InAs/GaAs量子点生长的KMC模拟
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摘要
采用动力学蒙特卡罗(kinetic Monte Carlo,KMC)模型模拟了Ga As应变弛豫图形衬底上In As量子点生长的初始阶段.Ga As应变弛豫图形衬底是通过在其衬底中埋藏已制备的In As量子点得到,并运用格林函数法计算在不同的埋藏深度下衬底表面的应变能,然后将计算结果运用到生长模拟过程中.模拟中分别考虑了温度、沉积速率和埋层深度对量子点生长的影响.模拟结果表明:通过控制生长温度和沉积速率能形成均匀、有序分布的2D岛;埋层深度越大,越不利于沉积原子聚集.
The kinetic Monte Carlo(KMC) model is used to simulate the initial phase of the growth of In As quantum dots on Ga As strain relaxation substrate. The strain relaxation of Ga As substrate can be obtained by burying In As quantum dot in the substrate. The Green's function method is used to calculate strain energy distributed in the substrate surface under different burial depths. The calculation results are applied to the growth process, in which the effects of temperature, deposition rate and buried depth on the growth are considered. Simulation results show that, by controlling the growth temperature and deposition rate, uniform and orderly distribution of 2 D islands can be obtained. In addition,the greater the depth of burial, the more unfavorable to the atomic aggregation.
The kinetic Monte Carlo(KMC) model is used to simulate the initial phase of the growth of In As quantum dots on Ga As strain relaxation substrate. The strain relaxation of Ga As substrate can be obtained by burying In As quantum dot in the substrate. The Green's function method is used to calculate strain energy distributed in the substrate surface under different burial depths. The calculation results are applied to the growth process, in which the effects of temperature, deposition rate and buried depth on the growth are considered. Simulation results show that, by controlling the growth temperature and deposition rate, uniform and orderly distribution of 2 D islands can be obtained. In addition,the greater the depth of burial, the more unfavorable to the atomic aggregation.
引文
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[3]刘珂,马文全,黄建亮,等.含有Al Ga As插入层的In As/Ga As三色量子点红外探测器[J].物理学报,2016,65(10):329-333.
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[6]Li X L,Wang C X,Yang G W.Thermodynamic theory of growth of nanostructures[J].Progress in Materials Science,2014,64:121-199.
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[16]杨园静,涂洁磊,李雷,等.生长温度对In As/Ga As量子点太阳电池的影响研究[J].人工晶体学报,2014,43(2):461-464.
[17]Nurminen L,Kuronen A,Kaski K.Kinetic Monte Carlo simulation of nucleation on patterned substrates[J].Phys Rev B,2001,63(3):03054.
[18]Sun L G,Xu K Y,Pan E.Irregular inhomogeneities in an anisotropic piezoelectric plane[J].Journal of Applied Mechanics,2012,79:021014.
[19]Chen Q D,Xu K Y,Pan E.Inclusion of arbitrary polygon with a graded eigenstrain in an anisotropic piezoelectric half plane[J].International Journal of Solids and Structures,2014,51(1):53-62.
[20]Pan E.Eshelby problem of polygonal inclusions in anisotropic piezoelectric full-and halfplanes[J].J Mech Phys Solids,2004,52:567-589.
[21]何菊生,张萌,肖祁陵.半导体外延层晶格失配度的计算[J].南昌大学学报(理科版),2006,30(1):63-67.
[22]吕建国,王成彪,于翔,等.薄膜的晶格失配应力分析[J].科技创新导报,2008,20:14-15.
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[24]Mura T.Micromechanics of defects in solids[M].2nd ed.Dordrecht:Kluwer Academic Publishers,1987.
[25]Zou W N,He Q C,Zheng Q S.General solution for eshelby’s problem of 2D arbitrarily shaped piezoelectric inclusions[J].International Journal of Solids and Structures,2011,48:2681-2694.
[26]Pan E.Eshelby problem of polygonal inclusions in anisotropic piezoelectric bimaterials[J].Proceedings of the Royal Society A,2004,460:537-560.
[2]魏育新,陈蕊丽.In As/Ga As量子点激光器增益特性[J].河北大学学报(自然科学版),2016,36(3):232-236.
[3]刘珂,马文全,黄建亮,等.含有Al Ga As插入层的In As/Ga As三色量子点红外探测器[J].物理学报,2016,65(10):329-333.
[4]李树玮,小池一步,矢野满明.垂直堆垛In As量子点材料的分子束外延生长[J].稀有金属,2004,28(1):207-209.
[5]Shchukin V A,Bimberg D.Spontaneous ordering of nanostructures on crystal surfaces[J].Reviews of Modern Physics,1999,71:1125-1171.
[6]Li X L,Wang C X,Yang G W.Thermodynamic theory of growth of nanostructures[J].Progress in Materials Science,2014,64:121-199.
[7]Sch¨oll E,Bose S.Kinetic Monte Carlo simulation of the nucleation stage of the self-organized growth of quantum dots[J].Solid-State Electron,1998,42:1587-1591.
[8]Thanh V L,Yam V.Superlattices of self-assembled Ge/Si(0 0 1)quantum dots[J].Applied Surface Science,2003,212/213(2):296-304.
[9]Ishikawa T,Nishimura T,Kohmoto S,et al.Site-controlled In As single quantum-dot structures on Ga As surfaces patterned by in situ electron-beam lithography[J].Applied Physics Letters,2000,76(2):167-169.
[10]杨红波,俞重远,刘玉敏,等.影响半导体量子点生长因素的分析[J].人工晶体学报,2004,33(6):1018-1021.
[11]胡冬枝,赵登涛,蒋伟荣,等.Si(0 0 1)斜切衬底上Ge量子点的固相外延生长[J].半导体学报,2002,23(6):604-608.
[12]Wang Q,Huang Y Q,Ren X M.The influence of growth parameters on the formation on In As/Ga As by MOCVD[J].The International Society for Optical Engineering,2012(3):277-298.
[13]Pan E,Sun M,Chung P W,et al.Three-dimensional kinetic Monte Carlo simulation of prepatterned quantum-dot island growth[J].Applied Physics Letters,2007,91(19):193110.
[14]Evans J W,Thiel P A,Bartelt M C.Morphological evolution during epitaxial thin film growth:formation of 2D islands and 3D mounds[J].Surface Science Reports,2006,61(1/2):1-128.
[15]宋禹忻.动力学蒙特卡罗法仿真量子点生长过程的统计分析与参数优化[D].北京:北京邮电大学,2007.
[16]杨园静,涂洁磊,李雷,等.生长温度对In As/Ga As量子点太阳电池的影响研究[J].人工晶体学报,2014,43(2):461-464.
[17]Nurminen L,Kuronen A,Kaski K.Kinetic Monte Carlo simulation of nucleation on patterned substrates[J].Phys Rev B,2001,63(3):03054.
[18]Sun L G,Xu K Y,Pan E.Irregular inhomogeneities in an anisotropic piezoelectric plane[J].Journal of Applied Mechanics,2012,79:021014.
[19]Chen Q D,Xu K Y,Pan E.Inclusion of arbitrary polygon with a graded eigenstrain in an anisotropic piezoelectric half plane[J].International Journal of Solids and Structures,2014,51(1):53-62.
[20]Pan E.Eshelby problem of polygonal inclusions in anisotropic piezoelectric full-and halfplanes[J].J Mech Phys Solids,2004,52:567-589.
[21]何菊生,张萌,肖祁陵.半导体外延层晶格失配度的计算[J].南昌大学学报(理科版),2006,30(1):63-67.
[22]吕建国,王成彪,于翔,等.薄膜的晶格失配应力分析[J].科技创新导报,2008,20:14-15.
[23]Eshelby J D.Elastic inclusions and inhomogeneities[J].Progress Solid Mechanics,1961,2:87-140.
[24]Mura T.Micromechanics of defects in solids[M].2nd ed.Dordrecht:Kluwer Academic Publishers,1987.
[25]Zou W N,He Q C,Zheng Q S.General solution for eshelby’s problem of 2D arbitrarily shaped piezoelectric inclusions[J].International Journal of Solids and Structures,2011,48:2681-2694.
[26]Pan E.Eshelby problem of polygonal inclusions in anisotropic piezoelectric bimaterials[J].Proceedings of the Royal Society A,2004,460:537-560.