Effect of dimensionality of a crystal lattice on the properties of a localized impurity

The changes of electron density due to the presence of a localized impurity in a crystal lattice are examined in dependence on the lattice dimensional ity. The Koster-Slater impurity model developed for the case of a three-dim ensional simple cubic lattice has been taken as the basis of examinations. Ordinary bound states, virtual bound states, and delocalized electron state s are considered in each lattice case. For the delocalized states extended in a one-dimensional lattice the amplitude of the oscillatory changes of th e electron density due to the impurity perturbation does not decrease with the distance from the impurity position, whereas for a two-dimensional latt ice this amplitude decreases roughly proportionally to the reciprocal value of the square root of the distance from the impurity. Let us note that a w ell-known amplitude characterizing the decrease of the oscillatory change o f the electron density in a three-dimensional system is proportional to the reciprocal value of the third power of the distance from the impurity posi tion. (C) 2000 John Wiley & Sons, Inc.