Ion Implantation and Activation - Volume 2 [1 ed.] 9781608057900, 9781608057917

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Ion Implantation and Activation (Volume 2) Authored By

Kunihiro Suzuki Fujitsu limited Minatoku kaigan 1-11-1 Tokyo Japan

Bentham Science Publishers

Bentham Science Publishers

Bentham Science Publishers

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CONTENTS Preface Acknowledgements

i iii

CHAPTERS 1.

Ion Implantation Profile in Patterned Substrate

3

2.

Analytical Model for Two-Dimensional Profile in MOSFET’s

18

3.

Three-Dimensional Ion Implantation Profile Based on Rp Line Concept

32

4.

Ion Implantation Profile in Multi-Layer Structure

54

5.

Dose Loss

69

6.

Amorphous Layer Thickness

78

7.

Recrystallization of Amorphous Layer

121

8.

Redistribution of Impurities During Solid Phase Epitaxy

129

9.

Activation of Ion Implanted Impurities

143

Subject Index

163

i

PREFACE Ion implantation is a standard technology, by which impurities are doped into Si substrates in very large scale integration (VLSI) processes in modern times. Defects are unintentionally generated in the substrate by the ion implantation simultaneously since impurities are introduced physically into the lattice, i.e., in non-thermal equilibrium. Hence, a subsequent thermal process is indispensable to recover the damage and activate the introduced impurities. Intensive studies on predicting the ion implantation profiles and activation processes have been done, and they are still under investigations. Many eBooks on fundamental ion implantation technology and detailed physics related to the ion implantation have been published. Furthermore, database for practical ion implantation profiles is also established and it is valid even for modern technologists and students. However, theoretical models and systematic fundamental experimental data are not closely related to each other, and how accurately the models reproduce the experimental data is not clear. We have been collecting systematic experimental data to evaluate and develop the models for a long time. We also try to compare the data with related models in this eBook. Details about the derivation process of fundamental and advanced models are described step by step and their related assumptions and approximations are clarified. If some mathematical and physical background is necessary, related appendixes will be added to make this eBook self-contained. Models that are not established well and under investigations are treated as well. Although it is not ensured to be accurate, knowing the details about models under investigations is interesting for furthering the models. The author aims at the readers who are experts and non-experts in various fields associated with the ion implantation, hoping that various members can cover some knowledge to collaborate with one another. It is not easy for non-expert members to understand this eBook, but it is believed that they can do it with time and efforts.

ii

This eBook consists of three volumes, and this volume treats the following. Ions are usually implanted into patterned substrates. Therefore, two-dimensional profiles in these substrates are also important to predict device characteristics. This becomes more important when devices are scaled down. We show the analytical models for two- and three-dimensional profiles in various shapes of the substrates. Sometimes, ions are implanted into multi-layer substrates. How we generate the profiles based on the profiles in each single layer is briefly shown. Damage is unintentionally introduced to the substrates by ion implantation. When the dose is increased, the damaged regions overlap and a continuous amorphous layer is formed. The activation and diffusion in the subsequent thermal process are significantly influenced regardless of the situation that the amorphous layer is formed. The damage formation by ion implantation is investigated with various temperatures, that is, hot or cold implantation is performed. We show the model to predict the amorphous layer thickness in wide ion implantation conditions at various ion implantation temperatures. Solid phase epitaxial recrystallization (SPE) occurs during low-temperature annealing. The speed of the regrowth of the amorphous layer and the redistribution of the profiles during SPE are shown. Impurities are highly activated during SPE, which is explained by introducing a concept of isolated impurities. CONFLICT OF INTEREST The author confirmed that this eBook has no conflict of interest.

Kunihiro Suzuki Fujitsu limited Minatoku kaigan 1-11-1 Tokyo Japan E-mail: [email protected]

iii

ACKNOWLEDGEMENTS Many members in various fields contributed to complete this eBook. Tsutomu Nagayama helped me to obtain many ion implantation samples with ion implantation machine, and Susumu Nagayama helped me to obtain many SIMS data. Yasuharu Fujimori helped me to obtain various carrier profiles. Masatoshi Yoshihara and Syuichi Kojima contributed to integrate models into a system which is used by many members. I also thank Ryo Tanabe for the analysis of profiles in MOS devices. I thank Prof. Fichtner for inviting me to his laboratory, where I started studying process modeling and enjoyed the collaboration with Dr. Alexander Hoefler, Dr. Thomas Feudel, and Dr. Nobert Strecker. Dr. Christoph Zechner gave cutting edge information on process modeling, and I enjoyed some collaboration with him in the field. He also gave me invaluable discussions, comments, and corrected my English. Hiroko Tashiro and Ritsuo Sudo helped me to simulate ion implantation and diffusion profiles. Kazuo Kawamura helped me to obtain various TEM data, which substantially contribute to construct a model for amorphous layer thickness. Hiroyo Miyamoto helped me to set format of word file. I owed to Dr. Min Yu a great deal for his invaluable discussions and correcting my English. His devotion made it possible to complete this eBook. Prof. Seijiro Furukawa and Prof. Hiroshi Ishihara directed me to become a researcher. I also want to give special thanks to Prof. Robert W. Dutton who always encouraged me from the beginning of my career as a researcher.

iv

Finally, I want to thank my family Kyoko, Yuji, Saori, Takayuki, Misato, Nahoko, Ryohei, and my parents Fukushi and Yae, and Kyoko’s ex-father Haruo Abe, and mother Chiyoko Abe with whom I enjoy comfortable life.

Kunihiro Suzuki Fujitsu limited Minatoku kaigan 1-11-1 Tokyo Japan

Send Orders for Reprints to [email protected] Ion Implantation and Activation, Vol. 2, 2013, 3-17 3

CHAPTER 1 Ion Implantation Profile in Patterned Substrate Abstract: We treat analytical models for two-dimensional profiles in patterned substrates. It is shown that the doses in the scaled MOSFET’s gates become significantly smaller that the doses in the large gate. We should therefore be careful about ion implantation conditions in scaled devices considering the two-dimensional effects. We further evaluated the relationship between vertical and lateral junction depth using the model.

Keywords: Ion implantation, two-dimensional profile, lateral distribution, gate, gate length, gate depletion, Gaussian, contact pattern, junction depth, lateral junction depth, Monte Carlo, As, B, MOSFET’s, Gaussian. INTRODUCTION Ion implantation is performed to patterned substrates. Even in ion implantation to plane substrate, it is usually performed using masking layers such as SiO2 or photo resist. We should then treat two-dimensional profiles in this case. The basic information for the profiles in this case is lateral straggling Rpt . We showed how we can evaluate Rpt in chapter 1. We can construct two-dimensional profiles by a convolution of a one-dimensional implantation profile with a Gaussian lateral profile. LATERAL DISTRIBUTION Ion implanted impurities are distributed laterally as well as vertically as shown in Fig. 1. We can evaluate this distribution with Monte Carlo simulation (MC) [1-3]. The MC [3] distribution profile of As ion implanted at 10 keV is shown in Fig. 2 for cross view (a) and plane view (b). A concentration at a certain location is determined by the integration of the concentration related to the ions implanted in other locations. We assume line beam with Gaussian lateral distribution, and can evaluate the lateral distribution Rpt as shown in chapter 1. The contribution of ions implanted at  xi , xi  dxi  to the concentration at x can be expressed by

  xx i dN  x, y   A  y  exp      2Rt 

  

2

  dxi  

Kunihiro Suzuki All rights reserved-© 2013 Bentham Science Publishers

(1)

4

Ion Implantation and Activation, Vol. 2

Kunihiro Suzuki

Figure 1: Schematic trajectory of ion implanted impurity.

10

x-distance (nm)

As 10 keV

5 0 -5 -10

0

5

10 15 Depth (nm) (a)

20

25

Ion Implantation Profile in Patterned Substrate

Ion Implantation and Activation, Vol. 2

5

10 As 10 keV

z-distance (nm)

5 0 -5 -10 -10

-5

0 5 x-distance (nm) (b)

10

Figure 2: Ion distribution (a) Cross view (b) Plane view.

A  y  is the depth dependent arbitrary constant, and can be related to the concentration at depth y of n  y  . n  y  at x can be obtained by the integration for all xi as 

   x  xi n  y    A  y  exp      2R pt    

   

2

  dxi  

(2)

 A  y  2 R pt

Therefore, we obtain A y 

n y

(3)

2 R pt

and Eq. 1 can be expressed by

  xx i dN  x, y   exp      2Rt 2 R pt  n y

  

2

  dxi  

(4)

6

Ion Implantation and Activation, Vol. 2

Kunihiro Suzuki

ION IMPLANTATION PROFILE IN PATTERNED SUBSTRATE An analytical model for two-dimensional impurity concentration profiles, where ions were implanted into the contact pattern (Fig. 3(a)), was derived by Furukawa et al. [4]. They derived a model for infinite large pattern. However, as the pattern size is scaled down, the concentration at the center of the contact pattern becomes different from the concentration in the infinite pattern. Furthermore, impurities implanted in both source and drain regions may contribute to the concentration in the center of the channel region in scaled devices. Therefore, the model should be extended to consider both edges of the contact pattern. The method proposed by Furukawa et al. can be easily extended to this case (Fig. 3(b)). Once we know Rpt , we can generate two-dimensional profile distribution [5, 6].

Figure 3: Ion implantation in patterned substrate. (a) Contact pattern, (b) Gate pattern.

Let us consider the ion implantation into substrates with a contact pattern with the length L as shown in Fig. 3(a). We assume that impurities are ion implanted in

Ion Implantation Profile in Patterned Substrate

Ion Implantation and Activation, Vol. 2

7

the region   L 2 , L 2  and set the origin at the center of the pattern. Then the concentration at  x, y  is given by L

2   n y  x  xi   exp   N  x, y     2R pt 2 R pt  L   

   

2

2

   erf   n y      

 L  2 x   2R pt 

    erf   2

  dxi  

 L  2x   2R pt 

         

(5)

The two-dimensional profile for a gate pattern is evaluated with a similar manner as follows:   L2   n  y      x  xi  exp N  x, y      2R pt 2 R pt            x  xi   exp        2R pt 2 R pt        L     2 x    erf    erf    2R pt        n  y 1  2     n y

   

2



     dxi   exp    x  xi    2R pt L    

   

2

   

2

2

   

2

L 2

     dxi   exp    x  xi    2R pt  L    2

L x 2 2R pt

         

    dxi           dxi      

(6)

8

Ion Implantation and Activation, Vol. 2

Kunihiro Suzuki

Note that we can use arbitrary vertical profile of n  y  , where we use tail function. Furthermore, the model can also accommodate depth dependent Rpt . Fig. 4 shows two-dimensional profiles calculated with Fab Meister-IM [7].

Figure 4: Two dimensional profiles using FabMeister-IM [7] simulated based on the analytical model.

22

10

As 10 keV 1 x 10 15 cm-2 L = 0.1 m

y = Rp

Concentration (cm-3)

21

10

20

10

19

10

18

10

17

10

16

10

-100

-50

0 50 Distance (nm) (a)

100

Ion Implantation Profile in Patterned Substrate

Ion Implantation and Activation, Vol. 2

As 10 keV 1 x 1015 cm-2 L = 0.1 m

22

10

9

y = Rp

Concentration (cm-3)

21

10

20

10

19

10

18

10

17

10

16

10

-100

-50

0 50 Distance (nm) (b)

100

Figure 5: Lateral distribution of impurities ion-implanted into (a) Contact pattern, (b) Gate pattern.

21

Concentration (cm-3)

10

B 5 keV 1 x 10 15 cm-2 Rpt = 10 nm

L = 200 nm L = 100 nm L = 50 nm L = 30 nm

20

10

19

10

18

10

-150 -100 -50 0 50 Distance (nm) (a)

100 150

10

Ion Implantation and Activation, Vol. 2 21

Concentration (cm-3)

10

B 5 keV 1 x 10 15 cm-2 Rpt = 10 nm

Kunihiro Suzuki L = 200 nm L = 100 nm L = 50 nm L = 30 nm

20

10

19

10

18

Concentration (cm-3)

10

-150 -100 -50 0 50 Distance (nm) (a')

10

21

10

20

10

19

10

18

10

17

B 5 keV 1 x 10 15 cm-2 Rpt = 10 nm

-150 -100 -50 0 50 Distance (nm) (b)

100 150

L = 200 nm L = 100 nm L = 50 nm L = 30 nm

100 150

Figure 6: Dependence of lateral impurity distribution profiles on L. (a) Contact pattern, (a’) Gate polySi pattern (b) Gate pattern.

These two-dimensional impurity distribution profiles become quite important for scaled devices. Fig. 6 shows the dependence of lateral distribution on pattern size. We cannot expect flat concentration profiles in the contact pattern for the

Ion Implantation Profile in Patterned Substrate

Ion Implantation and Activation, Vol. 2 11

decreased size (Fig. 6(a)) and hence we should be careful about contact resistance associated with such non uniform profiles. On the other hand the channel concentration is significantly influenced by impurities implanted in both source and drain regions (Fig. 6(b)). If we consider only the region   L 2 , L 2  in Eq. 5, the profile is corresponding to the one in gate polycrystalline Si (polySi) [8]. The gate length is scaled down according to the scaling theory, while the gate height is not scaled. It seems that the doping of gate polySi is not a severe problem. However, the two-dimensional effect influences the gate doping. The effective dose in the gate can be evaluated as  L  2 x  erf   2R pt      L  L 2

 eff 



    erf   2

 L  2x   2R pt 

     dx

(7)

2

L 1.0

eff/

0.8 0.6

Rpt = 5 nm

0.4

10 nm 20 nm

0.2 0.0

0

50 L (nm)

100

Figure 7: Effective dose in gate polySi. The dose is normalized by the dose where impurities are ion implanted in infinite plane substrate.

12

Ion Implantation and Activation, Vol. 2

Kunihiro Suzuki

Fig. 7 shows the dependence of eff on gate length. When L becomes comparable with Rpt , the effective dose becomes 30 % of the dose ion-implanted in plane substrate. Therefore, we should increase the dose, or decrease the ion implantation energy to avoid gate depletion [9-12]. Vertical and Lateral Junction Depth

It is interesting to understand the relationship between lateral and vertical junction depth.

Figure 8: Schematic ion concentration profile implanted in patterned substrate.

Let us consider the patterned substrate shown in Fig. 8. We set the origin at the left edge of the gate pattern. We focus on the region of x  , 0  . The concentration at  x, y  can be expressed by 0

N  x, y    dN  x, y   0

   x  xi 1   n y exp      2R pt  2 R pt    1 x  n  y  erfc   2R 2 pt 

   

   

2

  dxi  

(8)

Ion Implantation Profile in Patterned Substrate

Ion Implantation and Activation, Vol. 2

13

Note that the factor of 1 2 expresses that the right side contribution of the impurities is zero at the edge. Assuming Gaussian vertical impurity concentration profile, we reduce Eq. 8 to

  R y  p exp    N  x, y      2R p 2 R p 

   

2

  x  1 erfc   2R 2 pt  

   

(9)

The term  2 R p expresses the peak concentration and is denoted as nm . Setting x   , the vertical junction depth can be evaluated with the profile of

  R y N  x  , y   nm exp    p   2R p 

   

2

   

(10)

On the other hand, the lateral spread is the maximum at the depth of y  Rp , and the corresponding lateral distribution is given by  1 x N  x, y  R p   nm erfc   2R pt 2 

   

(11)

We set the critical concentration related to the junction depth as nc . The vertical junction depth is obtained from

 R y j nc  nm exp    p   2R p 

   

2

   

(12)

We then obtain a vertical junction depth. n  y j  R p  ln  m  2R p  nc 

(13)

14

Ion Implantation and Activation, Vol. 2

Kunihiro Suzuki

The distance between R p and junction depth y j is given by n  y j  ln  m  2R p  nc 

(14)

On the other hand, the lateral junction depth can be evaluated from nc  nm

 xj 1 erfc   2R pt 2 

   

(15)

We then obtain lateral junction depth as  2n  x j  erfc 1  c  2R pt  nm 

(16)

Table 1 shows the list of junction depth using parameters of Rp , R p , and Rpt evaluated with LSS theory [13]. Table 1: Lateral and vertical junction depth of (a) B, (b) As

(a) B Energy(keV) Rp(nm) ΔRp(nm) ΔRpt(nm) yj(nm) Δyj(nm) xj(nm) xj/yj xj/Δyj 10 39.83 20.88 19.59 117.44 77.61 60.54 0.52 0.78 20 76.73 34.31 32.85 204.26 127.53 101.51 0.50 0.80 40 147.70 53.58 53.89 346.85 199.15 166.53 0.48 0.84 80 277.51 77.82 84.26 566.76 289.25 260.38 0.46 0.90

(b) As Energy(keV) Rp(nm) ΔRp(nm) ΔRpt(nm) yj(nm) Δyj(nm) xj(nm) xj/yj xj/Δyj 10 12.73 4.67 3.75 30.09 17.36 11.59 0.39 0.67 20 19.59 7.25 5.71 46.54 26.95 17.65 0.38 0.65 40 32.47 11.79 9.00 76.29 43.82 27.81 0.36 0.63 80 56.58 20.11 14.75 131.33 74.75 45.58 0.35 0.61

The vertical and lateral junction depth are roughly expressed by

Ion Implantation Profile in Patterned Substrate

Ion Implantation and Activation, Vol. 2

 y j  R p  3R p   x j  2R pt

15

(17)

Rp is approximately between 1 2 and 13 of R p . Rpt and Rp are almost the same for light ions such as B. On the other hand, Rpt is smaller than Rp for heavy ion such as As. Consequently x j y j is almost 0.5 for light ions and smaller than 0.5 for heavy ions. The lateral spread for heavy ions is smaller. It is also interesting to know the gradient of the impurity concentration, which can be easily obtained by differentiating the profile. We move the vertical origin to the depth of R p for simplicity, and the corresponding vertical profile is given by   y N  x  , y   nm exp      2R p 

   

2

   

(18)

Differentiating this with respect to y, we obtain



N  x  , y  y

 y y j

  y 2nm exp      2R p 



2R p



   

2

 y  

2

y y j

  y 2  j 2nm exp      y    2R p   j    2 2R p





n  n  2 ln  m  c  nc  R p On the other hand, the gradient of lateral distribution is given by

(19)

16



Ion Implantation and Activation, Vol. 2

N  x, y  R p  x

Kunihiro Suzuki

  x  exp      2R pt 2 R pt   nm

x x j

  x nm j  exp      2R pt 2 R pt  

   

2

    x x j

   

2

   

(20)

The results are shown in Table 2. The lateral and vertical gradients are almost the same for B, but lateral gradient is much larger for As. The results are directory related to the ration of R pt R p . Table 2: Lateral and vertical impurity concentration gradient Energy(keV) 10 20 40 80

-3

B(cm /nm) y x 1.8e16 3.0e16 1.1e16 1.5e16 6.9e15 5.9e15 4.8e15 1.8e15

-3

As(cm y 8.0e16 5.1e16 3.2e16 1.8e16

/nm) x 49.0e16 36.1e16 27.4e16 20.7e17

The other practical method to evaluate the sharpness of the impurity concentration profiles is to measure the distance where the concentration decreases one order, which is shown in Table 3. Note that the difference becomes weak even for As with this method. Table 3: Lateral and vertical transition region. (a) B, (b) As (a) B Energy(keV) yj(1e17) yj(1e18) xj(1e17) xj(1e18) Δyj(nm) Δxj(nm) 10 117.44 103.20 60.54 45.57 14.24 14.96 20 204.26 180.86 101.51 76.42 23.40 25.09 40 346.85 310.31 166.53 125.37 36.55 41.17 80 566.76 513.68 260.38 196.02 53.08 64.37 (b) As Energy(keV) yj(1e17) yj(1e18) xj(1e17) xj(1e18) Δyj(nm) Δxj(nm) 10 30.09 26.90 11.59 8.72 3.19 2.86 20 46.54 41.59 17.65 13.28 4.95 4.36 40 76.29 68.25 27.81 20.94 8.04 6.88 80 131.33 117.61 45.58 34.31 13.72 11.27

Ion Implantation Profile in Patterned Substrate

Ion Implantation and Activation, Vol. 2

17

REFERENCES [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13]

J. F. Ziegler, J. P. Biersack, and U. Littmark, The stopping and range of ions in solid, Pergamon, 1885. SRIM-2003: http://www.srim.org/ K. Suzuki, Yoko Tada, Yuji Kataoka, and Tsutom Nagayama,“Monte Carlo Simulation of Ion Implantation Profiles Calibrated for Various Ions over Wide Energy Range,”J. Semiconductor Technology and Science, vol.9, No. 1, pp. 67-74, 2009. S. Furukawa, H. Matsumura, and H. Ishiwara, “Theoretical considerations on lateral spread of implanted ions,” Jpn J. Appl. Phys., vol. 11, pp. 134-142, 1972. H. –G. Lee and R. W. Dutton, “Two-dimensional low concentration boron profiles: modeling and measurement,” IEEE Trans. Electron Devices, ED-28, pp. 1136-1147, 1981. H. Ryssel, J. Lorentz, and W. Kruger, “Ion implantation into non-planar targets: Monte Carlo simulations and analytical models,” Nuclear Instruments and Methods in Physics Research, vol. B19-20, pp. 45-49, 1987. Mizuho Information & Research Institute, Inc.: Overview of the FabMeister-IM ion implantation profile simulator. http://www.mizuho-ir.co.jp/solution/research/semiconductor/fabmeister/ion/index.html K. Suzuki, “Ion Implantation Dose in Scaled Metal-Oxide-Semiconductor-Field-Effect-Transistor’s Gate,” Jpn. J. Appl. Phys., vol. 48, 010202, 2009. T. Aoyama, K. Suzuki, H. Tashiro, Y. Tada, T. Yamazaki, K. Takasaki, and T. Itoh, “Effect of florine on boron diffusion in thin silicon dioxide and oxynitride,” J. Appl. Phys., vol. 77, no. 1, pp. 417-419, 1995. K. Suzuki, A. Satoh, T. Aoyama, I. Namura, F. Inoue, Y. Kataoka, Y. Tada, and T. Sugii,"Thermal budget for fabricating a dual gate deep submicron CMOS with thin pure gate oxide," Jpn. J. Appl. Phys., vol. 35, pp. 1496-1502, 1996. P. Tuinhout, A. H. Montree, J. Schmitz, and P. A. Stolk, “Effects of gate depletion and boron penetration on matching of deep submicron CMOS transistors,” Electron Devices Meeting, Technical Digest., pp. 631 – 634,1997. M. Cao, P. V. Voorde, M. Cox, W. Wayne, “Boron diffusion and penetration in ultrathin oxide with poly-Si gate,” Electron Device Letters, EDL-19, pp. 291-293, 1998. K. Suzuki, “Extended Lindhard-Scharf-Schiott (LSS) Theory for Ion Implantation Profiles Expressed with Pearson Function,” Jpn. J. Appl. Phys., vol. 48, No. 4, 046510, 2009.

Send Orders for Reprints to [email protected] Ion Implantation and Activation, Vol. 2, 2013, 18-31

18

CHAPTER 2 Analytical Model for Two-Dimensional Profile in MOSFET’s Abstract: Two-dimensional profile model for ion implantation at high tilt angle was derived, in order to describe the pocket ion implantation of MOSFETs. Then we can generate two-dimensional profile of ion implantation for the full MOS process neglecting diffusion of dopants, in order to predict electrical characteristic of MOSFETs.

Keywords: Ion implantation, two-dimensional profile, lateral distribution, MOSFET’s, co-implantation, flash lamp annealing, redistribution, diffusion, inverse modeling, extension, straggling, lateral straggling, reverse short channel effect, pocket ion implantation, VLSI. INTRODUCTION The suppression of redistribution of ion implanted impurities is invoked as the device is scaled down, and thus co-implantation using C, N, and F [1-7] and flash lamp annealing [8-12] technologies have been intensively investigated. We want to predict device characteristics using the ion implantation profiles. If there are analytical ion implantation profiles in a MOS-structure substrate, we might be able to easily simulate the electrical characteristics of MOS devices. In this stage, inverse modeling [13-17] should be vital since we can predict optimal profile for given device characteristics without assuming artifact functions such as 2-D Gaussian and B-spline.

Figure 1: MOS structure. Kunihiro Suzuki All rights reserved-© 2013 Bentham Science Publishers

Analytical Model for Two-Dimensional Profile in MOSFET’s

Ion Implantation and Activation, Vol. 2 19

MOSFETs consist of four doping regions i.e., channel, pocket, extension, and source/drain. The corresponding four ion implantation processes are performed as shown in Fig. 1. An analytical model for two-dimensional profiles with a low tilt angle has been derived [18-20]. However, pocket ion implantation with high tilt angles has been commonly used to suppress the short channel effects [21]. Therefore, the models are extended to the case with high tilt angle, which is described in [22]. Analytical Model with Low-Tilt Angles Channel, extension, and source/drain ion implantations are usually performed with low tilt angles. Therefore, the analytical model for 2-D impurity profile [18-20] that is described in chapter 1, can be easily applied to these regions. In each process step, we have information of ion implantation conditions and device parameters of gate length LG and side wall thickness Lside , and we can get the moment parameters of R p , R p , R pt and  based on a database, where R p is the projected range, R p is the straggling, R pt is the lateral straggling, and  is the dose. Using the parameters, we can generate the corresponding profiles as follows.

(i) Substrate The concentration can be assumed to be constant given by N 0  x, y   N sub

(1)

(ii) Channel ion implantation It is performed in plane substrates, and the profile can be expressed as

  y  R 2   p  exp   N1  x, y    2R p 2  2 R p   (iii) Extension ion implantation

(2)

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Ion Implantation and Activation, Vol. 2

Kunihiro Suzuki

The ion is implanted into substrate with a gate pattern. The corresponding profile can be expressed as    erf   N 2  x, y   1      

 LG  2 x   2R pt 

    erf   2

 LG  2 x   2R pt 

      y  R 2   p   exp   2  2 R   R 2  p p      

(3)

where LG is the gate length. (iv) Source/drain ion implantation A side wall is usually formed before the source/drain ion implantation, and the corresponding profile can be expressed as    erf  N 3  x, y   1      

 LG  2 Lside  x  2    erf 2R pt     2

 LG  2 Lside   x   2   2R pt     y  R 2   p    (4) exp   2  2 R   2 R  p p      

where Lside is the thickness of the side wall. Analytical Model with High-Tilt Angles

Pocket ion implantation is usually performed with high tilt angles to increase the impurity penetration under the gate pattern, and also performed at four rotation angles to ensure symmetry as shown in Fig. 2. We focus on the rotation angle of 90o as shown in Fig. 2(a), and then it will be easy to derive the model for other rotation angles. It should be noted that we define the dose  on the plane perpendicular to the ion beam axis.

Analytical Model for Two-Dimensional Profile in MOSFET’s

Ion Implantation and Activation, Vol. 2 21

Figure 2: Schematic pocket ion implantation with four directions. (a) First time: rotation 90o (b) Second time: rotation 180o, (c) Third and Fourth times: rotation 0 and 270o.

22

Ion Implantation and Activation, Vol. 2

Kunihiro Suzuki

Figure 3: Axis system for the pocket ion implantation in the region a1 .

Region a1

We first focus on the source drain region a1 , which is far from the gate pattern, as shown in Fig. 2(a). We define axis system  t , s  regarding the beam direction, and  x, y  regarding the wafer surface as shown in Fig. 3. The corresponding profiles denoted as N 4 _ R 90 _ a1  t , s  , can be evaluated as the summation of the ions implanted into the region between t  ti and t  ti  dti , and can be evaluated as 

   s  t tan   R 2    t  ti 2  1 1 i p    N 4 _ R 90 _ a1  t , s    exp  exp    dti   2 R pt 2R p 2 2R pt 2   2 R p   s    tan   1 1    erf  2 2

 1   2 1R p R pt

    2 cos   t R p 2 cos   R p R pt 2 sin       sR p tan     

  s  R cos   t sin   2   p  cos    exp      2 12 2 1  

(5)

Analytical Model for Two-Dimensional Profile in MOSFET’s

Ion Implantation and Activation, Vol. 2 23

where

 12  R p 2 cos 2   R pt 2 sin 2 

t, s 

(6)

is related to  x, y  as

t  x cos   y sin    s  y cos   x sin 

(7)

We tentatively set the origin as D. Equation 5 is then converted to

  1 1 N 4 _ R 90 _ a1  x, y     erf 2 2 

 yR p 2   R p R pt 2 sin       tan   2 1R p R pt     

(8)

  y  R cos  2   cos  p  exp      2 12 2 1   Since the profile is in the region far from the gate pattern, it should be the same as the one implanted in plane substrate with high tile angles. Therefore, it should not depend on x, which is expressed by Eq. 8. Region a2

We then focus on region a2 in Fig. 2(a). The region is near the gate pattern, and thus the ion implantation at this region is influenced by the gate. We assume that the moment parameters of gate and gate insulator are the same, which is valid for typical system of polycrystalline Si for gate, and SiO2 for gate insulator. However, the assumption become questionable when we use HfO2 gate insulators, and therefore we must extend the model for multi-layers [23, 24] to this high tilt angle case, which has not been done. The corresponding profile is denoted as N 4 _ R 90 _ a2  t , s  , and can be evaluated as the summation of the ions implanted into the region between t  ti and t  ti  dti , and can be evaluated as

24

Ion Implantation and Activation, Vol. 2

N 4 _ R 90 _ a2  t , s 

Kunihiro Suzuki



0

2    ti   s R      p    t  ti 2  1 1 tan      exp  exp     dti 2   2 R pt 2R p 2 2 R p   2R pt       



   0

(9)

  s  t tan   R 2    t  ti 2  1 1 i p  exp   exp dti  2    2 R pt 2R p 2 2  R 2 R p   pt    

where we set a tentative origin at A in this analysis. We then convert the axis system from  t , s  to  x, y  , and obtain N 4 _ R 90 _ a2  x, y   1 1    erf  2 2

 y 2 2  R p R pt 2 cos   x  R pt 2  R p 2  sin  cos      2 2 R p R pt   

  x  R sin  2   sin  p  exp   2    2 2 2 2    1 1    erf 2 2 

(10)

 x 12  R p R pt 2 sin   y  R p 2  R pt 2  sin  cos      2 1R p R pt   

  y  R cos  2   cos  p  exp     2 12 2 1   where

 22  R p 2 sin 2   R pt 2 cos 2  Finally, we move the origin of A to the center of the gate, and obtain

(11)

Analytical Model for Two-Dimensional Profile in MOSFET’s

Ion Implantation and Activation, Vol. 2 25

Figure 4: Axis system for the pocket ion implantation in the region a2 .

N 4 _ R 90 _ a2  x, y   1 1     erf 2 2 

  LG   2 2 2 2  y 2  R p R pt cos    x  2   R pt  R p  sin  cos        2 2 R p R pt      

2     LG    x    R p sin    2   sin       exp  2   2 2 2 2    

 1 1     erf 2 2 

 LG  x  2   

  2 2 2 2   1  R p R pt sin   y  R p  R pt  sin  cos       2 1R p R pt    

  y  R cos  2   cos  p  exp   2   2  2 1 1  

(12)

26

Ion Implantation and Activation, Vol. 2

Kunihiro Suzuki

The regions of a1 and a2 are bounded by

L  y x G 2 

  tan  

(13)

Figure 5: Axis system for the pocket ion implantation in the region b.

Region b

We then focus on the region b in Fig. 2(a) and the corresponding axis system is shown in Fig. 5. We further assume that the gate perfectly shades the ion beam. The corresponding profile is denoted as N 4 _ R 90 _ b  t , s  , and it can be evaluated as the summation of the ions implanted into the region between t  ti and t  ti  dti , and can be evaluated as

Analytical Model for Two-Dimensional Profile in MOSFET’s

Ion Implantation and Activation, Vol. 2 27

N 4 _ R 90 _ b  t , s 

   s  t tan   R 2    t  ti  2  1 1 i p    exp  exp   dti  2    2 R pt 2 R p 2 2 R   2 R p   pt      s tan  0

(14)

where we set a tentative origin at B in this analysis. We then convert the axis system from  t , s  to  x, y  , and obtain N 4 _ R 90 _ b  x, y    1   erf 2 

 yR p 2   R p R pt 2 sin     tan   2 1R p R pt    

 x 12  R p R pt 2 sin   y  R p 2  R pt 2  sin  cos    1   erf   2 2 1R p R pt   

(15)

  y  R cos  2   cos  p  exp     2 12 2 1  

Finally, we move the origin of B to the center of the gate, and obtain N 4 _ R 90 _ b  x, y    1   erf 2 

 yR p 2   R p R pt 2 sin     tan   2 1R p R pt    

  LG   x  dG tan   2 1  erf    2  

  2 2 2 2   1  R p R pt sin   y  R p  Rpt  sin  cos       2 1R p R pt    

  y  R cos  2   cos  p  exp     2 12 2 1  

(16)

28

Ion Implantation and Activation, Vol. 2

Kunihiro Suzuki

We then finally obtain the ion implantation profile at a 90o rotation angle as

 N 4 _ R 90 _ a1  N 4 _ R 90 _ b N 4 _ R 90  x, y     N 4 _ R 90 _ a2  N 4 _ R 90 _ b

for region a1 for region a2

(17)

The ion implantation profile at a 270o rotation angle of N 4 _ R 270  x, y  can be simply expressed as N 4 _ R 270  x, y   N 4 _ R 90   x, y 

(18)

The regions a1 and a2 are bounded by

L  y   x  G 2 

  tan  

(19)

The ion implantation profile at a 0oand 180o rotation angle of N 4 _ R 0  x, y  , N 4 _ R180  x, y  can be simply expressed as N 4 _ R 0,180  x, y     erf    1     

 LG  2 x   2R pt 

    erf   2

 LG  2 x   2R pt 

   2       exp    y  R p cos     2   2 12 1      

(20)

The concentration for the pocket ion implantation is then given by N4   N4 _ R

(21)

R

Finally, we obtain the total net impurity concentration N net as N net   sgn i N i i

(22)

Analytical Model for Two-Dimensional Profile in MOSFET’s

Ion Implantation and Activation, Vol. 2 29

where sgn i depends on the type of the dopants given by N i : donor 1 sgn i   1 N i : acceptor

(23)

This model has been applied to the MOS process flow [22], and it was demonstrated that the analytical model agrees well with the numerical model over various LG as shown in Fig. 6. 1.0 Threshold voltage (V)

VD = 1.0 V

Analytical 5 keV Numerical 10 keV Numerical

0.5

0.0 0.00

0.05

0.10 LG (m)

0.15

0.20

Figure 6: Comparison of dependence of threshold voltage on gate length using analytical two-dimensional profile with one using 2-D process simulator.

REFERENCES [1]

[2]

[3]

J. C. Hu, A. Chaterjee, M. Mehrotra, J. Xu, W. –T. Shiau, and M. Rodder, “Sub-0.1 mm CMOS source/drain extension spacer formed using nitrogen implantation prior to thick gate re-oxidation,” Symposium on VLSI Tech., pp. 488-189, 2000. Y. Momiyama, K. Okabe, H. Nakao, M. Kojima, M. Kase, and T. Sugii, “Extension engineering using carbon co-implantation technology for low power CMOS design with phosphorus- and Boron-extension,“ Ext. abs. The 7th International Workshop on Junction Technology, pp. 63-64, 2007. P. A. Stolk, D. J. Eaglesham, H. –J. Gossmann, and J. M. Poate, “Carbon incorporation in silicon for suppressing interstitial-enhanced boron diffusion,” Appl. Phys. Lett., vol. 79, pp. 1370-1372, 1995.

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Kunihiro Suzuki

E. Napolitani, A. Coati, D. De Salvador, and A. Carnera, “Complete suppression of the transient enhanced diffusion of B implanted in preamorphized Si by interstitial trapping in a spatially separated C-rich layer,” Appl. Phys. Lett., vol. 79, pp. 4145-4147, 2001. G. Impellizzeri, J. H. R dos Santos, S. Mirabella, and F. Priolo, “Role of fluorine in suppressing boron transient enhanced diffusion,” Appl. Phys. Lett.,vol. 84, pp. 1862-1864, 2004. Giorgia M. Lopez and Vincenzo Fiorentini, Giuliana Impellizzeri and Salvatore Mirabella, “Fluorine in Si: Native-defect complexes and the suppression of impurity diffusion,“ Physical Review B, vol. 72, 045219, 2005. X. D. Pi, C. P. Burrows, and P. G. Coleman, “Fluorine in silicon: diffusion, trapping, and precipitation,” Physical Review Letters, vol. 90, 155901-1, 2003. S. H. Jain, P. B. Griffin, J. D. Plummer, S. McCoy, J. Gelpey, T. Selinger, and D. F. Downery, “Low resistance, low-leakage ultrashallow p+-junction formation using millisecond flash anneals,” IEEE Trans. Electron Devices, ED-52, No. 7, pp. 1610-1615, 2005. J. Gelepey, S. McCoy, D. D. Camm, W. Lerch, S. Paul, P. Pichler, J. O. Borland, P. Timans, “Flash annealing technology for USJ: Modeling and metrology,” 14th RTP, pp. 103-110, 2006. W. Lerch, S. Paul. J. Nisess, J. Chan, S. McCoy, J. Gelpey, F. Cristiano, F. Severac, P. F. Fazzini, D. Boltze, P. Pichler, A. Martinez, A. Mineji, and S. Shishiguchi, “Experimental and theoretical results of dopant activation by a combination of spike and flash annealing,” 7th International Workshop on Junction technology, pp. 129-134, 2007. K. T. Nishinohara, T. Ito, and K. Suguro, “Improvement of performance deviation and productivity of MOSFETs with gate length below 30 nm by flash lamp annealing,” IEEE Transactions on Semiconductor Manufacturing, vol. 17, No. 3, pp. 286-291, 2004. F. Ootsuka, A. Katakami, K. Shirai, T. Watanabe, H. Nakata, Y. Ohji, and M. Tanjyo, “Ultaralow-thermal-budget CMOS process using flash-lamp annealing for 45 nm Metal/high-k FETs,” IEEE Transactions on Electron Devices, ED-55, No. 4, pp. 1042-1049, 2008. N. Khalil, J. Faricelli, C. –L. Huang, and S. Serberherr, “Two-dimensional dopant profiling of submicron metal-oxide-semiconductor field-effect transistor using nonlinear least squares inverse modeling,” J. Vac. Sci. Technol. B, vol. 14, No. 1, pp. 224-230, 1996. Z. K. Lee, M. B. Mcllrash, and D. A. Antoniadis, “Two-dimensional doping profile characterization of MOSFET’s by inverse modeling using I-V characteristics in the subthreshold region,” IEEE Transactions on Electron Devices, ED-46, No. 8, pp. 1640-1649, 1999. C. Y. T. Chiang, Y. T. Yeow, and G. Ghodsi, “Inverse modeling of two-dimensional MOSFET dopant profile via capacitance of the source/drain gated diode,” IEEE Transactions on Electron Devices, ED-47, No. 7, pp. 1385-1392, 2000. I. J. Djomehri and D. A. Antoniadis, “Inverse modeling of sub-100 nm MOSFETs using I-V and C-V,” IEEE Transactions on Electron Devices, ED-49, No. 4, pp. 568-575, 2002. H. Hayashi, M. Matsuhashi, K. Fukuda, and K. Nishi, “Inverse modeling and its application to MOSFET channel profile extraction,” IEICE. Trans. Electron., vol. E82-C, No. 6, pp. 862-869, 1999. S. Furukawa, H. Matsumura, and H. Ishiwara, “Theoretical Considerations on Lateral Spread of Implanted Ions,” Jpn J. Appl. Phys., vol. 11, pp. 134-142, 1972.

Analytical Model for Two-Dimensional Profile in MOSFET’s

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H. –G. Lee and R. W. Dutton, “Two-dimensional low concentration boron profiles: modeling and measurement,” IEEE Trans. Electron Devices, ED-28, pp. 1136-1147, 1981. H. Ryssel, J. Lorenz, and W. Kruger, “Ion implantation into non-planar targets: Monte Carlo simulations and analytical models,” Nuclear Instruments and Methods in Physics Research, vol. B19-20, pp. 45-49, 1987. B. Yu, C. H. J. Wann, E. D. Nowak, K. Noda, and C. Hu, “Short-channel effect improved by lateral channel-engineering in deep-submicrometer MOSFET’s,” IEEE Trans. Electron Devices, vol. 44, No. 2, pp. 627-634, 1997. K. Suzuki, R. Tanabe, and S. Kojima, "Analytical model for two-dimensional ion implantation profile in MOS-structure substrate," IEEE Trans. Electron Devices, vol. ED-56, NO.12, pp.3083-3089, 2009. G. A. J. Amaratunga, K. Sabine, and A. G. R. Evens, “The modeling of ion implantation in a three-layer structure using the method of dose matching,” IEEE Trans. Electron Devices, vol. ED-32, pp. 1889-1890, 1985. R. Tielert, “Two-dimensional numerical simulation of impurity redistribution in VLSI processes,” IEEE Trans. Electron Devices, vol. ED-27, pp. 1479-1483, 1980.

Send Orders for Reprints to [email protected] Ion Implantation and Activation, Vol. 2, 2013, 32-53

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CHAPTER 3 Three-Dimensional Ion Implantation Profile Based on Rp Line Concept Abstract: We first simplify the existing model for two-dimensional profiles without losing accuracy. Then, a geometrical appreciation is given to the model. Next, a R p line concept is generated from the simplified model. We can generate three-dimensional ion implantation profiles related to the R p line for various device structures, and demonstrate that this procedure is applied to three-dimensional ion implantation profiles in FinFET. Furthermore, the models are extended to make Pearson function available.

Keywords: Ion implantation, three-dimensional profile, two-dimensional profile, lateral distribution, Pearson function, Gaussian profile, joined half Gauss, diffusion, device simulator, inverse modeling, diffusion, co-implantation, flash lamp annealing, MOS, Rp line, rotation angle, tilt angle, short channel effect, straggling. INTRODUCTION Ion implantation profiles are important to predict the device characteristics as an initial condition. Furthermore, it becomes more important for the state of the art devices since researchers have tried to suppress the diffusion by using co-implantation and flash lamp annealing [1-12]. An analytical ion implantation profile in a MOS-structure substrate including high tilt angles is derived and its accuracy is demonstrated by using a two-dimensional (2-D) device simulator [13]. This model is also vital for its application to inverse modeling [14-19]. However, the derivation process and final form of the model are rather complicated. If we change the device structure, we should derive the corresponding model by using similar elaborate derivation processes. In this chapter, we simplify the models described in chapter 2 without losing accuracy. The R p line concept is generated from the simplified model by geometrical appreciation of the model. We can draw R p lines for various shapes of devices easily, and the ion implantation concentration profiles can be generated based on the R p line concept.

Kunihiro Suzuki All rights reserved-© 2013 Bentham Science Publishers

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SIMPLIFICATION OF THE MODEL The ion implantation profiles in Fig. 1 were derived in chapter 2, and are given as follows. Region a1 :

  1 1 N 4 _ R 90 _ a1  x, y     erf 2 2 

 yR p 2   R p R pt 2 sin       tan   2 1R p R pt     

(1)

  y  R cos  2   cos  p  exp    2    2 2 1 1   Region a2 : N 4 _ R 90 _ a2  x, y   1 1     erf 2 2 

  LG   2 2 2 2  y 2  R p R pt cos    x  2   R pt  R p  sin  cos        2 2 R p R pt      

2   LG      x    R p sin    2   sin       exp  2    2 2 2 2    

 1 1     erf 2 2 

  LG  2 2 2 2 R sin  cos      x R R y R      sin   p pt p pt 1      2    2 1R p R pt      

  y  R cos  2   cos  p  exp     2 12 2 1  

(2)

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Figure 1: Schematic ion implantation into gate pattern substrate with rotation of 90o.

Region b: N 4 _ R 90 _ b  x, y    1   erf 2 

 yR p 2   R p R pt 2 sin     tan   2 1R p R pt    

L   x  dG tan   G   1 2  erf    2  

  2 2 2 2   1  R p R pt sin   y  R p  R pt  sin  cos       2 1R p R pt    

(3)

  y  R cos  2   cos  p  exp      12 2 2 1  

where

 12  R p 2 cos 2   R pt 2 sin 2 

(4)

 22  R p 2 sin 2   R pt 2 cos 2 

(5)

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We simplify the models hereafter. Approximating R p  R pt , that is： R p  R pt   1   2  

(6)

we reduce Eq. 2 to

N 4 _ R 90 _ a2  x, y  2   LG      x    R p sin     y  R p cos     sin  2   1 1         erf  exp   2   2 2 2  2 2           LG    y  R cos  2  1 1 x   R p sin     cos   p   2       erf   exp   2    2 2 2   2 2           

(7)

Let us compare the second tem in Eq. 7 and Eq. 1. When x  2 , the second term reduces to

  y  R cos  2   cos  p  N 4 _ R 90 _ a2  x, y   exp   2   2  2  

(8)

The pre-factor of Eq. 1 expresses that the integration area related to air cannot be negligible in very near surface. When the profile is deeper than 2 tan  , Eq. 1 reduces to

  y  R cos  2   cos  p  exp   N 4 _ R 90 _ a1  x, y     2 12 2 1  

(9)

and Eq. 9 becomes equal to Eq. 8 if we convert  to  1 in Eq. 8. We can regard the prefactor of the second term in Eq. 7 as lateral distribution, and hence

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convert  to  2 . Similar discussion can be done for the first term in Eq. 7. Based on the above discussion, we convert  to  1 or  2 , and modify Eq. 7 as N 4 _ R 90 _ a  x, y  2   LG      x    R p sin     y  R p cos     sin  2   1 1         erf  exp   2   2 2 2 1 2 2     2 2    

 1 1     erf 2 2 

LG   x  2   

(10)

    y  R cos  2    R p sin     cos  p     exp     2 12 2 2 2 1      

and Eq. 3 as

 1 1  N 4 _ R 90 _ b  x, y     erf 2 2 

LG     x  dG tan   2   2 2  

    R p sin          

(11)

  y  R cos  2   cos  p   exp     2 12 2 1   From the symmetrical appreciation, the profiles for a rotation angle of 270o can be obtained as N 4 _ R 270  x, y   N 4 _ R 90   x, y 

The ion implantation profile for rotation angles of 0 and 180o is given by

(12)

Three-Dimensional Ion Implantation Profile Based

   erf  N 4 _ R 0,180  x, y   1      

 LG  2 x   2R pt 

    erf   2

 LG  2 x   2R pt 

Ion Implantation and Activation, Vol. 2

   2       exp    y  R p cos     2   2 12 1      

37

(13)

It should be noted that Eq. 10 is valid for region a1 and a2 . Fig. 2 compared the simplified model and the analytical model for various conditions using R pt  r R p . The agreement is best for r  1 as is expected, but it is also good for other ones. The two-dimensional profiles are the same for both analytical and simplified model as shown in Fig. 3. The short channel effect is also verified as shown in Fig. 4, where the parameters are exactly the same as those in chapter 2. 19

Concentration (cm-3)

10

B 10 keV 9 x 1012 cm-2 tilt  = 27o Rp = 38.41 nm Rp = 30.9 nm

18

10

y = Rp cos R = 1.5 R pt

17

10

p

R = 1.0 R pt

p

R = 0.5 R pt

p

Simple model 16

10

0

0.1 Distance (m)

0.2

Figure 2: Comparison of simplified lateral distribution model with simple model for various R pt .

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Figure 3: Comparison of two-dimensional profile of analytical and simplified analytical model. B is ion implanted at 10 keV, tilt 27o and a dose of 9x1012 cm-2. The corresponding moment parameters are R p  38.41 nm, R p  30.9 nm, R pt  16.0 nm .

1.0 Threshold voltage (V)

VD = 1.0 V

5keV Simple 5keV Analytical 5 keV Numerical 10 kV Simple 10keV Analitical 10 keV Numerical

0.5

0.0 0.00

0.05

0.10 LG (m)

0.15

0.20

Figure 4: Dependence of threshold voltage Vth on gate length. The results for numerical, analytical and simplified analytical model are shown.

Three-Dimensional Ion Implantation Profile Based

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39

GEOMETRIC APPRECIATION OF SIMPLIFIED MODEL

Here, we introduce a R p line concept. Performing the following axis conversion   LG   R p sin   u a  x    2   v  y  R cos  p  a

(14)

Equation 10 reduces to a simple form of 1 1 N 4 _ R 90 _ a2  ua , va     erf  2 2 1 1    erf  2 2

 va    sin   ua 2  exp       2  2 2  2 2   2 1    ua    cos   va 2   exp     2  2  2    2 1   2  1

(15)

Similarly, performing the following axis conversion in region b   LG   dG sin   R p sin   ub  x    2   v  y  R cos  p  b

(16)

we can reduce Eq. 11 to a simple form of 1 1 N 4 _ R 90 _ b  ub , vb     erf  2 2

  vb 2  ub    cos    exp     2  2 2   2 1  2 1  

(17)

Equations 15 and 17 have a certain universal form and we can appreciate geometrically as follows. Inspecting Eqs. 15 and 17, we can draw lines in Fig. 5(a), where we call them R p lines. The R p line 3 is related to the first term in Eq. 15, the R p line 4 to the second term in Eq. 15, and R p line 1 to Eq. 17. If we redefine the axis system related to the R p line as shown in Fig. 5(a), all related profiles have the universal form of

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Ion Implantation and Activation, Vol. 2

 u 1 N  u, v   erfc   2 2 u 

  cos   v2  exp     2  2 v  2 v  

Kunihiro Suzuki

(18)

where v corresponds to the axis perpendicular to the surface, and u parallel, and  corresponds to the angle with respect to the vertical axis, and the origin is

Figure 5: R p line. (a) Half infinite (b) Infinite.

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41

set at the edge of the line. The first term in Eq. 18 has the same form as the lateral distribution function where the ion implantation region is half infinite and, hence, it can be appreciated that the profile is related to the half infinite R p line as we assumed in our derivation. This is a good approximation since we assume the infinite gate height, and we can regard the drain and source edge as the region not influenced by the ions implanted into the gate region. However, in a device structure, a R p line is a finite one in general as shown later. Therefore, Eq. 18 should be modified to correspond to the finite line. When ions are implanted into the patterned substrate, it is easy to draw the R p lines as shown in Fig. 5(b). We can easily extend to the lateral term in Eq. 15 to that for the finite line with length L given by L   2 u  erf    erf  2 u    N  u, v   2

L   2 u     2 u  2     cos  exp   v   2  2 v  2 v 

(19)

This corresponds to the R p lines shown in Fig. 6. We denote the first term in Eq. 19 as

 Lu   2 u  erf    erf 2  u     fu  u, Lu ,  u   2

Figure 6: Definition of Rp line

 Lu   2 u     2 u   

(20)

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Limiting the rotation angles to 0, 90, 180, and 270o, we can easily extend the model to include one more axis, that is, for three-dimensional (3-D) profiles. We denote this axis as s, which is perpendicular to the uv -plane, where the tilt angle was defined. Therefore, the related lateral straggling  to the s-axis is always R pt . There are typically four patterns for R p lines of s-direction as shown in Fig. 7. The corresponding profile is denoted by g s _ a , g s _ b , g s _ c , g s _ d and can be given by    s  1   g s _ a  s, Ls ,  s   erf  2  2 s     Ls   Ls   s s   2  erf  2   erf    2 2 s   s         g s  s, Ls ,  s    g s _ b  s, Ls ,  s   2    Ls   Ls    2 s  2 s erf     erf     2 s   2 s       g  s, L ,    1  s s  s_c 2   g s _ d  s,  s   1

(21)

The 3-D profile can be expressed by

N  s, u , v   g s  s, Ls ,  s  f u  u, Lu ,  u  

 v2   cos  exp   2  2 v  2 v 

(22)

where the straggling is comprised of

  R 2 cos 2   R 2 sin 2  p pt  v  2 2 2 2  u  R pt cos   R p sin    s  R pt 

(23)

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Ion Implantation and Activation, Vol. 2

43

Figure 7: Four typical Rp lines related to s-direction.

EXTENSION TO PEARSON PROFILE

We express the model as

L   2 u  erf    erf  2 u    N  u, v   2   erf    

L   2 u     2 u  2     cos  exp   v   2  2 v  2 v  L  L  u  u   2 2   erf   2 u   2 u      N v,    2

(24）

where

 v2   cos  N  v,    exp   2  2 v  2 v 

(25)

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Ion Implantation and Activation, Vol. 2

Kunihiro Suzuki

This is the projected Gaussian profile in infinite plane as shown in chapter 2. Therefore, the model can be extended to Pearson function by replacing the projected Gaussian profile by those for Pearson function as shown in chapter 8 of volume 1. We describe the procedure briefly again. Once the ion implantation condition is given, we can obtain the related parameters of Pearson function related to beam axis. We approximately obtain parameters R pf and R pb of a joined half Gauss from the Pearson parameters of R p and a as

 3  2 1  a Rpf  Rp 2    1 a  2 2  8 

(26)

 3  2 1  a Rpb  Rp 2    1 a  2 2  8 

(27)

 is uniquely determined by the ratio of R pf to R pb in the joined half Gauss, that is r  R R is given by pf

pb

2

 JHG 



 4   2  1  r  1  r     

 r  1 

 2   2 1     r  1  r    

3 2

(28)

R pf and R pb for tilt  are expressed by R pf    R pf 2 cos 2   R pt 2 cos 2 

(29)

R pb    R pb 2 cos 2   R pt 2 cos 2 

(30)

We can then obtain the r for tilt  as r    Rpf   Rpb   and rJHG   

R pf   R pb  

(31)

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45

 JHG   for tilt  is given by substituting r   in Eq. 28. We set  for Pearson with tilt  as    , and propose relating it to  JHG   as

   

  JHG

 JHG  

(32)

We used a simple expression for  given by

          3 2  3  2

(33)

which holds  in the limited cases of   0,90o . However, Eq. 33 is invalid when   0 . We then use

       3 cos   3

(34)

In this case, we used n of 1 as a default value. R pt depends on depth in general. The depth y correspond to y y cos along the beam, and hence

 v  R pt  v   R pt 0  ma   Rp   cos  

(35)

APPLICATION TO FINFET

We apply R p line concept to the FinFET [20, 21] with the height of H , device width of W , and gate length of LG as shown in Fig. 8. We suppose the ion implantation with a tilt angle of  at a rotation of 90 and 270o (Fig. 9 corresponds to a rotation of 90o). The origin of the axis system of  x, y, z  is set at the bottom of FinFET as shown in Fig. 8. (The origin of z is set at the center of the gate in the analysis).

46

Ion Implantation and Activation, Vol. 2

Figure 8: Bird’s eye view of FinFET.

Figure 9: R p lines in xy-plane of FinFET with rotation of 90o.

Kunihiro Suzuki

Three-Dimensional Ion Implantation Profile Based

Ion Implantation and Activation, Vol. 2

47

Let us consider the case of a rotation of 90o N R 90 . Fig. 9 shows the corresponding R p lines. Profiles can be generated related to the three lines as follows. R p line 1:

N R 90 _1  s1 , u1 , v1   f s  s1 , LG ,  s  f u  u1 ,W  R p sin  ,  u  f v  v1 

The axis conversion to the

 x, y , z 

(36)

system can be expressed by

     x  u  R p sin  1  2   y   v   H  R cos    p 1    z  s1

(37)

R p line 2:

N R 90 _ 2  s2 , u2 , v2   f s  s2 , LG ,  s  fu  u2 , H ,  u  f v  v2 

The axis conversion to

 x, y , z 

(38)

system can be expressed by

    2     W    x   v2   2  R p sin         H   y   u2    R p cos     2    z  s 2 

(39)

R p line 3:

N R 90 _ 3  s3 , u3 , v3   f s  s2 , LG ,  s  fu  u3 ,W ,  u  f v  v3 

The axis conversion to

 x, y , z 

system can be expressed by

(40)

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Ion Implantation and Activation, Vol. 2

    D W   x  u3   2  R p sin   2    y    v  R cos   3 p   z  s3

Kunihiro Suzuki

(41)

Therefore, N R 90 can be N R 90  N R 90 _1  N R 90 _ 2  N R 90 _ 3

(42)

The profile with rotation 270o is symmetrical with respect to the yz-plane at x  0 and, hence, given by N R _ 270  x, y, z   N R _ 90   x, y, z 

(43)

The device parameters used here are W = 50 nm H = 200 nm LG = 0.1m and ion implantation conditions are As 30 keV 1 x 1015 cm-2, tilt 30o、rotation 90, 270o ( R p  25.9 nm, R p  11.2 nm, R pt  11.0 nm ) We evaluated 3-D profiles using the analytical model and numerical one using a process simulator called the Hyper Synthesized Process Simulator (SyProS) implemented in a Hyper Environment for Exploration of Semiconductor Simulation (HyENEXSS) [22, 23]. Fig. 10 compares the analytical 2-D profiles on the x-y plane, that is, the cross section of the bulk source region, with a numerical one. The analytical model agrees well with the numerical data.

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49

Figure 10: Analytical and numerical 2-D profiles on x-y plane, that is, bulk cross section of bulk source region.

21

Concentration (cm-3)

10

20

10

x=0 y direction z = LG/2

Analytical Numerical

19

10

0.0

0.10

0.20 0.30 0.40 Distance (m) (a)

0.50

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Ion Implantation and Activation, Vol. 2

Kunihiro Suzuki

21

Concentration (cm-3)

10

20

10

x direction y = Rp cos z = LG/2 Analytical Numerical

19

10 -0.03 -0.02 -0.010 0 0.01 0.02 0.03 Distance (m) (b) Figure 11: 1-D cut ion implantation profiles in x-y plane of FinFET. (a) y direction. (b) x direction.

Fig. 11 shows the one-dimensional (1-D) cut profiles of Fig. 10, y-direction (a), and x-direction (b). The analytical models agree well with the numerical ones. We have a rather high concentration at the height of H  R p cos  in the y direction, which is an inevitable profile within our ion implantation doping. The profile along the x-direction has a peak at the center, which shape can be controlled. Fig. 12 compares analytical and numerical 2-D profiles in the z-direction on the zx- and zy-planes, and Fig. 13 compares the 1-D cut profile of the z-direction. The analytical model well reproduces the numerical ones. Our analytical model readily expresses the lateral spread of ions under the edge of the gate, that is, an in-homogeneous effective gate length in 3-D spaces.

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Ion Implantation and Activation, Vol. 2

51

Concentration (cm-3)

Figure 12: 2-D ion implantation profile in zy- and zx-planes.

10

21

10

20

10

19

10

18

10

17

10

16

Source

x=0 y = H- Rp cos z direction

-0.10

Gate

Drain

Analytical Numerical

-0.050 0.0 0.050 Distance (m)

0.10

Figure 13: Comparison of analytical and numerical lateral spread of ion concentration profiles under a gate.

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Ion Implantation and Activation, Vol. 2

Kunihiro Suzuki

REFERENCES [1] [2]

[3] [4] [5] [6] [7] [8]

[9] [10]

[11] [12]

[13]

J. C. Hu, A. Chaterjee, M. Mehrotra, J. Xu, W. –T. Shiau, and M. Rodder, “Sub-0.1 m CMOS source/drain extension spacer formed using nitrogen implantation prior to thick gate re-oxidation,” Sysmposium on VLSI Tech., pp. 488-189, 2000. Y. Momiyama, K. Okabe, H. Nakao, M. Kojima, M. Kase, and T. Sugii, “Extension engineering using carbon co-implantation technology for low power CMOS design with phosphorus- and Boron-extension,“ Ext. abs. The 7th International Workshop on Junction Technology, pp. 63-64, 2007. P. A. Stolk, D. J. Eaglesham, H. –J. Gossmann, and J. M. Poate, “Carbon incorporation in silicon for suppressing interstitial-enhanced boron diffusion,” Appl. Phys. Lett., vol. 79, pp. 1370-1372, 1995. E. Napolitani, A. Coati, D. De Salvador, and A. Carnera, “Complete suppression of the transient enhanced diffusion of B implanted in preamorphized Si by interstitial trapping in a spatially separated C-rich layer,” Appl. Phys. Lett., vol. 79, pp. 4145-4147, 2001. G. Impellizzeri, J. H. R dos Santos, S. Mirabella, and F. Priolo, “Role of fluorine in suppressing boron transient enhanced diffusion,” Appl. Phys. Lett., vol. 84, pp. 1862-1864, 2004. Giorgia M. Lopez and Vincenzo Fiorentini, Giuliana Impellizzeri and Salvatore Mirabella, “Fluorine in Si: Native-defect complexes and the suppression of impurity diffusion,“ Physical Review B, vol. 72, 045219, 2005. X. D. Pi, C. P. Burrows, and P. G. Coleman, “Fluorine in silicon: diffusion, trapping, and precipitation,“ Physical Review Letters, vol. 90, 155901-1, 2003. S. H. Jain, P. B. Griffin, J. D. Plummer, S. McCoy, J. Gelpey, T. Selinger, and D. F. Downery, “Low resistance, low-leakage ultrashallow p+-junction formation using millisecond flash anneals,” IEEE Trans. Electron Devices, ED-52, No. 7, pp. 1610-1615, 2005. J. Gelepey, S. McCoy, D. D. Camm, W. Lerch, S. Paul, P. Pichler, J. O. Borland, P. Timans, “Flash annealing technology for USJ: Modeling and metrology,” 14th RTP, pp. 103-110, 2006. W. Lerch, S. Paul. J. Nisess, J. Chan, S. McCoy, J. Gelpey, F. Cristiano, F. Severac, P. F. Fazzini, D. Boltze, P. Pichler, A. Martinez, A. Mineji, and S. Shishiguchi, “Experimental and theoretical results of dopant activation by a combination of spike and flash annealing,” 7th International Workshop on Junction technology, pp. 129-134, 2007. K. T. Nishinohara, T. Ito, and K. Suguro, “Improvement of performance deviation and productivity of MOSFETs with gate length below 30 nm by flash lamp annealing,” IEEE Transactions on Semiconductor Manufacturing, vol. 17, No. 3, pp. 286-291, 2004. F. Ootsuka, A. Katakami, K. Shirai, T. Watanabe, H. Nakata, Y. Ohji, and M. Tanjyo, “Ultaralow-thermal-budget CMOS process using flash-lamp annealing for 45 nm Metal/high-k FETs,” IEEE Transactions on Electron Devices, ED-55, No. 4, pp. 1042-1049, 2008. K. Suzuki, R. Tanabe, and Shuichi Kojima, "Analytical model for two-dimensional ion implantation profile in MOS-structure substrate," IEEE Trans. Electron Devices, vol. ED-56, NO. 12, pp. 3083-3089, 2009.

Three-Dimensional Ion Implantation Profile Based

[14] [15]

[16] [17] [18]

[19] [20] [21] [22] [23]

Ion Implantation and Activation, Vol. 2

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H. Ahn, and M. A. E. Nokali, “Inverse modeling and its application in the design of high electron mobility transistors,” IEEE Transactions on Electron Devices, ED-42, No. 4, pp. 598-604, 1995. Z. K. Lee, M. B. Mcllrash, and D. A. Antoniadis, “Two-dimensional doping profile characterization of MOSFET’s by inverse modeling using I-V characteristics in the subthreshold region,” IEEE Transactions on Electron Devices, ED-46, No. 8, pp. 1640-1649, 1999. C. Y. T. Chiang, Y. T. Yeow, and G. Ghodsi, “Inverse modeling of two-dimensional MOSFET dopant profile via capacitance of the source/drain gated diode,” IEEE Transactions on Electron Devices, ED-47, No. 7, pp. 1385-1392, 2000. I. J. Djomehri and D. A. Antoniadis, “Inverse modeling of sub-100 nm MOSFETs using I-V and C-V,” IEEE Transactions on Electron Devices, ED-49, No. 4, pp. 568-575, 2002. G. Curatora, G. Doornbos, J. Loo, Y. V. Ponomarev, and G. I. Iannaccone, “Detailed modeling of sub-100-nm MOSFETs based on Schrödinger DD per subband and experiments and evaluation of the performance gap to ballistic transport,” IEEE Transactions on Electron Devices, ED-52, No. 8, pp. 1851-1858, 2005. H. Hayashi, M. Matsuhashi, K. Fukuda, and K. Nishi, “Inverse modeling and its application to MOSFET channel profile extraction,” IEICE. Trans. Electron., vol. E82-C, No. 6, pp. 862-869, 1999. D. Hisamoto, W. –C. Lee, J. Kedzierski, H. Takeuchi, K. Asano, C. Kuo, E. Anderson, T. –J. King, J. Bokor, and C. Hu, “FinFET-A self-alinged double-gate MOSFET scalable to 20 nm,” IEEE Trans. Electron Devices, ED-47, No. 12, pp. 2320-2325, 2000. S. –W. Ryu, J. –W. Han, C. –J. Kim, and Y. –K. Choi, “Investigation of isolation-dielectric effects of PDSOI FinFET on capacitorless 1T-DRAM” IEEE Trans. Electron Devices, ED-56, No. 12, pp. 3232-3235,2009. T. Wada, N. Kotani, “Design and development of 3-dimensional process simulator,” IEICE. Trans. Electron., vol. E82-C, No. 6, pp. 839-847, 1999. http://www.selete.co.jp/?lang=EN&act=Research&sel_no=103: Semiconductior Leading Edge Technology.

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54

CHAPTER 4 Ion Implantation Profile in Multi-Layer Structure Abstract: It is important to predict ion implanted profiles in substrates comprised of different materials, where related moment parameters are different. We describe two procedures to generate profiles in multi-layers by using data for each layer, that is, dose matching method, and R p normalized method, where R p is the projected range. We show the process in which the methods are applied to multi-layers. Dose matching method is a simple and effective method. However, it provides unstable results sometimes, while R p normalized method provides stable results.

Keywords: Ion implantation, multi-layer, dose, dose matching method, Rp normalized method, projected range, straggling, profile, effective thickness, Monte Carlo, P, W, Si, SiO2, channeling. INTRODUCTION Sometimes, ions are implanted into multi-layer substrates, for example, SiO2/Si structure. There are vast matrixes for the system: combinations of material and thickness of each layer. Therefore, it is impractical to establish corresponding database. Two kinds of procedures to generate profiles in multi-layers are proposed, which are dose matching and R p normalized method. R p and R p normalized method is also described as one alternative method. DOSE MATCHING METHOD Consider a situation where ions are implanted into a substrate composed of two layers of material 1 and material 2. We assume that we already have database of implantation profiles in the single layer substrate of material 1 and single layer substrate of material 2 and denote each profile N1  x  , and N 2  x  . The procedure of dose matching is shown in Fig. 1 [1, 2]. First, consider the first layer, and generate the profile in it N1  x  . Evaluate the dose retained in the thickness of the first layer d1 , and denote it as 1 , that is,

1 =

d1 0

N 1 x dx

(1) Kunihiro Suzuki All rights reserved-© 2013 Bentham Science Publishers

Ion Implantation Profile in Multi-Layer Structure

Ion Implantation and Activation, Vol. 2

55

Consider the second layer, and generate the profile in it as N 2  x  . Integrate the profile and find the location  2 where the dose matches 1 , that is, 1 =

2 0

N 2 x dx

(2)

Connect the profile in the first layer in the region between 0 and d1 the profile in the second layer in the region that is deeper than  2. This method automatically ensures the total dose, and hence it is called as dose matching method.

Figure 1: Procedure for generating profiles in double layers based on dose matching method.

This procedure can easily be extended to substrates with more than two layers as shown in Fig. 2. Generate the profile in the first layer and use it as the profile in the region 0  x  d1 . N x = N 1 x for 0 < x < d 1

(3)

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Ion Implantation and Activation, Vol. 2

Kunihiro Suzuki

Evaluate the dose in the first layer.

1 =

d1 0

N 1 x dx

(4)

Generate the profile in the second layer material, and find the depth  2 where the dose matches 1 , that is 1 =

2 0

N 2 x dx

(5)

Connect the profiles so that N 2 x becomes N 2  2 for x = d 1, that is, N x = N2 x - d1 - 2

for d 1 < x < d 1 + d 2

(6)

Evaluate the dose in the second layer

2 =

2 + d2 2

N 2 x dx

(7)

Generate the profile in the third layer material, and find the depth  3 where the dose matches 1 + 2, that is 1 + 2 =

3 0

N 3 x dx

(8)

Connect the profiles so that N 3 x becomes N 3  3 for x = d 1 + d 2, that is, N x = N3 x - d1 + d2 - 3

for d 1 + d 2 < x < d 1 + d 2 + d 3

(9)

Evaluate the dose in the third layer

3 =

3 + d3 3

N 3 x dx

(10)

The n-th step of this method is following: Generate the profile in the n-th layer material, and find the depth  n where the dose matches the dose summed up to (n-1)-th layer, that is

Ion Implantation Profile in Multi-Layer Structure

n

n-1

=

i=1

i

0

Ion Implantation and Activation, Vol. 2

N n x dx

57

(11) n-1

d i, that is, Connect the profiles so that N n x becomes N n  n for x = i =1 N x = Nn x -

n-1

d

i=1

i

- n

for

n-1

d

i=1

i