness of the layer with band bending is 1–3 atomic layers, electrons can tunnel without encountering the barrier. This is why there is no Schottky barrier at metal–metal contacts. Details of nonideal interfaces in a Schottky contact or a MOSFET structure are given in Chap. 6.

5.2 Modification of Band Alignment

103

(a)

(b) Specimen Pt

Secondary electron cutoff spectra

Cu 4

Work func on mapping

X 104

-4V intensity for mapping

100 μm

c/s

3 2

1

Cu Pt

0 1482 1482 1478 1476 1474 1472 Binding Energy (eV)

100 μm

Fig. 5.9 a Band diagram of interface between two different metals (see text for explanation). b Work function mapping of a specimen with two different metals at contact [4] (see text for explanation)

5.2 Modification of Band Alignment From Sect. 5.1, it is clear that for most cases, the work function is one of the important factors determining the band alignment at the interface, regardless of whether or not the interface contact is ideal. Therefore, to modify the band alignment, it is effective to modify the work function of the electrode metals. As an example, SBHs at the interface between n-type ZnO and various metals are given in Table 5.1 [5]. Pauling’s electronegativity is also shown in Table 5.1. It can be seen that when a metal species forms strong bonds with oxygen, the interface becomes an ohmic contact. Metals that form an ohmic contact tend to have smaller electronegativity values, which is expected from the general relationship between Pauling’s electronegativity and the work function (Fig. 2.10 in Chap. 2) and Fig. 5.2. In Fig. 5.10, the energy difference between the Fermi level (EF ) and the valence band maximum (EV ), which is called the p-type Schottky barrier (p-SBH), is plotted as a function of the electronegativity of various metals for interfaces with Si and Ge [6]. The figure clearly shows the linear

104 Table 5.1 Examples of Schottky barrier height difference for different metals in contact with n-ZnO

5 Modification of Band Alignment via Work Function Control Interface electric Metals Pauling’s Schottky barrier property electronegativity height (eV) Ohmic

Schottky

Ti

1.54

Re

1.9

Al

1.61

Ru

2.2

In

1.78

Au

2.54

0.59

Ag

1.93

1.69–0.83

Au

2.54

0.37–0.66

Pd

2.2

0.59–0.68

Ag

1.93

Ag

1.93

Au

2.54

Au

2.54

0.6–0.71

Au

2.54

0.64–0.69

Ag

1.93

Pt

2.28

0.89–0.93

Pt

2.28

0.79

Ag

1.93

0.5–0.6

Au

2.54

Au

2.54

Pd

2.2

0.84

0.59–0.67

relationship between p-SBH and electronegativity. These results prove that modification of the band alignment by tuning the work functions of metals is reasonably effective. The ways of modifying the band alignment are analogous to those of modifying the work function. The strategies of modification are schematically illustrated in Fig. 5.11. There are three main strategies: (a) interface termination, (b) the insertion of an interfacial layer, and (c) interface segregation. In the following, examples of each strategy are presented. SBHs between ZnO and Pt-Ru alloys are compared for O-terminated and Zn-terminated interfaces in Fig. 5.12 [7]. The SBHs for differently terminated interfaces differ for Pt-Ru alloys with the same composition, indicating that interface termination affects the band alignment at the interface. Figure 5.13 schematically illustrates the principle of modifying the band alignment by interface layer insertion. By inserting a thin layer of a metal with work function φmB , the SBH is significantly reduced. Depending on the work function of the inserted layer, the SBH can be increased or decreased, or an ohmic contact can be formed. Examples of SBH modification by the insertion of an interfacial layer are demonstrated in Fig. 5.14a–c [8] for interfaces between n-type Ge and various metals. The SBH between either

5.2 Modification of Band Alignment

105

Fig. 5.10 Energy difference between Fermi level (E F ) and valence band maximum (E V ) as a function of electronegativity of various metals for interfaces with Si and Ge [6]

n-type Ge(111) or n-type Ge(001) and various metals is rather insensitive to the work function of the metal in contact. However, upon inserting a few monolayers of amorphous Ge3 N4 , the SBH becomes more sensitive to changes in the metal work function. The mechanism of this phenomenon is not straightforward, in contrast to the case of metal insertion shown in Fig. 5.13. However, these examples show that the insertion of a thin layer is a powerful method for modifying the band alignment. One should carefully consider the type of layer that should be inserted to modify the band alignment. Figure 5.15 illustrates a case of interface layer insertion without any effect. When a layer is inserted inside a semiconductor, not at the interface, there is no effect on the band alignment at the metal–semiconductor interface. If the inserted layer has similar carrier characteristics but different crystallinity from the semiconductor and no p-n type junction is formed at the interface between the inserted layer and the semiconductor, then there is almost no effect of inserting a layer on the band alignment.

106

5 Modification of Band Alignment via Work Function Control

a) Interface termina on

b) Inserted layer

c) Interface segrega on

or

or

red atoms are inserted

Fig. 5.11 Schematic illustration of strategies for band alignment modification (see text for explanation)

Fig. 5.12 Schottky barrier height between ZnO and Pt-Ru alloys for O-terminated and Znterminated interfaces [7]. The barrier height is dependent on the composition and also the terminating atoms of ZnO

5.2 Modification of Band Alignment

Metal A Metal B

107

Band diagram of interface between metal A and n-semiconductor EVAC EA EVAC SBH

EC EF EV

EF

Band diagram of interface with inser on of interface layer of metal B EVAC

EVAC EA

EF

SBH

EVAC EC EF EV

Fig. 5.13 Schematic illustration of band diagrams with/without interface layer insertion (see text for explanation)

In practical applications of interface layer insertion, problems due to atomic diffusion and an interfacial reaction often arise, as schematically illustrated in Fig. 5.16. Even when a thin interface layer is inserted at the interface, as shown in the left figure, the inserted layer often has nonuniform thickness or aggregates as a result of heat treatment, causing part of the interface to be in contact not with the inserted layer but with the initial metal (middle figure). Alternatively, atomic diffusion occurs during interface formation or postprocessing, and the initial metal and the inserted layer react, forming a stable phase near the interface (right figure). When such deviation of the interface structure occurs, the band alignment of the resulting specimen is considerably different from the designed band alignment. In Fig. 5.17, the interface reaction for Ti/W/SiO2 /Si with different thicknesses of the inserted W layer is shown as an example, where the band alignment is evaluated by C–V measurement (Fig. 5.17b [9]). Without annealing (i), the band alignment changes with the insertion of a 2.5-nm-thick W layer and it is not strongly affected by the resulting increase in thickness, as expected. After annealing at 400 °C (ii), the band alignment changes with the thickness of the W layer. An example of band alignment modification by interface segregation is demonstrated in Fig. 5.18. In MOSFET devices, band alignment not only along gateinsulator–semiconductor contacts but also along source–semiconductor and drain– semiconductor contacts is important (Fig. 5.18a). For these contacts, ohmic contacts

108

5 Modification of Band Alignment via Work Function Control

(a)

(b)

(c)

Fig. 5.14 a SBH plotted against metal work function at interface between n-type Ge(111) and metals [8]. b SBH plotted against metal work function at interface between n-type Ge(001) and metals [8]. c SBH plotted against metal work function at interface between n-type Ge and metals with the insertion of a few monolayers of amorphous Ge3 N4 [8]

are preferable for low energy consumption. In this example, the dopant in the semiconductor segregates during annealing, which also causes the interfacial reaction between the source (Ni) and semiconductor (Si), forming nickel silicide (NiSi). This segregation layer (normally less than a couple of monolayers in thickness) reduces the SBH between Si and NiSi (Fig. 5.18b [10]). The advantage of utilizing interface segregation for interface layer insertion is that the segregation layer is thermodynamically stable and does not change upon further annealing.

Si

EVAC

φ A SBH EF

109

metal

metal

5.2 Modification of Band Alignment

Si Si

Amorphous and/or nanocrystal Si

EVAC

EA

EVAC

EC EF EV

φ

A

SBH EF

Amorphous and/or nanocrystal Si

EA

EVAC EC EF EV

change in only crystallinity does not change band alignment Fig. 5.15 Example of ineffective insertion of interlayer (see text for explanation)

Metal A Metal B

Fig. 5.16 Schematic cross-sectional atomic illustrations of ideal interface with insertion layer (left), atomic diffusion at the interface (middle), and interfacial reaction (right) (see text for explanation)

110

5 Modification of Band Alignment via Work Function Control

(a)

(b) (i )

(ii)

Fig. 5.17 a Schematic of interface reaction of inserted layer (see text for explanation). b Changes in C − V curve before (i) and after (ii) heating for system in (a) [9] (see text for explanation)

5.2 Modification of Band Alignment

111

(a) Si-MOS gate

source n

oxide

drain

p-Si

n

Ohmic contact required



Ni

NiSi

Si(DP)

Si(DP)

Interface segrega on of dopant during Ni-Si reac on to lower SBH

(b)

Fig. 5.18 a Schematic illustration of Si-MOS and interface segregation for realizing ohmic contact at both source–Si and drain–Si interfaces with electrodes. b SBH as a function of concentration of segregated S at NiSi/Si interface [10]

References 1. Afanasev VV, Stesmans A, Pantisano L, Schram T (2005) Electron photoemission from conducting nitrides (TiNx , TaNx ) into SiO2 and HfO2 . Appl Phys Lett 86:232902-1-232902–3 2. Yeo YC (2004) Metal gate technology for nanoscale transistors—material selection and process integration issues. Thin Solid Films 462–463:34–41 3. Robertson J (2006) High dielectric constant gate oxides for metal oxide Si transistors. Rep Prog Phys 69:327–396 4. Yoshitake M (2006) Evaluation of electric potential at metal-insulator interface using electron spectroscopy and Kelvin probe techniques. Mater Res Soc Proc 894:45–53 5. Ip K, Thaler GT, Yang H, Han SY, Li Y, Norton DP, Pearton SJ, Jang S, Ren F (2006) Contacts to ZnO. J Cryst Growth 287:149–156 6. Chang Y, Hwu Y, Hansen J, Zanini F, Margaritondo G (1989) Nature of the Schottky term in the Schottky barrier. Phys Rev Lett 63:1845–1848 7. Nagata T, Ahmet P, Yoo YZ, Yamada K, Tsutsui K, Wada Y, Chikyow T (2006) Schottky metal library for ZNO-based UV photodiode fabricated by the combinatorial ion beam-assisted deposition. Appl Surf Sci 252:2503–2506

112

5 Modification of Band Alignment via Work Function Control

8. Lieten RR, Afanas’ev VV, Thoan NH, Degroote S, Walukiewicz W, Borghs G (2011) Mechanisms of Schottky barrier control on n-type germanium using Ge3 N4 interlayers. J Electrochem Soc 158:H358–H362 9. Lu CH, Wong GMT, Deal MD, Tsai W, Majhi P, Chui CO, Visokay MR, Chambers JJ, Colombo L, Clemens BM, Nishi Y (2005) Characteristics and mechanism of tunable work function gate electrodes using a bilayer metal structure on SiO2 and HfO2 . IEEE Electron Device Lett 26:445–447 10. Zhao QT, Breuer U, Rije E, Lenk S, Mantl S (2005) Tuning of NiSi/Si Schottky barrier heights by sulfur segregation during Ni silicidation. Appl Phys Lett 86:062108-1–62113

Chapter 6

Advanced Models for Practical Devices

6.1 S Parameter: Indicator of Nonideality In this chapter, nonideal band alignment, which is often observed in practical devices, will be discussed. As mentioned in Sect. 5.1, the following equations are satisfied in the case of ideal band alignment. SBH = φm − EA

(6.1)

Here, SBH , φm , and EA are the Schottky barrier height, the work function of the metal, and the electron affinity of the semiconductor, respectively (Fig. 6.1a). VFB = φm − φs

(6.2)

Here, VFB and φs are the flat-band voltage and the work function of the semiconductor, respectively (Fig. 6.1b). When ideal band alignment is realized, the desired SBH or VFB can be achieved by tuning φm , because SBH or VFB linearly increases with φm (Fig. 6.2a). In practical cases, the above equations are often not satisfied. In such cases, the effective work function φm,eff is sometimes defined for metals such that it satisfies Eqs. (6.3) or (6.4). SBH = φm,eff − EA

(6.3)

VFB = φm,eff − φs

(6.4)

Even in a nonideal case, it is often observed that SBH or VFB (or the effective work function) is linearly dependent on φm , although the proportionality coefficient is not equal to 1 but less than 1 in most cases (Fig. 6.2b). The proportionality coefficient is © The Author(s), under exclusive license to Springer Japan KK, part of Springer Nature 2021 M. Yoshitake, Work Function and Band Alignment of Electrode Materials, NIMS Monographs, https://doi.org/10.1007/978-4-431-56898-8_6

113

114

6 Advanced Models for Practical Devices

(b)

(a)

SBH

EF

EA ΔE

EVAC

EVAC EC EF

EF

insulator

EVAC

EV

EVAC EA ΔE EC EF EV

ΔE =

VFB =

-

-

Fig. 6.1 Energy level diagram of a ideal Schottky contact and b ideal MOS (see text for explanation)

Fig. 6.2 Schematic of relationships between a metal work function and SBH and b metal work function and effective work function (see text for explanation)

called the S parameter, which is defined as S≡

d (SBH ) d φm

(6.5)

S≡

d (VFB ) . d φm

(6.6)

or

6.1 S Parameter: Indicator of Nonideality Table 6.1 Several reported S values [1]

115

Material

S value

Si

~0.05

GaAs

~0.09

GeSe

~0.06

GaS

~0.9

SiO2

~1.0

In some references, the S parameter is defined using electronegativity instead of φm . This is based on the relationship between electronegativity and φm as discussed in Chap. 2. Hereafter, the discussion is based on SBH , but the same discussion applies for VFB . In Table 6.1, some reported S values are listed [1]. The S values are material-dependent. When S = 0, the SBH is constant regardless of the value of φm , and this situation is called Fermi level pinning. The S parameter has been defined from experiments. The physical meaning of the S parameter is discussed later in Sect. 6.3. Some examples of SBH plotted against φm or φm,eff are shown in Fig. 6.3 [2–4]. A band diagram of a nonideal Schottky contact is drawn by introducing a potential difference , as in Fig. 6.4. Here, SBH = φm − EA − . Therefore, from Eq. (6.3), φm,eff = φm −  S≡

d φm,eff d (SBH ) = d φm d φm =1−

d . d φm

(6.7) (6.8) (6.9)

The ideal case is  = 0, for which S = 1. For S = 0, meaning that any change in the metal work function does not affect the band alignment,  changes with the metal work function as ddφm = 1. For 0 < S < 1, ddφm is less than 1 but constant, meaning that  is linearly dependent on φm , making it possible to tune the SBH via φm . In some cases  is not a simple function of φm and is affected by other factors, which will be discussed in Chap. 7.

6.2 Origin of Nonideality Many ideas have been proposed to explain nonideality from different viewpoints. One viewpoint is that the origin of nonideality is either intrinsic or extrinsic. Here, an “intrinsic origin” means that nonideality originates from the nature of the materials and cannot be changed by changing the process of interface formation. On the other hand, an “extrinsic origin” is the process of interface formation and can

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(a)

Effective Work Function

(b)

Ideal Schoky

Vacuum Metal Work Function

(c)

Fig. 6.3 a Examples of metal work function versus SBH for interfaces between GaAs{110} or GaAs{100} and various metals [2]. b Examples of metal work function versus effective work function for interfaces between SiO2 or ZrO2 and various metals [3]. c Examples of metal work function versus effective work function for MOS with metal–HfO2 –Si structure, where the slope of the red broken line is nearly 1, indicating that the system is almost under the ideal condition [4]

EVAC EA SBH EF

Δ EVAC EC EF EV

Fig. 6.4 Schematic energy diagram for nonideal Schottky contact (see text for explanation)

6.2 Origin of Nonideality

117

be utilized to establish an ideal contact on the interface, which is intrinsically a nonideal contact. Another viewpoint is the utilization of either a band-based picture or an interface-bonding picture. In the band-based picture, the formation of interface states is considered, while an electric dipole formed by a polarized chemical bond at the interface is considered in the interface-bonding picture. Different sources of interface states have been proposed. The two main sources considered are a metal-induced gap states (MIGS) and a disorder-induced gap states (DIGS).

6.2.1 Metal-Induced Gap States (MIGS) Model The idea of the MIGS model [5, 6] is briefly explained below. Metal electrons near the Fermi level penetrate into the semiconductor at the interface (similarly to electrons at the surface penetrating into vacuum in Chap. 2 (Fig. 2.6)). The valence and conduction bands of the semiconductor branch into many states (interface states) in the energy band gap at the interface owing to the nonperiodicity of electrons. The interface states should have a mixed character comprising both valence and conduction bands. The proportion of each type of band will depend on the energy position of the interface states: the closer to the valence band, the greater the proportion of the valence band. Figure 6.5 schematically shows the proportion of the valence and conduction bands as a function of the energy level of the interface states. The energy level where the proportions of the valence and conduction bands are equal is called the charge neutrality level (CNL). If the electrons occupy the interface state up to CNL, the semiconductor becomes charge-neutral. If the CNL and the Fermi level dovetail,

interface semiconductor metal insulator CB-derived

EVAC

EF

EVAC

EC EF CNL EV VB-derived

50%

MIGS 0

100%

Proporon of orbitals forming MIGS Fig. 6.5 Proportion of the valence and conduction bands as a function of the energy level of the interface states in MIGS model as an origin of nonideality (see text for explanation)

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the penetration of electrons into the semiconductor does not cause any charging at the interface. However, the position of the CNL is usually different from that of the Fermi level, resulting in the generation of interface charge. This charge causes the potential gap  in Fig. 6.4, which is the origin of nonideality. One can understand that the MIGS is intrinsic. The CNL and the S parameter will be discussed in more detail in Sect. 6.3.

6.2.2 Disorder-Induced Gap States (DIGS) Model The concept of the DIGS model is that disorder in the atomic arrangement is introduced at the interface upon interface formation, which breaks the periodicity and generates gap states in the band gap. In some cases, disorder might be introduced unintentionally, i.e., a disordered arrangement in the thermodynamic equilibrium state. In other cases, disorder can be introduced intentionally, i.e., an artificial disordered arrangement in the nonequilibrium state. Therefore, the DIGS can be either intrinsic or extrinsic. In the interface-bonding picture without an atomic viewpoint, the polarized chemical bonding [7] or Coulomb potential [8] at the interface is considered. The polarized chemical bonding results in the formation of an electric dipole through interface bonding, and a similar equation for nonideality to that in the MIGS model is satisfied [7]. In this picture, however, interface bonding can be artificially induced, so the resulting nonideality can be either intrinsic or extrinsic. The Coulomb potential at an interface of one atom thickness was initially proposed for a Si–insulator interface, not a metal–semiconductor interface, and the interface was regarded as being in thermodynamic equilibrium [8]. The authors of Ref. [8] showed that the Coulomb potential is linearly dependent on the atomic distance at the interface for the series of alkali-earth metals, indicating that the charge of the dipole is the same and only atomic distance is different for different alkali-earth metals. Since Ref. [8] concerns the Si–oxide interface, no discussion on the S parameter was given.

6.2.3 Interface-Induced Gap States (IFIGS) Model Regardless of whether the gap states originate from the MIGS or DIGS, it is important to know which part is intrinsic or extrinsic for the control of the SBH including the ohmic contact. In the IFIGS model, the origin of the intrinsic part of the induced gap [6, 9] can be either a MIGS or a DIGS. By comparing metal–semiconductor interfaces with a non-ionic semiconductor such as Si or Ge and those with an ionic semiconductor such as ZnS, it is suggested that if the MIGS decay length is large, the DIGS part is negligible [6].

6.3 Charge Neutrality Level (CNL) and S Parameter

119

6.3 Charge Neutrality Level (CNL) and S Parameter In Sect. 6.2, the CNL was introduced as the origin of nonideality in the MIGS model. If the position of the CNL is different from that of the Fermi level, the distribution of metal electrons penetrating into the semiconductor at the interface changes, generating the potential  in Fig. 6.4. By using an analogy of a capacitor where the potential between the two plates depends on the dielectric constant of the material between them, it is reasonable to expect that the potential  will depend on the dielectric constant of the semiconductor in contact with the metal. In Fig. 6.6, the effective work function φm,eff for different metals is plotted as a function of the dielectric constant for some oxides (calculated from data in Ref. [10]). The value of φm,eff at a dielectric constant of 1 is for the interface with a vacuum and the value of φm,eff is φm . On the basis of more detailed discussion, the following empirical relationship has been proposed [1, 11]. S=

1 1 + 0.1(ε∞ − 1)2

(6.10)

Here, ε∞ is the optical dielectric constant. Figure 6.7 shows the experimentally obtained relationship between the dielectric constant and the S parameter for various semiconductors and insulators [3]. When Fermi level pinning occurs, i.e., the SBH does not change upon modification of the metal work function, the S value is nearly zero. This means that  in Fig. 6.4 increases linearly with φm . In practice, the range of φm modification is about 3 eV. If the S value is 0.01, the SBH changes by at most 0.03 V, which can be regarded as strong Fermi level pinning. According to Eq. (6.10), a dielectric constant of 32.5 will give an S value of 0.01. For readers’ convenience, some materials with relatively

Fig. 6.6 Effective work function φm,eff for different metals in contact with several oxides plotted as a function of dielectric constant of the oxides (see text for explanation)

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Fig. 6.7 Experimentally obtained relationship between dielectric constant and S parameter for various semiconductors and insulators [3]

high dielectric constants are given here: BaTiO3 : 80–3600, Fe3 O4 : 20, PbS: ~200, Ta2 O5 (α): 30–65, TiO2 (rutile): 86–170 [12]. Because the S value is determined only by the semiconductor in contact with the metal in the MIGS model, it is intrinsic and will not be affected by the process of interface formation. However, different S values have been observed experimentally for the same combination of semiconductor and metal. The DIGS model was introduced with this background. In the DIGS model, where dangling bonds at the interface are considered as the origin of interface states in the framework of the tight binding model, different interface states can be obtained from the same combination of metal and semiconductor by different interface treatments (extrinsic). Owing to the difference in interface states, the S values can differ in accordance with the interface treatment in this model. Different interface treatments cause a different density of states (DOS) in the gap states. However, the level where charge neutrality is achieved is expected to be the same as that for a perfect crystal (without atomic disorder) and independent of the S values. Therefore, plots of the work function φm against SBH for different interface treatments should cross at one point (CNL). Actually, such a point has been experimentally observed for 6H-SiC(0001), as shown in Fig. 6.8 [13]. The crossing point was different from the CNL theoretically predicted in the MIGS model. The existence of such a crossing point implies that the CNL is intrinsic for a semiconductor but the dielectric property of the interface changes with the interface treatment. In Fig. 6.8, φm and SBH at the crossing point are 4.65 eV and 0.797 eV, respectively. Since the electron affinity (EA) of 6H-SiC is reported to be 3.3 eV [14], the

6.3 Charge Neutrality Level (CNL) and S Parameter

121

Fig. 6.8 SBH plotted against metal work function for metal/6H-SiC(0001) interfaces for different interface treatments (DHF: 5% HF solution, O/E: DHF + thermal oxidation + 5% HF solution, BW: O/E + boiling water), showing a crossing point (CNL) [13]

relationship represented by Eq. (6.1) is not satisfied, although S = 1 is achieved by a specific interface treatment. The relationship among φm , SBH , and EA is expressed as SBH = φm −  − EA

(6.11)

from Eqs. (6.3) and (6.7).  in the above case is approximately 0.55 eV. This means that there is a case with S = 1 and  = const. = 0. The case of  = const. = 0 has often been observed at metal–organic interfaces. Figure 6.9a shows the experimentally measured change in the work function upon triphenyl diamine (TPD; IP = 5.34 eV, EA = 2.29 eV) deposition on Au and Cu [15]. Upon TPD deposition, the same decrease in the work function (εF vac in Fig. 6.9a) was observed for both Au and Cu. The band alignment is illustrated in Fig. 6.9b. Here, the value corresponding to the SBH, the energy difference between the LUMO and the Fermi level of the metal, changes with the work function of the metal, giving an S value of 1. εF vac is constant with the further deposition of TPD, even when the thickness reaches more than 100 nm. The difference in εF vac between TPD/Au and TPD/Cu is the same as the difference in the work function between Au and Cu. This indicates that there is no band bending in TPD, as is expected from its very low carrier density (see the relationship between the carrier density and the width of the band bending region in Chap. 2). Figure 6.10 provides an interpretation of this situation.

122

(a)

6 Advanced Models for Practical Devices

(b)

LUMO

Δ EF(Cu) EF(Au)

εFvac εFvac TPD/Cu TPD/Au

Fig. 6.9 a Experimentally measured change in work function upon TPD deposition on Au and Cu and b molecular structure of TPD and band alignment between TPD molecule and Au and Cu [15]

Fig. 6.10 Interpretation of band alignment observed in Fig. 6.9 (see text for explanation)

6.4 Modification of S Parameter by Inserting Insulator

(a)

123

(b)

Fig. 6.11 a Example of changing S parameter by Si3 N4 layer insertion at interface between metal and n-Si. Inserting the layer changes the slope (= S parameter) (see text for explanation) [16]. b Example of changing S parameter by Ge3 N4 layer insertion at interface between metal and n-Ge. Inserting the layer changes the slope (= S parameter) (see text for explanation) [16]

6.4 Modification of S Parameter by Inserting Insulator An experimentally developed technique to adjust the band alignment by inserting an ultrathin insulating layer such as Si3 N4 , Al2 O3 , TiO2 , or MgO has been basically explained as the intentional modification of the S parameter through dielectric constant modification in Eq. (6.10). It has been demonstrated that inserting 1-nmthick dielectric layers actually changes S values for n-Si and n-Ge (Fig. 6.11) [16], although the positions of the branch point (corresponding to the CNL) shifted from the predicted one in the IFIGS model. Another example of TiO2 insertion at a metal– Ge interface has been demonstrated (Fig. 6.12) [17]. In this case, the S value for pure Ge, 0.052, increased to 0.144 upon inserting a 1-nm-thick TiO2 film between the Ge and metal, where the S value estimated from the dielectric constant was 0.153, which is close to the experimentally obtained value. However, inserting a 7-nm-thick TiO2 film resulted in an S value of 0.126, which cannot be explained by the model described in the previous section. In general, the model succeeds in explaining the modification of the S parameter by inserting an ultrathin insulator layer, but the quantitative agreement is still not perfect.

6.5 Generalized CNL When nonideality is described using the S parameter, the potential gap  in Fig. 6.4 linearly depends on φm , i.e., ddφm = const., as expressed in Eq. (6.9). The basic concept is that the origin of the potential gap is charge accumulation caused by the

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Fig. 6.12 Example of changing S parameter by TiO2 layer insertion at interface between metal and Ge [17]

energy level difference between E F and the CNL with the dielectric constant ε∞ . However, when so-called high-k oxides, which have a high dielectric constant, were introduced in CMOS with a metal/high-k oxide/Si structure, it was experimentally found that the S parameter exceeded 1 (S > 1). First-principles calculations revealed that the manner of the interaction between the metal-derived wave function and that derived from the dielectric oxide varies with the metal species [18]. Under such conditions, the generalized CNL model, which takes this difference into account for the CNL in the MIGS model, has been proposed for high-k dielectric and metal gate interfaces [18]. The CNL in the MIGS model is determined by the balance between the valence band (VB) component and the conduction band (CB) component in the degenerated orbitals of the semiconductor (50–50% for the VB and CB). This level is independent of the metal in contact and determined solely by the bulk of the semiconductor. In order to take into account the interaction of the metal-derived wave function, the concept of the generalized CNL, which is the CNL with a weighted VB and CB, has been introduced. Weights of (tm−V B )2 × Munocc for the VB and (tm−CB )2 × Mocc for the CB are used, where tm−V B , tm−CB , Munocc , and Mocc are the transfer energy between the unoccupied metal states and VB states of the oxide, that between the occupied metal states and the CB states of the oxide, and the DOSs of the unoccupied and occupied states of metals, respectively [19] (Fig. 6.13). ∅G CNL = EV B + (ECB − EV B ) ×

|tm−V B |2 Munocc NV B |tm−V B |2 Munocc NV B + |tm−CB |2 Mocc NCB

(6.12)

This means that the position of the generalized CNL is intrinsic and dependent on the combination of the metal and oxide, so the S parameter, which is the slope in the φm versus SBH plot, no longer applies. This model is useful for explaining the phenomena but cannot predict the SBH in advance without calculating all the

6.5 Generalized CNL

125

metal

CB-derived

Munocc

CNL

Semiconductor/ insulator

tm-CB

CB

EF VB-derived 50% 0

Mocc

tm-VB

VB

100 %

Proporon of orbitals forming MIGS Fig. 6.13 Schematic illustration of modification of CNL model (left) to generalized CNL model (right) (see text for explanation)

transfer energies and DOSs involved. Although this model is primarily based on the band picture, the atomic view of interface bonding is taken into account, which is different from the polarized chemical bonding or Coulomb potential described in Sect. 6.2.

References 1. Mönch W (1987) Role of virtual gap states and defects in metal-semiconductor contacts. Phys Rev Lett 58:1260–1263 2. Mönch W (1990) On the physics of metal-semiconductor interfaces. Rep Prog Phys 53:221–278 3. Yeo YC (2004) Metal gate technology for nanoscale transistors—material selection and process integration issues. Thin Solid Films 462–463:34–41 4. Robertson J (2006) High dielectric constant gate oxides for metal oxide Si transistors. Rep Prog Phys 69:327–396 5. Heine V (1965) Theory of surface states. Phys Rev 138:A1689–A1696 6. Tersoff J (1984) Schottky barrier heights and the continuum of gap states. Phys Rev Lett 52:465–468 7. Tung RT (2000) Chemical bonding and Fermi level pinning at metal-semiconductor interfaces. Phys Rev Lett 84:6078–6081 8. McKee RA, Walker FJ, Nardelli MB, Shelton WA, Stocks GM (2003) The interface phase and the Schottky barrier for a crystalline dielectric on silicon. Science 300:1726–1730 9. Mönch W (2011) Branch-point energies and the band-structure lineup at Schottky contacts and heterostructures. J Appl Phys 109:113724-1-113724–10 10. Yeo YC, King TJ, Hu C (2002) Metal-dielectric band alignment and its implications for metal gate complementary metal-oxide-semiconductor technology. J Appl Phys 92:7266–7271 11. Mönch W (1988) Mechanisms of Schottky-barrier formation in metal–semiconductor contacts. J Vac Sci Technol B 6:1270–1276

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12. Young KF, Frederikse HPR (1973) Compilation of the static dielectric constant of inorganic solids. J Phys Chem Ref Data 2:313–409 13. Hara S (2001) The Schottky limit and a charge neutrality level found on metal/6H-SiC interfaces. Surf Sci 494:L805–L810 14. Lu W, Collins WE, Mitchel WC (2004) SiC power materials: devices and applications. In: Feng ZC (ed) Springer series in materials science. Springer-Verlag, Berlin 15. Hayashi N, Ito E, Oji H, Yoshimura D, Seki K (2001) Energy level alignment and band bending at TPD/metal interfaces studied by Kelvin probe method. Synth Met 121:1717–1718 16. Mönch W (2012) On the alleviation of Fermi-level pinning by ultrathin insulator layers in Schottky contacts. J Appl Phys 111:073706-1-073706–7 17. Tsui BY, Kao MH (2013) Mechanism of Schottky barrier height modulation by thin dielectric insertion on n-type germanium. Appl Phys Lett 103:032104-1-032104–4 18. Shiraishi K, Nakayama T, Akasaka Y, Miyazaki S, Nakaoka T, Ohmori K, Ahmet P, Torii K, Watanabe H, Chikyow T, Nara Y, Iwai H, Yamada K (2006) New theory of effective work functions at metal/high-k dielectric interfaces—application to metal/high-k HfO2 and La2 O3 dielectric interfaces. ECS Trans 2:25–40 19. Nakayama T, Shiraishi K, Miyazaki S, Akasaka Y, Nakaoka T, Torii K, Ohta A, Ahmet P, Ohmori K, Umezawa N, Watanabe H, Chikyow T, Nara Y, Iwai H, Yamada K (2006) Physics of metal/high-k interfaces. ECS Trans 3:129–140

Chapter 7

Utilization of Interface Potential

The discussion in Chap. 6 revealed that the interface potential gap  and the S parameter determine how the band is aligned at the interface by modifying the work function of a metal. When the terminating species of a semiconductor (or insulator) changes at the interface depending on the metals in contact, the concept of the S parameter no longer applies. This means that the difference in the metal in contact cannot be handled simply by considering the work function φm within the frame of the jellium model. In this chapter, some examples of band alignment modification beyond jellium-based models, i.e., the intentional, direct tuning of the interface potential gap , are demonstrated.

7.1 Control of Interface-Terminating Species The generalized charge neutrality level (generalized CNL) in Sect. 6.5 was proposed on the basis of the experimental finding that the S parameter exceeds 1 (S > 1) when the interface-terminating species depends on the metals in contact. However, this model does not explicitly include interface-terminating species in its definition of the generalized CNL. It has been experimentally shown that interface-terminating species can be modified by controlling the formation of Cu–Al2 O3 interfaces [1, 2]. The interface-terminating species is known to strongly affect the strength of Cu– Al2 O3 interface bonding [3–5]. Interface termination with other metals has been studied from the thermodynamic viewpoint [6]. In short, for the same metal–oxide material combination, interface-terminating species can be different, as shown in Fig. 7.1, and stable termination is determined by the thermodynamics of each system. Regarding the Schottky barrier height (SBH) for a differently terminated interface, first-principles calculations have predicted that the p-type Schottky barrier height (pSBH) (or band offset, i.e., the energy difference between the Fermi level and the © The Author(s), under exclusive license to Springer Japan KK, part of Springer Nature 2021 M. Yoshitake, Work Function and Band Alignment of Electrode Materials, NIMS Monographs, https://doi.org/10.1007/978-4-431-56898-8_7

127

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7 Utilization of Interface Potential

Fig. 7.1 Schematic illustration of different interface terminations (interface bonding) for the same metal (M)–oxide (Ax Oy ) interface, where two different terminations, A–M and O–M bonding, are possible

valence band maximum of a semiconductor or insulator) depends on the interfaceterminating species even for the same metal–oxide material combination [7]. The calculated density of states (DOS) at the interface for two different terminations is shown in Fig. 7.2. The position of the peak energy near and below the Fermi level (zero energy in the figure) for O termination is located very near the Fermi level, whereas that for Al termination is located about 4 eV below the Fermi level. This difference leads to a calculated p-SBH of 2.1 eV for O termination and 3.6 eV for Al termination. Corresponding experiments using photoelectron spectroscopy have been carried out on Cu–Al2 O3 and Ni–Al2 O3 interfaces using epitaxial Al2 O3 grown on single-crystal metals [8]. Because the thermodynamics indicates that for an extremely low oxygen partial pressure or higher activity of Al (meaning Al alloying to metals), an Al-terminated interface is realized [6], alloying of Al with Cu or Ni was used to modify the interface in the experiments. In Fig. 7.3, the observation of interface-terminating species using the Al 2p peak is demonstrated for the (a) Cu–Al2 O3 system and (b) Ni–Al2 O3 system. Since Al atoms that terminate at the interface bond with both oxygen and Cu or Ni, the binding energy is located between those of Al2 O3 (Al atoms bond only with oxygen) and metallic Al (in alloys, Al bonds only with metals). Therefore, interface-terminating species can be observed by the presence or absence of the interface-derived peak. Figure 7.4 depicts the photoelectron spectra near the valence band for (a) Cu–Al2 O3 and (b) Ni–Al2 O3 systems, revealing the large difference in the position of the valence band maximum Fig. 7.2 Calculated DOS for two different terminations at Cu–Al2 O3 interface [7]

7.1 Control of Interface-Terminating Species

129

Fig. 7.3 Observation of interface-terminating species using Al 2p peak for a Cu–Al2 O3 system and b Ni–Al2 O3 system (see text for explanation)

Fig. 7.4 Photoelectron spectra near the valence band for a Cu–Al2 O3 and b Ni–Al2 O3 systems and band diagram deduced from photoelectron spectra (see text for explanation)

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7 Utilization of Interface Potential

Metal–alumina

alumina

CB

O term

EF

Pure Ni Pure Cu

Δ:small

Summary of p-type Schoky barrier height VB

Al term

NiAl Cu(Al)

CB

EF

Δ:large

Δ: calc./ exp. Ni: O term: 1.5 / 2.8 eV Al term: 3.8 / 4.5 eV Cu: O term: 2.1 / 3.2 eV Al term: 3.6 / 4.4 eV

VB

Fig. 7.5 Summary of results of interface termination and p-SBH () (see text for explanation)

between the pure metal (O termination) and Al alloy (Al termination). Below the spectra, measured energy levels of other transitions from Al2 O3 (Al 2p and O 1s) are illustrated. From this diagram, it is revealed that for both the Cu and Ni systems, the whole energy level related to Al2 O3 shifts in relation to the metal in contact (pure metal or alloy), resulting in the difference in the p-SBH (the position of the valence band maximum relative to the Fermi level). The results for the interface termination and p-SBH [8] are summarized in Fig. 7.5. As explained above, the interface is Oterminated with pure Cu and Ni, where the p-SBH is small (upper part of the figure), and the interface is Al-terminated with NiAl and Cu(Al), where p-SBH is large (lower part of the figure). The right side of the figure shows values of p-SBH obtained by first-principles calculations and by experiments on O-terminated and Al-terminated interfaces for a Ni system (pure Ni and NiAl) and Cu system (pure Cu and Cu(Al)). The relationship between the work function of metals and the p-SBH is plotted in Fig. 7.6, where the straight line in the figure has a slope of −1. The slope of −1 corresponds to an ideal Schottky contact because of the following relationship: p − S B H = E A + E G − φm , where E G is the band gap (= E C − E V ). It can be seen from Fig. 7.6 that the two points for O termination are along the line and those for Al termination have almost the same p-SBH values. It is speculated that perfect pinning occurs because the Alterminated surface of Al2 O3 has a high DOS at the middle of the band gap [9] and metal electrons near the Fermi level interact with the electrons at the middle of the band gap, keeping the position of the Fermi level aligned with the middle of the band

7.1 Control of Interface-Terminating Species

131

Fig. 7.6 Relationship between work function of metals and p-SBH obtained in Fig. 7.4

gap of Al2 O3 for all metals. On the other hand, metal electrons near the Fermi level interact with O 2p level at O-terminated interface, resulting in the p-SBH change in accordance with the metal work function. In most previous reports, controlling SBH by the work function of metal was effective. Therefore, the interface of those cases might have been terminated by oxygen. Another example of the interface whose interface-terminating species are controlled is the metal-ZnO interface, as shown in Chap. 5, Fig. 5.12 [10]. In this case, the S parameter was effective for controlling the SBH of interfaces with a metal deposited on both O-terminated ZnO and Zn-terminated ZnO, although the S parameter was different in the two cases. From a photoelectron spectroscopic study on the interfaces formed by Pt deposition on O-terminated ZnO and Zn-terminated ZnO, it has been demonstrated that the interface between Pt and ZnO is stable with O termination, regardless of whether Pt is deposited on O-terminated ZnO or on Zn-terminated ZnO [11]. Therefore, the O-terminated interface also seems to be always stable in the case of Fig. 5.12, though atomic arrangement at the interface may different between the two differently terminated ZnO. Thus, the example in Fig. 5.12 shows that the S parameter was effective for controlling the SBH because the interface was terminated by oxygen. This system appears to fit the DIGS model, where the S parameter can be modified by manipulating the atomic arrangement of the interface. The effect of interface termination on band alignment can be deduced from firstprinciples calculations [12]. The SBH has been calculated for O- and Zn-terminated ZnO (c-plane) in contact with (111) planes of Al, Ag, and Au. From the results of the calculations, the interface termination was shown to depend on the metal in contact with ZnO, and a smaller p-SBH (= larger SBH) was predicted for the O term and a

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7 Utilization of Interface Potential

larger p-SBH (= smaller SBH) was predicted for the Zn term, which is similar to the case of Al2 O3 . The results are schematically illustrated in Fig. 7.7. In Fig. 7.8, the SBH is plotted as a function of the work function of the metal in contact. Again, a similar trend to the case of Al2 O3 is observed, that is, very strong Fermi level pinning (S is nearly zero) is observed for the Zn-terminated interface, whereas an S value close to the ideal case is obtained for O termination. At least for Al2 O3 and ZnO, we have some guidelines for band alignment, that is, nearly complete Fermi level pinning occurs for interfaces terminated by the metal component of oxides. On the other hand, for oxygen-terminated interfaces, the SBH changes with a relatively large S value according to the work function of the metal in Fig. 7.7 Schematic illustration of the influence of interface termination on SBH for ZnO (c-plane) in contact with metals, obtained by first-principles calculations (see text for explanation)

Metal–ZnO

ZnO O term

CB EF

metal

SBH p-SBH VB

Zn term CB EF metal

p-SBH VB

Fig. 7.8 Relationship between work function of metals and SBH for metal–ZnO interface obtained by first-principles calculations

7.1 Control of Interface-Terminating Species

133

contact, enabling the tuning of the SBH by work function modification. Note that the thermodynamic stability of interface termination must be considered in the control of interface-terminating species for band alignment.

7.2 Insertion of a 1-ML-Thick Material Another commonly used way of tuning the interface potential gap  is to insert a material as thin as 1 ML between a semiconductor and a metal. Here 1 ML means that the thickness is near the lattice constant; at such thicknesses, many of the properties of the material considerably differ from those of the bulk. In Sect. 6.5, the effect of inserting a dielectric layer was discussed, where the thickness of the layer was 1 ML or above and the dielectric constant of the inserted layer was treated as a parameter that determines the S parameter. The interface termination mentioned in the previous section can be referred to as 1 ML insertion, where the dielectric constant is not known for such a system. Inserting 1 ML of a dielectric resembles interface termination from the viewpoint of the interface potential gap, except that other species that are not components of the two materials in contact are involved. Figure 7.9 shows the effect of H passivation on the relationship between the SBH and the electronegativity of the metal for interfaces between different metals and p-diamond [13]. The passivation of p-diamond with hydrogen is also an example Fig. 7.9 Relationship between SBH and electronegativity of metal at interfaces between metal and p-diamond with (broken line) and without (full line) H passivation [13]

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Table 7.1 Drive voltages necessary to obtain a current density of 100 mA/cm2 in EL device with different electrodes [14] (see text for explanation) Al LiF (0.5 nm)/Al MgO (0.5 nm)/Al Drive voltage needed for 100

A/cm2

current density 17 10

11

Fig. 7.10 Current density Jsc versus voltage V characteristic of amorphous Si solar cell under photoirradiation with and without LiF insertion between amorphous Si and back contact of Al electrode. The left picture shows a schematic representation of the specimen [15] (see text for explanation)

of 1 ML insertion. As another example, the drive voltages necessary to obtain a current density of 100 mA/cm2 in an EL device with different electrodes are given in Table 7.1 [14]. The device is composed of an Alq emissive layer formed on an indium tin oxide (ITO) top electrode and an Al bottom electrode, which works as an electron injection electrode. When 0.5-nm-thick LiF or MgO is inserted between Alq and Al, a marked decrease in the drive voltage is observed. As yet another example, Fig. 7.10 shows the effect of LiF insertion between amorphous Si and the back contact of an Al electrode in an amorphous Si solar cell [15]. The obtained current density (J ) versus voltage (V ) characteristic of a solar cell under photoirradiation revealed that the curves for LiF layers with thicknesses of 0.4 and 0.7 nm are similar, whereas that for a 1.5 nm layer is different. This suggests that for a 1.5-nm-thick or thicker layer, the characteristics can be explained by the dielectric constant of the inserted layer described in Sect. 6.5, but the interface layer is specially modified when a thinner layer is inserted. The insertion of a LiF or CsF layer at the interface between an organic semiconductor and a metal has also been investigated rigorously. One of the application fields of such interfaces is organic light-emitting diodes (OLEDs). Here, we give the example of a light-emitting polymer sandwiched by poly(ethylenedioxythiophene)/poly(styrene sulfonic acid) (PEDOT:PSS)-coated ITO and a cathode electrode [16]. A schematic diagram of the relative energy positions of the Fermi levels at the flat band for diodes with different cathode materials is illustrated

7.2 Insertion of a 1-ML-Thick Material Fig. 7.11 a Schematic diagram of relative energy positions of Fermi levels at zero bias and b experimentally obtained band diagram for diodes with different cathode materials. More details in Ref. [16]

135

anode

(a)

polymer

CB SBH(2)

VBI(1)

EF p-SBH(anode)

EG

cathode SBH(1) EF(2) EF(1)

VBI(2)

VB (b)

VBI(1)

EF

EG

cathode LiF/Ca CsF/Al Ca(50 nm) LiF/Al EF Ca(1.5 nm) Al VBI(Al)

PEDOT:PSS polymer in Fig. 7.11, which was obtained from electro-absorption response (degree of photon absorption) measurements. Although band alignment cannot be explained simply, the insertion of such a monolayer improves the band alignment, especially on the cathode side, where an electrode with a low work function is required. In the case of inserting a dielectric layer as thin as 1 ML, electrons can tunnel through the layer and reach the electrode, which is different from the cases described in Sect. 6.4 (the insertion of layers that are regarded as having a bulk dielectric constant).

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