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Multi-scale simulations of single particle displacement damage in silicon

Tang Du He Chao-Hui Zang Hang Li Yong-Hong Xiong Cen Zhang Jin-Xin Zhang Peng Tan Peng-Kang

Multi-scale simulations of single particle displacement damage in silicon

Tang Du, He Chao-Hui, Zang Hang, Li Yong-Hong, Xiong Cen, Zhang Jin-Xin, Zhang Peng, Tan Peng-Kang
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  • Silicon devices are extensively used in space and other radiation-rich environments. They must withstand radiation damage processes that occur over wide range of time and length. Ion implantation technique, one of the most important process in the fabrication of integrated circuits, can also create the displacement damage in silicon lattice. Exposure of silicon wafer or silicon device to radiation causes the creations of variety of defects and has adverse effects on the electrical properties of devices. Although phenomenological studies on the radiation effects in silicon have been carried out in the past decades, the features of multi-scale of displacement damage make it difficult to characterize the defect production and evolution experimentally or theoretically. Recently, the silicon device with ultra-low leakage current was shown to be very sensitive to the permanent displacement damage induced by single particles, called single particle displacement damage (SPDD) event. To the best of our knowledge, the investigation of single particle displacement damage (SPDD) event in silicon device by the coupling molecular dynamics (MD) and kinetic Monte Carlo (KMC) techniques has not yet been reported so far. In this paper, MD simulations are combined with KMC simulations to investigate the formation and evolution of SPDD event in silicon. In MD simulations, Tersoff potential is used to describe the Si-Si atomic interactions. The potential smoothly joins to Ziegler-Biersack-Littmark potential that describes the energetic short range interactions well. All atoms in the MD cell are allowed to evolve 0.205 ns to track the damage production and short-term evolution. A multi-phase simulations are performed to improve the simulation efficiency. Then the nearest neighbor criterion is employed to identify the configurations and spatial distributions of interstitials and vacancies, which are used as input in KMC simulations to study the thermal diffusion and interactions of those defects in the time interval from 0.205 ns to 1000 s. The results show that no defects are missing when transferring from MD to KMC simulation and the whole damage obtained in MD simulations is reproduced in KMC simulations. Since the production and evolution of defects are simulated, the SPDD current could be calculated based on Shockley-Read-Hall theory. We derive the formula to calculate the SPDD current and its annealing factor related to interstitials and vacancies in the depletion region. The calculated annealing factors of defects are compared with the annealing factors of SPDD currents and also with the experimental results. The results show that an annealing factor of defects has the same value as the annealing factor of an SPDD current when only one type of defect is considered in the calculations, while there are some differences between these two annealing factors when two and more types of defects are considered. The annealing factors of defects can be used to represent the annealing behaviors of SPDD currents since the divergences between these two annealing factors are not significant. Finally, SPDD current annealing factor based MD simulation results obtained with Tersoff potential are compared with the results in our previous study in which the Stillinger-Weber potential is used, and also compared with experimental results. The comparisons show that the simulation results with considering both Stillinger- Weber potential and Tersoff potential are in good agreement with experimental results. Compared with the calculated results with considering the Tersoff potential, the results with considering the Stillinger-Weber potential are closer to experimental results.
      Corresponding author: He Chao-Hui, hechaohui@mail.xjtu.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11175138), the Key Program of the National Natural Science Foundation of China (Grant No. 11235008), the State Key Laboratory Program, China (Grant No. 20140134), and the Specialized Research Fund for the Doctoral Program of Higher Education, China (Grant No. 20130201120090).
    [1]

    Zhang Z G, Liu J, Hou M D, Sun Y M, Zhao F Z, Liu G, Han Z S, Geng C, Liu J D, Xi K, Duan J L, Yao H J, Mo D, Luo J, Gu S, Liu T Q 2013 Chin. Phys. B 22 096103

    [2]

    Yu J T, Chen S M, Chen J J, Huang P C 2015 Chin. Phys. B 24 119401

    [3]

    Bogaerts J, Dierickx B, Mertens R 2002 IEEE Trans. Nucl. Sci. 49 1513

    [4]

    Goiffon V, Magnan P, Saint-P O, Bernard F, Rolland G 2009 Nucl. Instrum. Methods Phys. Res. A 610 225

    [5]

    Battaglia M, Bisello D, Contarato D, Denes P, Doering D, Giubilato P, Kim T S, Mattiazzoc S, Radmilovicb V, Zaluskya S 2010 Nucl. Instrum. Methods Phys. Res. A 624 425

    [6]

    Virmontois C, Goiffon V, Magnan P, Girard S, Inguimbert C, Petit S, Rolland G, Saint-Pe O 2010 IEEE Trans. Nucl. Sci. 57 3101

    [7]

    Doeringa D, Deveauxa M, Domachowskia M, Dritsaa C, Froehlicha I, Koziela M, Muentza C, Ottersbacha S, Wagnerc F M, Strotha J 2011 Nucl. Instrum. Methods Phys. Res. A 658 133

    [8]

    Wang Z J, Tang B Q, Xiao Z G, Liu M B, Huang S Y, Zhang Y 2010 Acta Phys. Sin. 59 4136 (in Chinese) [王祖军, 唐本奇, 肖志刚, 刘敏波, 黄绍艳, 张勇 2010 物理学报 59 4136]

    [9]

    Zeng J Z, Li Y D, Wen L, He C F, Guo Q, Wang B, Ma L Y, Wei Y, Wang H J, Wu D Y, Wang F, Zhou H 2015 Acta Phys. Sin. 64 194208 (in Chinese) [曾骏哲, 李豫东, 文林, 何承发, 郭旗, 汪波, 玛丽娅, 魏莹, 王海娇, 武大猷, 王帆, 周航 2015 物理学报 64 194208]

    [10]

    Auden E C, Weller R A, Mendenhall M H, Reed R A, Schrimpf R D, Hooten N C, King M P 2012 IEEE Trans. Nucl. Sci. 59 3054

    [11]

    Auden E C, Weller R A, Schrimpf R D, Mendenhall M H, Reed R A, Hooten N C, Bennett W G, King M P 2013 IEEE Trans. Nucl. Sci. 60 4094

    [12]

    Raine M, Goiffon V, Paillet P, Duhamel O, Girard S, Gaillardin M, Virmontois C, Belloir J, Richard N, Magnan P 2014 IEEE Trans. Nucl. Sci. 61 2826

    [13]

    Otto G, Gerhard H, Grtner K 2003 Nucl. Instrum. Methods Phys. Res. B 202 114

    [14]

    Borodin V A 2012 Nucl. Instrum. Methods Phys. Res. B 282 33

    [15]

    Nordlund K, Averback M G S, Tarus J 1998 Phys. Rev. B 57 7556

    [16]

    Delarubia T D, Gilmer G H 1995 Phys. Rev. Lett. 74 2507

    [17]

    Jaraiz M, Rubio E, Castrillo P, Pelaz L, Bailon L, Barbolla J, Gilmer G H, Rafferty C S 2000 Mat. Sci. Semicon. Proc. 3 59

    [18]

    Martin-Bragado I, Riverab A, Vallesb G, Gomez-Sellesa J L, Caturla M J 2013 Comput. Phys. Commun. 184 2703

    [19]

    Nordlund K, Djurabekova F 2014 J. Comput. Electron 13 122

    [20]

    Plimpton S 1995 J. Comput. Phys. 117 1

    [21]

    Tersoff J 1989 Phys. Rev. B 39 5566

    [22]

    Ziegler J F, Biersack J P, Littmark U 1985 The Stopping and Range of Ions in Matter (Vol.1)(New York: Pergamon Press) p25ff

    [23]

    Farrell D E, Bernstein N, Liu W K 2009 J. Nucl. Mater. 385 572

    [24]

    Srour J R, Hartmann R A 1989 IEEE Trans. Nucl. Sci. 36 1825

    [25]

    Lazanu I, Lazanu S 2006 Phys. Scripta 74 201

    [26]

    Tang D, Martin-Bragado I, He C H 2015 International Conference on Radiation Effects of Electronic Devices Proceedings Harbin, China, October 19-21, 2015 p6

    [27]

    Aboy M, Santos I, Pelaz L 2015 J. Comput. Electron 13 40

  • [1]

    Zhang Z G, Liu J, Hou M D, Sun Y M, Zhao F Z, Liu G, Han Z S, Geng C, Liu J D, Xi K, Duan J L, Yao H J, Mo D, Luo J, Gu S, Liu T Q 2013 Chin. Phys. B 22 096103

    [2]

    Yu J T, Chen S M, Chen J J, Huang P C 2015 Chin. Phys. B 24 119401

    [3]

    Bogaerts J, Dierickx B, Mertens R 2002 IEEE Trans. Nucl. Sci. 49 1513

    [4]

    Goiffon V, Magnan P, Saint-P O, Bernard F, Rolland G 2009 Nucl. Instrum. Methods Phys. Res. A 610 225

    [5]

    Battaglia M, Bisello D, Contarato D, Denes P, Doering D, Giubilato P, Kim T S, Mattiazzoc S, Radmilovicb V, Zaluskya S 2010 Nucl. Instrum. Methods Phys. Res. A 624 425

    [6]

    Virmontois C, Goiffon V, Magnan P, Girard S, Inguimbert C, Petit S, Rolland G, Saint-Pe O 2010 IEEE Trans. Nucl. Sci. 57 3101

    [7]

    Doeringa D, Deveauxa M, Domachowskia M, Dritsaa C, Froehlicha I, Koziela M, Muentza C, Ottersbacha S, Wagnerc F M, Strotha J 2011 Nucl. Instrum. Methods Phys. Res. A 658 133

    [8]

    Wang Z J, Tang B Q, Xiao Z G, Liu M B, Huang S Y, Zhang Y 2010 Acta Phys. Sin. 59 4136 (in Chinese) [王祖军, 唐本奇, 肖志刚, 刘敏波, 黄绍艳, 张勇 2010 物理学报 59 4136]

    [9]

    Zeng J Z, Li Y D, Wen L, He C F, Guo Q, Wang B, Ma L Y, Wei Y, Wang H J, Wu D Y, Wang F, Zhou H 2015 Acta Phys. Sin. 64 194208 (in Chinese) [曾骏哲, 李豫东, 文林, 何承发, 郭旗, 汪波, 玛丽娅, 魏莹, 王海娇, 武大猷, 王帆, 周航 2015 物理学报 64 194208]

    [10]

    Auden E C, Weller R A, Mendenhall M H, Reed R A, Schrimpf R D, Hooten N C, King M P 2012 IEEE Trans. Nucl. Sci. 59 3054

    [11]

    Auden E C, Weller R A, Schrimpf R D, Mendenhall M H, Reed R A, Hooten N C, Bennett W G, King M P 2013 IEEE Trans. Nucl. Sci. 60 4094

    [12]

    Raine M, Goiffon V, Paillet P, Duhamel O, Girard S, Gaillardin M, Virmontois C, Belloir J, Richard N, Magnan P 2014 IEEE Trans. Nucl. Sci. 61 2826

    [13]

    Otto G, Gerhard H, Grtner K 2003 Nucl. Instrum. Methods Phys. Res. B 202 114

    [14]

    Borodin V A 2012 Nucl. Instrum. Methods Phys. Res. B 282 33

    [15]

    Nordlund K, Averback M G S, Tarus J 1998 Phys. Rev. B 57 7556

    [16]

    Delarubia T D, Gilmer G H 1995 Phys. Rev. Lett. 74 2507

    [17]

    Jaraiz M, Rubio E, Castrillo P, Pelaz L, Bailon L, Barbolla J, Gilmer G H, Rafferty C S 2000 Mat. Sci. Semicon. Proc. 3 59

    [18]

    Martin-Bragado I, Riverab A, Vallesb G, Gomez-Sellesa J L, Caturla M J 2013 Comput. Phys. Commun. 184 2703

    [19]

    Nordlund K, Djurabekova F 2014 J. Comput. Electron 13 122

    [20]

    Plimpton S 1995 J. Comput. Phys. 117 1

    [21]

    Tersoff J 1989 Phys. Rev. B 39 5566

    [22]

    Ziegler J F, Biersack J P, Littmark U 1985 The Stopping and Range of Ions in Matter (Vol.1)(New York: Pergamon Press) p25ff

    [23]

    Farrell D E, Bernstein N, Liu W K 2009 J. Nucl. Mater. 385 572

    [24]

    Srour J R, Hartmann R A 1989 IEEE Trans. Nucl. Sci. 36 1825

    [25]

    Lazanu I, Lazanu S 2006 Phys. Scripta 74 201

    [26]

    Tang D, Martin-Bragado I, He C H 2015 International Conference on Radiation Effects of Electronic Devices Proceedings Harbin, China, October 19-21, 2015 p6

    [27]

    Aboy M, Santos I, Pelaz L 2015 J. Comput. Electron 13 40

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  • Received Date:  01 September 2015
  • Accepted Date:  27 December 2015
  • Published Online:  20 April 2016

Multi-scale simulations of single particle displacement damage in silicon

    Corresponding author: He Chao-Hui, hechaohui@mail.xjtu.edu.cn
  • 1. School of Nuclear Science and Technology, Xi'an Jiaotong University, Xi'an 710049, China
Fund Project:  Project supported by the National Natural Science Foundation of China (Grant No. 11175138), the Key Program of the National Natural Science Foundation of China (Grant No. 11235008), the State Key Laboratory Program, China (Grant No. 20140134), and the Specialized Research Fund for the Doctoral Program of Higher Education, China (Grant No. 20130201120090).

Abstract: Silicon devices are extensively used in space and other radiation-rich environments. They must withstand radiation damage processes that occur over wide range of time and length. Ion implantation technique, one of the most important process in the fabrication of integrated circuits, can also create the displacement damage in silicon lattice. Exposure of silicon wafer or silicon device to radiation causes the creations of variety of defects and has adverse effects on the electrical properties of devices. Although phenomenological studies on the radiation effects in silicon have been carried out in the past decades, the features of multi-scale of displacement damage make it difficult to characterize the defect production and evolution experimentally or theoretically. Recently, the silicon device with ultra-low leakage current was shown to be very sensitive to the permanent displacement damage induced by single particles, called single particle displacement damage (SPDD) event. To the best of our knowledge, the investigation of single particle displacement damage (SPDD) event in silicon device by the coupling molecular dynamics (MD) and kinetic Monte Carlo (KMC) techniques has not yet been reported so far. In this paper, MD simulations are combined with KMC simulations to investigate the formation and evolution of SPDD event in silicon. In MD simulations, Tersoff potential is used to describe the Si-Si atomic interactions. The potential smoothly joins to Ziegler-Biersack-Littmark potential that describes the energetic short range interactions well. All atoms in the MD cell are allowed to evolve 0.205 ns to track the damage production and short-term evolution. A multi-phase simulations are performed to improve the simulation efficiency. Then the nearest neighbor criterion is employed to identify the configurations and spatial distributions of interstitials and vacancies, which are used as input in KMC simulations to study the thermal diffusion and interactions of those defects in the time interval from 0.205 ns to 1000 s. The results show that no defects are missing when transferring from MD to KMC simulation and the whole damage obtained in MD simulations is reproduced in KMC simulations. Since the production and evolution of defects are simulated, the SPDD current could be calculated based on Shockley-Read-Hall theory. We derive the formula to calculate the SPDD current and its annealing factor related to interstitials and vacancies in the depletion region. The calculated annealing factors of defects are compared with the annealing factors of SPDD currents and also with the experimental results. The results show that an annealing factor of defects has the same value as the annealing factor of an SPDD current when only one type of defect is considered in the calculations, while there are some differences between these two annealing factors when two and more types of defects are considered. The annealing factors of defects can be used to represent the annealing behaviors of SPDD currents since the divergences between these two annealing factors are not significant. Finally, SPDD current annealing factor based MD simulation results obtained with Tersoff potential are compared with the results in our previous study in which the Stillinger-Weber potential is used, and also compared with experimental results. The comparisons show that the simulation results with considering both Stillinger- Weber potential and Tersoff potential are in good agreement with experimental results. Compared with the calculated results with considering the Tersoff potential, the results with considering the Stillinger-Weber potential are closer to experimental results.

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