One‐Band One‐Site Model for Crystal Imperfections

The one‐band one‐site model for crystal imperfections, introduced by Koster and Slater, is critically examined. A simple improvement scheme, which is equivalent to a many‐band one‐site model, is proposed. These ideas are tested on a case for which exact solutions are known, namely, a one‐dimensional potential well. It is found that the one‐band one‐site approximation gives rather unreliable results, in general, and that the improvement scheme is indeed an improvement, converging to the exact answer as the one‐site approximation becomes exact.