Finite difference method for analyzing band structure in semiconductor heterostructures without spurious solutions

To stably employ multiband k.p model for analyzing the band structure in semiconductor heterostructures without spurious solutions (SSs), the Hermitian forward and backward difference (HFBD) scheme for finite difference method (FDM) is presented. The HFBD is the discretization scheme that eliminates the difference instability and employs the Burt-Foreman Hermitian operator ordering without geometric asymmetry. The difference instability arises from employing Foreman's strategy (FS). FS removes SSs caused by unphysical bowing in bulk dispersion curve meanwhile the HFBD is the only difference scheme that can accurately adapt for it. In comparison with other recent strategies, the proposed method in this paper is as accurate and reliable as FS, along with preserving the rapidness and simplicity of FDM. This difference scheme shows stable convergence without any SSs under variable grid size. Therefore, a wide range of experiment-determined band parameters can be applied to large-scale stable simulation with this method regardless of the SSs they originally generate. (C) 2014 AIP Publishing LLC.