Unraveling the effects of non-parabolicity on electron energy levels in InP/InAs/InP heterostructures

Abstract

In this research, electron energy levels were calculated analytically using Nelson's formula, the shooting method, and Garrett's formula for effective mass. These calculations were performed for a rectangular finite deep potential well, focusing on the InP/InAs/InP heterostructure, which is a narrow-bandgap semiconductor system. Our results demonstrate that the nonparabolicity of the dispersion has a more significant effect on higher energy levels compared to lower ones, with deviations of up to 15% for the third energy level. An equation estimating the number of observable energy levels in the potential well is suggested, revealing that considering nonparabolicity leads to a 20% increase in the number of levels compared to the parabolic dispersion case. The relationship between the widths of infinite and finite potential wells for equivalent energy levels follows a linear behaviour, with bonding coefficients ranging from 95,93% to 97,49% and a maximum difference of 1.5% between parabolic and non-parabolic cases. The transcendental equation for the energy levels is linearized, yielding a fourth-order equation that provides results within 98% accuracy compared to the original equation. These findings contribute to the understanding of the energy distribution in InP/InAs/InP heterostructures with a view to their application in optoelectronic devices such as lasers, light-emitting diodes