单轴应变锗带隙特性和电子有效质量计算

doi:10.3969/j.issn.1001-2400.2018.03.005

西安电子科技大学学报

单轴应变锗带隙特性和电子有效质量计算

底琳佳1,2;戴显英1,2;苗东铭1,2;吴淑静1,2;郝跃1,2

(1. 西安电子科技大学微电子学院，陕西西安 710071；
2. 西安电子科技大学宽带隙半导体国家重点学科实验室，陕西西安 710071)

收稿日期:2017-06-23 出版日期:2018-06-20 发布日期:2018-07-18
作者简介:底琳佳(1992-)，男，西安电子科技大学硕士研究生，E-mail：ljdi@stu.xidian.edu.cn
基金资助:
国家部委重点基金资助项目(9140A08020115DZ01024)；中央高校基本科研业务费专项资金资助项目(XJS17061，JBX171102)；中国博士后科学基金资助项目(2017M613061)；高等学校学科创新引智计划资助项目(B12026)

Calculation of bandgap characteristic and electron effective mass in uniaxial strained Germanium

DI Linjia1,2;DAI Xianying1,2;MIAO Dongming1,2;WU Shujing1,2;HAO Yue1,2

(1. School of Microelectronics, Xidian Univ., Xi'an 710071, China;
2. State Key Lab. of Wide Bandgap Semiconductor Technology Disciplines, Xidian Univ., Xi'an 710071, China)

Received:2017-06-23 Online:2018-06-20 Published:2018-07-18

摘要/Abstract

摘要：

应变工程在提升Ge器件性能方面起着重要作用，而能带结构是研究应变Ge电学、光学性质的理论基础．文中通过对角化一个包含自旋轨道相互作用和应变效应的30k·p哈密顿矩阵，得到了单轴应变锗在整个布里渊区内的能带结构．根据能带色散关系，研究了单轴应变锗导带能谷分裂与偏移、纵向和横向电子有效质量、电子态密度有效质量等随应力的变化情况．计算结果表明:在［001］、［111］方向单轴张应力作用下，锗由间接带隙转变成直接带隙; 导带L和Δ能谷纵向、横向电子有效质量并不明显依赖于单轴应力，但沿［111］和［001］方向的单轴压应力可分别使L和Δ能谷态密度有效质量最小，这有利于减小电子散射几率，提升迁移率．

关键词: Strain engineering plays an important role in improving Ge devices performance, while energy band structure is the theoretical basis for studying the electrical and optical properties of strained Ge. In this paper, the energy band structure of uniaxial strained Ge, over the entire Brillouin zone, is obtained by diagonalizing a 30-band k·p Hamiltonian matrix which includes the spin-orbit coupling interaction and strain effect. According to the band dispersion relation, the conduction band valleys shift and split, as well as electron effective masses, including longitudinal, transverse and density-of-states effective masses are quantitatively evaluated. Calculation results indicate that Ge is converted from an indirect to direct bandgap semiconductor under the ［001］ and ［111］ uniaxial tensile stress. The longitudinal and transverse effective masses of L and &Delta, valleys are not obviously dependent on the uniaxial stress. However, the density-of-states effective masses of L and &Delta, valleys can be minimized by the ［111］ and ［001］ uniaxial compressive stress respectively, which is of benefit to increase the mobility by reducing the probability of electron scattering. These results can provide a theoretical reference for the design of high-performance uniaxial strained Ge devices.

Abstract:

Strain engineering plays an important role in improving Ge devices performance, while energy band structure is the theoretical basis for studying the electrical and optical properties of strained Ge. In this paper, the energy band structure of uniaxial strained Ge, over the entire Brillouin zone, is obtained by diagonalizing a 30-band k·p Hamiltonian matrix which includes the spin-orbit coupling interaction and strain effect. According to the band dispersion relation, the conduction band valleys shift and split, as well as electron effective masses, including longitudinal, transverse and density-of-states effective masses are quantitatively evaluated. Calculation results indicate that Ge is converted from an indirect to direct bandgap semiconductor under the ［001］ and ［111］ uniaxial tensile stress. The longitudinal and transverse effective masses of L and Δ valleys are not obviously dependent on the uniaxial stress. However, the density-of-states effective masses of L and Δ valleys can be minimized by the ［111］ and ［001］ uniaxial compressive stress respectively, which is of benefit to increase the mobility by reducing the probability of electron scattering. These results can provide a theoretical reference for the design of high-performance uniaxial strained Ge devices.

Key words: 30k·p method, uniaxial strained Ge, energy band structure, electron effective mass

底琳佳;戴显英;苗东铭;吴淑静;郝跃. 单轴应变锗带隙特性和电子有效质量计算[J]. 西安电子科技大学学报, 2018, 45(3): 24-29.

DI Linjia;DAI Xianying;MIAO Dongming;WU Shujing;HAO Yue. Calculation of bandgap characteristic and electron effective mass in uniaxial strained Germanium[J]. Journal of Xidian University, 2018, 45(3): 24-29.

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单轴应变锗带隙特性和电子有效质量计算

Calculation of bandgap characteristic and electron effective mass in uniaxial strained Germanium

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