双轴拉伸应变对锗能带退简并的影响
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摘要
采用第一性原理方法研究了沿(001)、(101)和(111)面施加双轴拉伸应变下锗能带退简并行为。研究表明,布里渊区价带顶Γ点退简并行为相对简单,导带底L点退简并行为较复杂,不同L点到Γ点的能量差均不同,所对应能隙也不同。具体而言,沿(001)面施加双轴拉伸不会引起L点电子态退简并;沿(101)和(111)面施加双轴拉伸均可引起L点电子态退简并。因此,计算应变锗能隙时需考察不同导带L点与价带顶Γ点的能量差值。
By using the first principle method,the removal of degeneracy of band structure of Ge under biaxial tensile strain parallel to(001),(101) and(111) was investigated.It was found that the removal of degeneracy of valance band at Γ point was relatively simple,while the removal of degeneracy of conduction band at L point was relatively elaborate.The energy difference of electronic states from different L points to Γ point was different,naturally corresponding different values of band gap.Specially,biaxial tensile strain parallel to(001) would not induce removal of degeneracy of electronic state,while biaxial tensile strain parallel to(101) and(111) would induce removal of degeneracy of electronic state at L point.Therefore,the energy difference of electronic states from every L point to Γ point should be considered in the calculation of band gap of Ge under stain.
By using the first principle method,the removal of degeneracy of band structure of Ge under biaxial tensile strain parallel to(001),(101) and(111) was investigated.It was found that the removal of degeneracy of valance band at Γ point was relatively simple,while the removal of degeneracy of conduction band at L point was relatively elaborate.The energy difference of electronic states from different L points to Γ point was different,naturally corresponding different values of band gap.Specially,biaxial tensile strain parallel to(001) would not induce removal of degeneracy of electronic state,while biaxial tensile strain parallel to(101) and(111) would induce removal of degeneracy of electronic state at L point.Therefore,the energy difference of electronic states from every L point to Γ point should be considered in the calculation of band gap of Ge under stain.
引文
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[2]YANG Y J,HO W S,HUANG C F,et al.Electron mobility enhancement in strained-germanium n-channel metal-oxidesemiconductor field-effect transistors[J].Applied Physics Letters,2007,91(10):102103-102105.
[3]屠海令.半导体硅及硅基材料研究中的几个问题[J].上海金属,2008,30(5):1-7.
[4]CHEN M J,TSAI C S,WU M K.Optical gain and Costimulated emissions of photons and phonons in indirect band gap semiconductors[J].Japanese Journal of Applied Physics,2006,45(8B):6576-6588.
[5]CHANG G E,CHENG H H.Optical gain of germanium infrared lasers on different crystal orientations[J].Journal of Physics:Condensed Matter,2013,46(6):065103-065316.
[6]HUO Y J,LIN H,CHEN R,et al.Strong enhancement of direct transition photoluminescence with highly tensile-strained Ge grown by molecular beam epitaxy[J].Applied Physics Letters,2011,98(1):011111-011113.
[7]BLOCHL P E.Projector augmented-wave method[J].Physical Review B,1994,50(24):17953-17979.
[8]KRESSE G,FURTHMüLLER J.Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set[J].Physical Review B,1996,54(16):11169-11186.
[9]KRESSE G,JOUBERT D.From ultra soft pseudo potentials to the projector augmented-wave method[J].Physical Review B,1999,59(3):1758-1775.
[10]PERDEW J P,BURKE K,ERNZERHOF M.Generalized gradient approximation made simple[J].Physical Review Letters,1996,77(18):3865-3868.
[11]MONKHORST H J,PACK J D.Special points for Brillouinzone integrations[J].Physical Review B,1976,13(12):5188-5192.
[12]TAHINI H,CHRONEOS A,GRIMES R W,et al.Diffusion of tin in germanium:A GGA+U approach[J].Applied Physics Letters,2011,99(16):162103-162105.
[13]INAOKA T,FURUKAWA T,TOMA R,et al.Tensile-strain effect of inducing the indirect-to-direct band-gap transition and reducing the band-gap energy of Ge[J].Journal of Applied Physics,2015,118(10):105704-105714.