Impact of symmetrized and Burt–Foreman Hamiltonians on spurious solutions and energy levels of InAs/GaAs quantum dots

doi:10.1088/1674-1056/19/8/088102

中国物理B ›› 2010, Vol. 19 ›› Issue (8): 88102-088102.doi: 10.1088/1674-1056/19/8/088102

Impact of symmetrized and Burt–Foreman Hamiltonians on spurious solutions and energy levels of InAs/GaAs quantum dots

谷永先, 杨涛, 季海铭, 徐鹏飞, 王占国

Key Laboratory of Semiconductor Materials, Institute of Semiconductors, Chinese Academy of Sciences, P.O. Box 912, Beijing 100083, China

收稿日期:2010-02-02 修回日期:2010-03-01 出版日期:2010-08-15 发布日期:2010-08-15

Impact of symmetrized and Burt–Foreman Hamiltonians on spurious solutions and energy levels of InAs/GaAs quantum dots

Gu Yong-Xian(谷永先), Yang Tao(杨涛)^†ger, Ji Hai-Ming(季海铭), Xu Peng-Fei(徐鹏飞), and Wang Zhan-Guo(王占国)

Key Laboratory of Semiconductor Materials, Institute of Semiconductors, Chinese Academy of Sciences, P.O. Box 912, Beijing 100083, China

Received:2010-02-02 Revised:2010-03-01 Online:2010-08-15 Published:2010-08-15

摘要/Abstract

摘要： We present a systematic investigation of calculating quantum dots (QDs) energy levels using the finite element method in the frame of the eight-band bm kcdot bm p method. Numerical results including piezoelectricity, electron and hole levels, as well as wave functions are achieved. In the calculation of energy levels, we do observe spurious solutions (SSs) no matter Burt–Foreman or symmetrized Hamiltonians are used. Different theories are used to analyse the SSs, we find that the ellipticity theory can give a better explanation for the origin of SSs and symmetrized Hamiltonian is easier to lead to SSs. The energy levels simulated with the two Hamiltonians are compared to each other after eliminating SSs, different Hamiltonians cause a larger difference on electron energy levels than that on hole energy levels and this difference decreases with the increase of QD size.

Abstract: We present a systematic investigation of calculating quantum dots (QDs) energy levels using the finite element method in the frame of the eight-band k·p method. Numerical results including piezoelectricity, electron and hole levels, as well as wave functions are achieved. In the calculation of energy levels, we do observe spurious solutions (SSs) no matter Burt–Foreman or symmetrized Hamiltonians are used. Different theories are used to analyse the SSs, we find that the ellipticity theory can give a better explanation for the origin of SSs and symmetrized Hamiltonian is easier to lead to SSs. The energy levels simulated with the two Hamiltonians are compared to each other after eliminating SSs, different Hamiltonians cause a larger difference on electron energy levels than that on hole energy levels and this difference decreases with the increase of QD size.

Key words: quantum dot, symmetrized Hamiltonian, Burt–Foreman Hamiltonian, finite element method, spurious solutions

中图分类号: (Quantum dots)

73.21.La

71.20.Nr (Semiconductor compounds) 73.63.Kv (Quantum dots) 77.65.Ly (Strain-induced piezoelectric fields)

谷永先, 杨涛, 季海铭, 徐鹏飞, 王占国. Impact of symmetrized and Burt–Foreman Hamiltonians on spurious solutions and energy levels of InAs/GaAs quantum dots[J]. 中国物理B, 2010, 19(8): 88102-088102.

Gu Yong-Xian(谷永先), Yang Tao(杨涛), Ji Hai-Ming(季海铭), Xu Peng-Fei(徐鹏飞), and Wang Zhan-Guo(王占国). Impact of symmetrized and Burt–Foreman Hamiltonians on spurious solutions and energy levels of InAs/GaAs quantum dots[J]. Chin. Phys. B, 2010, 19(8): 88102-088102.

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Impact of symmetrized and Burt–Foreman Hamiltonians on spurious solutions and energy levels of InAs/GaAs quantum dots

Impact of symmetrized and Burt–Foreman Hamiltonians on spurious solutions and energy levels of InAs/GaAs quantum dots

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