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

Abstract

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

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.

References

［1］ LIU Y, NIU J B, WANG H J, et al. Strained Germanium Quantum Well PMOSFETs on SOI with Mobility Enhancement by External Uniaxial Stress［J］. Nanoscale Research Letters, 2017, 12(1): 120-124.
［2］ LEE C F, HE R Y, CHEN K T, et al. Strain Engineering for Electron Mobility Enhancement of Strained Ge NMOSFET with SiGe Alloy Source/Drain Stressors［J］. Microelectronic Engineering, 2015, 138(C): 12-16.
［3］ LIU J S, CLAVEL M B, HUDAIT M K. An Energy-efficient Tensile-strained Ge/InGaAs TFET 7T SRAM Cell Architecture for Ultralow-voltage Applications［J］. IEEE Transactions on Electron Devices, 2017, 64(5): 2193-2200.
［4］ MA J L, FU Z F, LIU P, et al. Hole Mobility Enhancement in Uniaxial Stressed Ge Dependence on Stress and Transport Direction［J］. Science China: Physics, Mechanics and Astronomy, 2014, 57(10): 1860-1865.
［5］白敏, 宣荣喜, 宋建军, 等. 压应变Ge/(001)Si₁-xGe_x空穴散射与迁移率模型［J］. 物理学报, 2015, 64(3): 038501-038506.
BAI Min, XUAN Rongxi, SONG Jianjun, et al. Hole Scattering and Mobility in Compressively Strained Ge/(001)Si_1-xGe_x ［J］. Acta Physica Sinica, 2015, 64(3): 038501-038506.
［6］ KURDI M E, FISHMAN G, SAUVAGE S, et al. Band Structure and Optical Gain of Tensile-strained Germanium Based on a 30 Band k·p Formalism［J］. Journal of Applied Physics, 2010, 107(1): 013710-013717.
［7］ TANI K, SAITO S, ODA K, et al. Room-temperature Direct Band-gap Electroluminescence from Germanium(111)-Fin Light-emitting Diodes［J］. Japanese Journal of Applied Physics, 2017, 56(3): 032102.
［8］ DAI X Y, SHAO C F, HAO Y. Uniaxially Strained Silicon on Insulator with Wafer Level Prepared by Mechanical Bending and Annealing［J］. Applied Physics Express, 2013, 6(8): 081302.
［9］ SUN Y, THOMPSON S E, NISHIDA T. Strain Effect in Semiconductors:Theory and Device Applications［M］. New York: Springer, 2010: 118.
［10］ CARDONA M, PQLLAK F H. Energy-band Structure of Germanium and Silicon: the k·p Method［J］. Physical Review, 1966, 142(2): 530-543.
［11］ RICHARD S, ANIEL F, FISHMAN G. Energy-band Structure of Ge, Si, and GaAs: a Thirty-band k·p Method［J］. Physical Review B, 2004, 70(23): 18976-18984.
［12］ RIDEAU D, FERAILLE M, CIAMPOLINI L, et al. Strained Si, Ge, and Si_1-xGe_x Alloys Modeled with a First-principles-optimized Full-zone k·p Method［J］. Physical Review B, 2006, 74(19): 195208-195227.
［13］戴显英, 李金龙, 郝跃. 应变锗的导带结构计算与分析［J］. 西安电子科技大学学报, 2014, 41(2): 120-124.
DAI Xianying, LI Jinlong, HAO Yue. Calculation and Analysis of the Conduction Band-structure of Strained Germanium［J］. Journal of Xidian University, 2014, 41(2): 120-124.
［14］ LIU L, ZHANG M, HU L, et al. Effect of Tensile Strain on the Electronic Structure of Ge: a First-principles Calculation［J］. Journal of Applied Physics, 2014, 116(11): 113105.
［15］ SUKHDEO D S, NAM D, KANG J H, et al. Direct Bandgap Germanium-on-Silicon Inferred from 5.7% 100 Uniaxial Tensile Strain［J］. Photonics Research, 2014, 2(3): A8-A13.
［16］ MADELUNG O, RSSLER U, SCHULZ M. Semiconductors·Group Ⅳ Elements, Ⅳ-Ⅳ and Ⅲ-Ⅴ Compounds. Part b - Electronic, Transport, Optical and Other Properties［M］. Berlin: Springer, 2002: 2854.
［17］ KIM J, FISCHETTI M V. Electronic Band Structure Calculations for Biaxially Strained Si, Ge, and Ⅲ-Ⅴ Semiconductors［J］. Journal of Applied Physics, 2010, 108(1): 013710.
［18］ NIQUET Y M, RIDEAU D, TAVERNIER C, et al. Onsite Matrix Elements of the Tight-binding Hamiltonian of a Strained Crystal: Application to Silicon, Germanium, and Their Alloys［J］. Physical Review B, 2009, 79(24): 245201-245213.
［19］ SONG J J, CHAO Y, ZHANG H M, et al. Longitudinal, Transverse, Density-of-states, and Conductivity Masses of Electrons in (001), (101) and (111) Biaxially-strained-Si and Strained-Si_1-xGe_x［J］. Science China: Physics, Mechanics and Astronomy, 2012, 55(11): 2033-2037.

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

PDF (PC)

Like

Knowledge

Abstract

Cite this article

share this article

References

Related Articles 0

Metrics

Comments

Recommended 10