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

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.