纤锌矿相GaN材料空穴输运特性的全带多粒子Monte Carlo模拟研究
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摘要
本文报告了采用全带多粒子Monte Carlo 方法模拟纤锌矿相GaN 体材料空穴输运特性的研究结果。首先介绍了纤锌矿相GaN 材料的结构特性和全带多粒子Monte Carlo 方法的原理,并将全带方法和常规分析带方法进行了比较。模拟的主要步骤包括定义物理系统、计算散射率、确定空穴运动的初始条件、确定自由飞行时间、选择散射机理、散射最终态的选择以及结果的处理, 其中引入了自散射以简化自由飞行时间的计算。模拟中包含的散射机理主要有声学声子散射、极性光学声子散射、电离杂质散射等。在散射率的计算中将空穴能量分成低能区和高能区,在低能区这些散射的散射率根据费米黄金规则计算得出;在高能区的散射率采用态密度标度化来实现。模拟所需的能带结构数据由经验赝势法得出。最后,列出了模拟程序的流程图。给出了平均能量、平均漂移速度与电场强度关系曲线等模拟结果,并对结果进行了分析。
In this paper, we study the hole transport properties of bulk wurtzite phase GaN by the full band ensemble Monte Carlo method. At first, we introduces the structure and characteristics of wurtzite phase GaN and the full band ensemble Monte Carlo method, and compares the full band Monte Carlo method with the general analytic band Monte Carlo method.The main steps include the definition of the physical system,the calculation of scattering rates,initial conditions of motion,calculation of free flight time,choice of the scattering mechanism, choice of the final state and treating result. Self-scattering method is used to simplify the calculation of free flight time. In our simulation model,the scattering mechanisms include acoustic phonon scattering, polar optical phonon scattering,and ionized impurity scattering and so on. The energy range of the holes is divided into two parts for the purpose of calculating the scattering rates. At low energy region,scattering rates are calculated using Fermi′s golden rule.At higher energy region,scattering rates are normalized by the final density of states.The band structure data is calculated using the empirical pseudopotential method. At final, flow chart of program is shown. The simulation results include average energy and average velocity as a function of electric field and so on.Analysis of the simulation results are also given.
In this paper, we study the hole transport properties of bulk wurtzite phase GaN by the full band ensemble Monte Carlo method. At first, we introduces the structure and characteristics of wurtzite phase GaN and the full band ensemble Monte Carlo method, and compares the full band Monte Carlo method with the general analytic band Monte Carlo method.The main steps include the definition of the physical system,the calculation of scattering rates,initial conditions of motion,calculation of free flight time,choice of the scattering mechanism, choice of the final state and treating result. Self-scattering method is used to simplify the calculation of free flight time. In our simulation model,the scattering mechanisms include acoustic phonon scattering, polar optical phonon scattering,and ionized impurity scattering and so on. The energy range of the holes is divided into two parts for the purpose of calculating the scattering rates. At low energy region,scattering rates are calculated using Fermi′s golden rule.At higher energy region,scattering rates are normalized by the final density of states.The band structure data is calculated using the empirical pseudopotential method. At final, flow chart of program is shown. The simulation results include average energy and average velocity as a function of electric field and so on.Analysis of the simulation results are also given.
引文
[1] H.Kosina,M.Nedjalkov.The Monte Carlo method for semiclassical charge transport in semiconductordevices[J]. Mathematics and Computers in Simulation,2001,55:93-102
[2] S.H.Gamal,T.S.Al-Harbi.Simple and efficient Monte Carlo simulation of high-temperature hot transport in silicon and diamond[J]. Microelectronics Journal,2001,32:327-329
[3] Baozeng Guo,Umberto Ravaiolib,Dengyuan Song.Properties of wurtzite GaN MESFETs studied by two-dimensional full band Monte Carlo approach[J]. Microelectronics Journal,2004,35:117-123
[4] 郭宝增,Umberto Ravaioli.深亚微米纤锌矿相AlGaN/GaN MODFET 输出特性的微分负阻效应[J].中国科学(E 辑),2003,33(6):568-576
[5] 郭宝增,孙荣霞, Umberto Ravaioli.用二维全带多粒子Monte Carlo 方法模拟纤锌矿相GaN 静电感应晶体管(SIT)特性[J].电子学报,2003,31(8):1121-1124
[6] Stephen K.O’Leary,Brian E.Foutz,Michael S.Shur,Udayan V.Bhapkar,Lester F.Eastman. Monte Carlo simulation of electron transport in wurtzite Aluminum nitride[J].Solid State Communications,105(10):621-626
[7] S.Jallepalli,M.Rashed,W.K.Shih,C.M.Maziar,A.F.Tasch,Jr.A full-band Monte Carlo model for hole transport in silicon[J].J.Appl.Phys,1997,81(5):2250-2255
[8] Ismail H.Oguzman,Jan Kolnik,Kevin F.Brennan,Rongping Wang,Tzu-Ning Fang,P.Paul Ruden. Hole transport properties of bulk zinc-blende and wurtzite phases of GaN based on an ensemble Monte carlo calculation including a full zone band structure[J].J.Appl.Phys,1996,80(8):4429-4436
[9] I.H.Oguzman,J.Kolnik,K.F.Brennan,R.Wang,P.P.Ruden.Monte Carlo Calculation of hole transport in bulk zincblende phase of GaN including a pseudopotential calculated band structure[J].Mat.Res.Soc.Symp.Proc,1996,395:479-483
[10] J.D.Albrecht,P.P.Ruden,T.L.Reinecke.Hole scattering near the valence band edge in wurtzite gallium nitride[J].Journal of applied physics,2002,92(7):3803-3814
[11] Yasuhiko Hayashi,Tetsuo Soga,Masayoshi Umeno,Takashi Jimbo.Analysis of hole transport in cubic phase of p-type GaN by relaxation time approximation[J].Physica B,1999,272:256-259
[12] A.A.Burk Jr.,M.J.O'Loughlin,R.R.Siergiej,et al. SiC and GaN wide bandgap semiconductor materials and devices[J]. Solid State Electronics,1999,43:1459-1464
[13] F.Schwierz,M.kittler,H.forster,D.Schipanski.The Potential of SiC and GaN for application in high speed devices[J]. Diamond and Related Materials,1997,6:1512-1514
[14] 顾彪,王三胜,徐茵等.GaN 基材料及其在短波光电器件领域的应用[J].高技术通讯,2002,03:104-110
[15] 刘恩科,朱秉升,罗晋生等.半导体物理学[M].国防工业出版社.1994,第4 版
[16] 梁春广,张冀.GaN——第三代半导体的曙光[J], 半导体学报,1999,20(2):89-99
[17] 顾忠良.GaN 半导体研究与进展[J].半导体情报,1999,36(4):10-14
[18] 宋登元,王秀山.GaN 材料系列的研究进展[J]. 微电子学,1998,28(2):124-128
[19] 谢世勇,郑有科,陈鹏,张荣. GaN 材料p 型掺杂[J]. 固体电子学研究与进展,2001,21(2):204-210
[20] C.J.Pan,G.C.Chi.The doping of GaN with Mg diffusion[J].Solid State Electronics,1999,43:621-623
[21] 薛松,韩彦军,郭文平,孙长征,郝智彪,罗毅.p 型GaN 材料的表面物理特性[J],半导体学报,2003,24(12):1280-1284
[22] AmanoH,KitoM,HiramatsuK,et al.P-type conductionin Mg-doped GaN treated with low-energy electron beam irradiation(LEEBI)[J].Jpn J Appl Phys,1989,28(12):2112
[23] Nakamura S,Mukai T,Senoh M,et al.Thermal annealing effects on P-type Mg-doped GaN films[J].Jpn J Appl Phys,1992,31(2B):139
[24] Bernardini F,Fiorentini V,Bosin A.Theoretical evidence for efficient p-typ doping of GaN using beryllium[J].Appl Phys Lett,1997,70(22):2990
[25] N.MetroPolis and S.Ulam.The monte carlo method[J]. J.Am.stat.Ass.,1949,44:335-341
[26] Carlo Jacoboni,Lino Reggiani.The Monte Carlo method for the solution of charge transport in semiconductors with applications to covalent materials[J]. Rev.Mod.Phys,1983,55(3):645-703
[27] 叶良修. 小尺寸半导体器件的Monte Carlo 模拟[M].科学出版社.1997,第1 版
[28] H.E.Nilsson,E.Bellotti,M.Hjelm,K.Brennan.A comparison between different Monte Carlo models in simulation of hole transport in 4H-SiC[J]. Mathematics and Computers in Simulation,2001, 55:199-208
[29] 裴鹿成,张孝泽著. Monte Carlo 方法及其在载流子输运问题中的应用[M],科学出版社,1980,第1版
[30] 徐钟济著.Monte Carlo 方法[M].上海科学技术出版社,1985,第1 版
[31] Mark Lundstrom.Fundamentals of carrier transport[M].Modular series on solid state devices. 1990,V10
[32] 黄昆原著,韩汝琦改编.固体物理学[M].高等教育出版社.1988
[33] 赵平,魏同立,吴金. 在MonteCarlo器件模拟中确定自由飞行时间的自散射方法[J]. 固体电子学研究与进展, 2000,20(3):250-255
[34] 郭宝增,Umberto Ravaioli.用全带方法模拟纤锌矿相GaN 和ZnO 材料的电子输运特性[J].物理学报,2002,51(10):2344-2348
[35] Ismail H.Oguzman,Enrico Bellotti,Kevin F.Brennan,Jan Kolnik,Rongping Wang,P.Paul Ruden. Theory of hole initiated impact ionization in bulk zincblende and wurtzite GaN[J]. J.Appl.Phys,1997,81(12):7827-7834
[36] Y.Kamakura,H.Mizuno,M.Yamaji,M.Morifuji,K.Taniguchi,C.Hamaguchi,T.kunikiyo,M.Takenaka. Impact ionization model for full band Monte Carlo simulation[J].J.Appl.Phys,1994,75(7):3500-3505
[37] J.kolnik,I.H.Oguzman,K.F.Brennan,et al.Electronic transport studies of bulk zincblende and wurtzite phases of GaN based on an ensemble Monte Carlo calculation including a full zone band structure[J].J.Appl.Phys,1995,78:1033-1037
[38] U.V.BhaPkar,M.S.Shur.Monte Carlo calculation of velocity-fleld characteristics of wurtzite GaN[J].J.Appl.Phys,1997,82:1649-1655
[39] Wim Geerts,J.D.Mackenzie,C.R.Abernathy,et al.Electrical transport In P-GaN,n-InN and n-InGaN[J].Solid state electronics,1996,39(9):1289-1294
[40] J.D.Wiley. Valence-band deformation potentials for the Ⅲ-Ⅴcompounds[J].Solid state communications,1970(8):1865-1868
[41] 袁斌,马维新.UNIX 操作系统下FORTRAN 语言与C 语言混合编程的方法[J].小型微型计算机系统,1994,15(12):30-33
[2] S.H.Gamal,T.S.Al-Harbi.Simple and efficient Monte Carlo simulation of high-temperature hot transport in silicon and diamond[J]. Microelectronics Journal,2001,32:327-329
[3] Baozeng Guo,Umberto Ravaiolib,Dengyuan Song.Properties of wurtzite GaN MESFETs studied by two-dimensional full band Monte Carlo approach[J]. Microelectronics Journal,2004,35:117-123
[4] 郭宝增,Umberto Ravaioli.深亚微米纤锌矿相AlGaN/GaN MODFET 输出特性的微分负阻效应[J].中国科学(E 辑),2003,33(6):568-576
[5] 郭宝增,孙荣霞, Umberto Ravaioli.用二维全带多粒子Monte Carlo 方法模拟纤锌矿相GaN 静电感应晶体管(SIT)特性[J].电子学报,2003,31(8):1121-1124
[6] Stephen K.O’Leary,Brian E.Foutz,Michael S.Shur,Udayan V.Bhapkar,Lester F.Eastman. Monte Carlo simulation of electron transport in wurtzite Aluminum nitride[J].Solid State Communications,105(10):621-626
[7] S.Jallepalli,M.Rashed,W.K.Shih,C.M.Maziar,A.F.Tasch,Jr.A full-band Monte Carlo model for hole transport in silicon[J].J.Appl.Phys,1997,81(5):2250-2255
[8] Ismail H.Oguzman,Jan Kolnik,Kevin F.Brennan,Rongping Wang,Tzu-Ning Fang,P.Paul Ruden. Hole transport properties of bulk zinc-blende and wurtzite phases of GaN based on an ensemble Monte carlo calculation including a full zone band structure[J].J.Appl.Phys,1996,80(8):4429-4436
[9] I.H.Oguzman,J.Kolnik,K.F.Brennan,R.Wang,P.P.Ruden.Monte Carlo Calculation of hole transport in bulk zincblende phase of GaN including a pseudopotential calculated band structure[J].Mat.Res.Soc.Symp.Proc,1996,395:479-483
[10] J.D.Albrecht,P.P.Ruden,T.L.Reinecke.Hole scattering near the valence band edge in wurtzite gallium nitride[J].Journal of applied physics,2002,92(7):3803-3814
[11] Yasuhiko Hayashi,Tetsuo Soga,Masayoshi Umeno,Takashi Jimbo.Analysis of hole transport in cubic phase of p-type GaN by relaxation time approximation[J].Physica B,1999,272:256-259
[12] A.A.Burk Jr.,M.J.O'Loughlin,R.R.Siergiej,et al. SiC and GaN wide bandgap semiconductor materials and devices[J]. Solid State Electronics,1999,43:1459-1464
[13] F.Schwierz,M.kittler,H.forster,D.Schipanski.The Potential of SiC and GaN for application in high speed devices[J]. Diamond and Related Materials,1997,6:1512-1514
[14] 顾彪,王三胜,徐茵等.GaN 基材料及其在短波光电器件领域的应用[J].高技术通讯,2002,03:104-110
[15] 刘恩科,朱秉升,罗晋生等.半导体物理学[M].国防工业出版社.1994,第4 版
[16] 梁春广,张冀.GaN——第三代半导体的曙光[J], 半导体学报,1999,20(2):89-99
[17] 顾忠良.GaN 半导体研究与进展[J].半导体情报,1999,36(4):10-14
[18] 宋登元,王秀山.GaN 材料系列的研究进展[J]. 微电子学,1998,28(2):124-128
[19] 谢世勇,郑有科,陈鹏,张荣. GaN 材料p 型掺杂[J]. 固体电子学研究与进展,2001,21(2):204-210
[20] C.J.Pan,G.C.Chi.The doping of GaN with Mg diffusion[J].Solid State Electronics,1999,43:621-623
[21] 薛松,韩彦军,郭文平,孙长征,郝智彪,罗毅.p 型GaN 材料的表面物理特性[J],半导体学报,2003,24(12):1280-1284
[22] AmanoH,KitoM,HiramatsuK,et al.P-type conductionin Mg-doped GaN treated with low-energy electron beam irradiation(LEEBI)[J].Jpn J Appl Phys,1989,28(12):2112
[23] Nakamura S,Mukai T,Senoh M,et al.Thermal annealing effects on P-type Mg-doped GaN films[J].Jpn J Appl Phys,1992,31(2B):139
[24] Bernardini F,Fiorentini V,Bosin A.Theoretical evidence for efficient p-typ doping of GaN using beryllium[J].Appl Phys Lett,1997,70(22):2990
[25] N.MetroPolis and S.Ulam.The monte carlo method[J]. J.Am.stat.Ass.,1949,44:335-341
[26] Carlo Jacoboni,Lino Reggiani.The Monte Carlo method for the solution of charge transport in semiconductors with applications to covalent materials[J]. Rev.Mod.Phys,1983,55(3):645-703
[27] 叶良修. 小尺寸半导体器件的Monte Carlo 模拟[M].科学出版社.1997,第1 版
[28] H.E.Nilsson,E.Bellotti,M.Hjelm,K.Brennan.A comparison between different Monte Carlo models in simulation of hole transport in 4H-SiC[J]. Mathematics and Computers in Simulation,2001, 55:199-208
[29] 裴鹿成,张孝泽著. Monte Carlo 方法及其在载流子输运问题中的应用[M],科学出版社,1980,第1版
[30] 徐钟济著.Monte Carlo 方法[M].上海科学技术出版社,1985,第1 版
[31] Mark Lundstrom.Fundamentals of carrier transport[M].Modular series on solid state devices. 1990,V10
[32] 黄昆原著,韩汝琦改编.固体物理学[M].高等教育出版社.1988
[33] 赵平,魏同立,吴金. 在MonteCarlo器件模拟中确定自由飞行时间的自散射方法[J]. 固体电子学研究与进展, 2000,20(3):250-255
[34] 郭宝增,Umberto Ravaioli.用全带方法模拟纤锌矿相GaN 和ZnO 材料的电子输运特性[J].物理学报,2002,51(10):2344-2348
[35] Ismail H.Oguzman,Enrico Bellotti,Kevin F.Brennan,Jan Kolnik,Rongping Wang,P.Paul Ruden. Theory of hole initiated impact ionization in bulk zincblende and wurtzite GaN[J]. J.Appl.Phys,1997,81(12):7827-7834
[36] Y.Kamakura,H.Mizuno,M.Yamaji,M.Morifuji,K.Taniguchi,C.Hamaguchi,T.kunikiyo,M.Takenaka. Impact ionization model for full band Monte Carlo simulation[J].J.Appl.Phys,1994,75(7):3500-3505
[37] J.kolnik,I.H.Oguzman,K.F.Brennan,et al.Electronic transport studies of bulk zincblende and wurtzite phases of GaN based on an ensemble Monte Carlo calculation including a full zone band structure[J].J.Appl.Phys,1995,78:1033-1037
[38] U.V.BhaPkar,M.S.Shur.Monte Carlo calculation of velocity-fleld characteristics of wurtzite GaN[J].J.Appl.Phys,1997,82:1649-1655
[39] Wim Geerts,J.D.Mackenzie,C.R.Abernathy,et al.Electrical transport In P-GaN,n-InN and n-InGaN[J].Solid state electronics,1996,39(9):1289-1294
[40] J.D.Wiley. Valence-band deformation potentials for the Ⅲ-Ⅴcompounds[J].Solid state communications,1970(8):1865-1868
[41] 袁斌,马维新.UNIX 操作系统下FORTRAN 语言与C 语言混合编程的方法[J].小型微型计算机系统,1994,15(12):30-33