Abstract:
A simple numerical method for determining the energy spectrum and wave functions of charge carriers in semiconductor heterostructures (quantum wells, wires, dots, and superlattices) is proposed that employs the effective mass approximation in the general case of multiband $kp$ Hamiltonian corresponding to the $\Gamma$ point of the Brillouin zone. The method is based on the Fourier transform for structures with periodic potential. For single heterostructures, this periodicity is introduced artificially. In the framework of the proposed approach, the effective matrix Hamiltonian of a heterostructure can be written in two unitarily-equivalent $a$- and $k$-representations. As an example, single-band $kp$ models of a heterostructure with one parabolic, triangular, or rectangular quantum well are considered and the influence of interfacial $kp$ corrections on the behavior of envelope functions at sharp heteroboundaries is studied.
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