Spectrum of Electron in Quantum Well with Continuous Position-Dependent Effective Mass

Within the model of rectangular potential profile and continuous position-dependent effective mass of electron in the double-barrier open semiconductor plane nano-heterostructure, the exact solutions of Schrodinger equation are obtained. Using them, the transmission coefficient, resonance energies, and widths of sub-barrier quasi-stationary electron states are calculated for the structure with In0.53Ga0.47As wells and In0.52Al0.48As barriers. The transmission coefficient and spectral characteristics of electron states are analyzed as functions of the width of near-interface region where the effective mass linearly depends on coordinate. It is shown that the increasing width of near-interface region between wells and barriers does not change the heights of maxima of transmission coefficient peaks but shifts and broadens them.