Electron States in Semiconductor Microstructures

Abstract

The particle-in-a-box model of confinement pictured in Fig.1 accounts for the presence and approximate positions of levels in GaAs wells confined by Ga_1−xAl_xAs (x < 0.35). The only parameters required are the effective mass derived from the relevant band edge, the well width and the barrier height. In this model, it is assumed that the rapidly varying component u_n $\vec k\left( {\vec r} \right)$ of the total wave function does not change at the interfaces, i.e. that near the band edges the Bloch functions associated with a given band n and wave vector $\vec k$ are the same in GaAs and Ga_1−xAl_xAs. Although a number of corrections has been introduced to improve the accuracy and scope of predictions based on this simple picture, it is clear that at least further from the band edges, and in structures consisting of more dissimilar materials, the above approximation will break down.