We present a rigorous model for the overall band structure calculation using the perturbative k p
approach for arbitrary layered cubic zincblende semiconductor nanostructures. This approach, first pioneered by Kohn and Luttinger, is faster than atomistic ab initio approaches and provides sufficiently accurate information for optoelectronic processes near high symmetry points in semiconductor crystals. k p
Hamiltonians are discretized and diagonalized using a finite element method (FEM) with smoothed mesh near interface edges and different high order Lagrange/Hermite basis functions, hence enabling accurate determination of bound states and related quantities with a small number of elements. Such properties make the model more efficient than other numerical models that are usually used. Moreover, an energy-dependent effective mass non-parabolic model suitable for large gap materials is also included, which offers fast and reasonably accurate results without the need to solve the full multi-band Hamiltonian. Finally, the tools are validated on three semiconductor nanostructures: (1) the bound energies of a finite quantum well using the energy-dependent effective mass non-parabolic model; (2) the InAs bulk band structure; and (3) the electronic band structure for the absorber region of photodetectors based on a type-II InAs/GaSb superlattice at room temperature. The tools are shown to work on simple and sophisticated designs and the results show very good agreement with recently published experimental works.
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