The theory of local conditions in the semiconductor crystals taking into account the full dispersion law in the bands

The new method of creation the effective single-zone Hamiltonian of electron in crystal with smooth external field are presented in the article with taking into account all conditions of Brillouin zone. This method allows to calculate the energy spectrum and wave functions of electron with high accurate in the whole considered zone. While standard method of effective mass can give a calculation of the value of energy and wave functions of electron only for several conditions. The authors demonstrate a necessary of exact ac-counting the law of electron dispersion and the periodicity condition for the matrix elements in the k-space of the Bloch basis. Introduced method differ the accuracy, ease of use and universality to all forms of the external fields.

Authors: G. F. Glinskii, V. A. Smirnova

Direction: Physics

Keywords: envelope wave function, impurities in semiconductors, the effective mass method, effective Hamiltonian

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