One-Band Model for Crystal Imperfections

Abstract

The one-band model for an impurity in a crystal is critically discussed. In this model the wave functions for low-energy states in the presence of the impurity are considered to be composed only of wave functions from the lowest conduction band. This is shown to be invalid when the potential is smaller in size than the unit cell. It is pointed out that the model can be correctly used in this case only when the strength of the potential is treated as a parameter to be fitted after the calculation and is not presumed known at the beginning.