Scattering states of a particle, with position-dependent mass, in a double heterojunction

TL;DR

This paper derives exact analytical solutions for a particle with position-dependent mass in a semiconductor double heterojunction, revealing how mass variation affects scattering states and transmission properties.

Contribution

It provides the first exact analytical scattering solutions for particles with position-dependent mass in double heterojunctions, highlighting the nonlinear effects on wave functions.

Findings

Transmission coefficient increases with energy, approaching unity.

Reflection coefficient decreases with energy, approaching zero.

Mass variation introduces nonlinear components in wave solutions.

Abstract

In this work we obtain the exact analytical scattering solutions of a particle (electron or hole) in a semiconductor double heterojunction - potential well / barrier - where the effective mass of the particle varies with position inside the heterojunctions. It is observed that the spatial dependence of mass within the well / barrier introduces a nonlinear component in the plane wave solutions of the continuum states. Additionally, the transmission coefficient is found to increase with increasing energy, finally approaching unity, whereas the reflection coefficient follows the reverse trend and goes to zero.