Open AccessПростой численный метод определения энергетического спектра носителей заряда в полупроводниковых гетероструктурах
Author(s) -
Г.Ф. Глинский
Publication year - 2018
Publication title -
pisʹma v žurnal tehničeskoj fiziki
Language(s) - English
Resource type - Journals
eISSN - 1726-7471
pISSN - 0320-0116
DOI - 10.21883/pjtf.2018.06.45763.17113
Subject(s) - brillouin zone , heterojunction , hamiltonian (control theory) , superlattice , fourier transform , effective mass (spring–mass system) , quantum well , electronic band structure , physics , wave function , hamiltonian matrix , semiconductor , fourier series , condensed matter physics , mathematical analysis , quantum mechanics , mathematics , symmetric matrix , eigenvalues and eigenvectors , mathematical optimization , laser
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 Γ 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.