A k·p analytical model for valence band of biaxial strained Ge on (001) Si1-xGex

doi:10.1088/1674-1056/21/5/057103

中国物理B ›› 2012, Vol. 21 ›› Issue (5): 57103-057103.doi: 10.1088/1674-1056/21/5/057103

A k·p analytical model for valence band of biaxial strained Ge on (001) Si_1-xGe_x

王冠宇,张鹤鸣,高翔,王斌,周春宇

Key Laboratory of Wide Band-Gap Semiconductor Materials and Devices, School of Microelectronics, Xidian University, Xi'an 710071, China

收稿日期:2011-09-16 修回日期:2012-04-27 出版日期:2012-04-01 发布日期:2012-04-01
基金资助:
Project supported by the Fundamental Research Funds for the Central Universities, China (Grant Nos. 72105499 and 72104089) and the Natural Science Basic Research Plan in Shaanxi Province, China (Grant No. 2010JQ8008).

A k·p analytical model for valence band of biaxial strained Ge on (001) Si_1-xGe_x

Wang Guan-Yu(王冠宇)^†, Zhang He-Ming(张鹤鸣), Gao Xiang(高翔), Wang Bin(王斌), and Zhou ChunYu(周春宇)

Key Laboratory of Wide Band-Gap Semiconductor Materials and Devices, School of Microelectronics, Xidian University, Xi'an 710071, China

Received:2011-09-16 Revised:2012-04-27 Online:2012-04-01 Published:2012-04-01
Supported by:
Project supported by the Fundamental Research Funds for the Central Universities, China (Grant Nos. 72105499 and 72104089) and the Natural Science Basic Research Plan in Shaanxi Province, China (Grant No. 2010JQ8008).

摘要/Abstract

摘要： In this paper, the dispersion relationship is derived by using the k穚 method with the help of the perturbation theory, and we obtain the analytical expression in connection with the deformation potential. The calculation of the valence band of the biaxial strained Ge/(001)Si_1-xGe_x is then performed. The results show that the first valence band edge moves up as Ge fraction x decreases, while the second valence band edge moves down. The band structures in the strained Ge/ (001)Si_0.4Ge_0.6 exhibit significant changes with x decreasing in the relaxed Ge along the [0, 0, k] and the [k, 0, 0] directions. Furthermore, we employ a pseudo-potential total energy package (CASTEP) approach to calculate the band structure with the Ge fraction ranging from x=0.6 to 1. Our analytical results of the splitting energy accord with the CASTEP-extracted results. The quantitative results obtained in this work can provide some theoretical references to the understanding of the strained Ge materials and the conduction channel design related to stress and orientation in the strained Ge pMOSFET.

关键词: strained Ge, valence band, k穚 method, dispersion relationship

Abstract: In this paper, the dispersion relationship is derived by using the k·p method with the help of the perturbation theory, and we obtain the analytical expression in connection with the deformation potential. The calculation of the valence band of the biaxial strained Ge/(001)Si_1-xGe_x is then performed. The results show that the first valence band edge moves up as Ge fraction x decreases, while the second valence band edge moves down. The band structures in the strained Ge/ (001)Si_0.4Ge_0.6 exhibit significant changes with x decreasing in the relaxed Ge along the [0, 0, k] and the [k, 0, 0] directions. Furthermore, we employ a pseudo-potential total energy package (CASTEP) approach to calculate the band structure with the Ge fraction ranging from x=0.6 to 1. Our analytical results of the splitting energy accord with the CASTEP-extracted results. The quantitative results obtained in this work can provide some theoretical references to the understanding of the strained Ge materials and the conduction channel design related to stress and orientation in the strained Ge pMOSFET.

Key words: strained Ge, valence band, k·p method, dispersion relationship

中图分类号: (Electron density of states and band structure of crystalline solids)

71.20.-b

73.20.At (Surface states, band structure, electron density of states)

王冠宇, 张鹤鸣, 高翔, 王斌, 周春宇. A k·p analytical model for valence band of biaxial strained Ge on (001) Si_1-xGe_x[J]. 中国物理B, 2012, 21(5): 57103-057103.

Wang Guan-Yu(王冠宇), Zhang He-Ming(张鹤鸣), Gao Xiang(高翔), Wang Bin(王斌), and Zhou ChunYu(周春宇) . A k·p analytical model for valence band of biaxial strained Ge on (001) Si_1-xGe_x[J]. Chin. Phys. B, 2012, 21(5): 57103-057103.

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A k·p analytical model for valence band of biaxial strained Ge on (001) Si_1-xGe_x

A k·p analytical model for valence band of biaxial strained Ge on (001) Si_1-xGe_x

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