Shallow-impurity states in semiconductor quantum-well structures.

Abstract

The ground-state energy of a shallow impurity in a semiconductor quantum well of finite barrier height is calculated using a variational method. The binding energy U is obtained as a function of the well width L, the impurity position ${z}_{i}$, and the height of the potential barrier ${V}_{0}$. The behavior of the variational parameter \ensuremath{\lambda}, which determines the extension of the wave function around the impurity, is also studied. The maximum binding energy corresponds to the minimum value of \ensuremath{\lambda}. Larger values of ${V}_{0}$ result in faster variation of U with ${z}_{i}$. Our results agree very well with published experimental data.