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

• Published in: Chinese physics B Vol. 19; no. 8; pp. 619 - 627
• Main Author: 谷永先 杨涛 季海铭 徐鹏飞 王占国
• Format: Journal Article
• Language: English
• Published: IOP Publishing 01.08.2010
• Subjects: Energy levels; Gallium arsenide; Mathematical analysis; Mathematical models; Piezoelectricity; Quantum dots; Simulation; Wave functions; 对称; 杂散; 砷化铟; 砷化镓; 能源利用; 能级; 能量水平; 量子点
• ISSN: 1674-1056; 2058-3834
• DOI: 10.1088/1674-1056/19/8/088102

We present a systematic investigation of calculating quantum dots （QDs） energy levels using finite element method in the frame of 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.