Magnetic Properties of Impurity Clusters in Semiconductors: A Hubbard Model Approach

Abstract

This thesis presents a theoretical investigation of the magnetic properties of impurity clusters in semiconductors using a Hubbard model. Our primary goal is to provide specific examples of clusters with large spin quantum numbers and identify properties of these clusters that favor high spin ground states. We first describe the theory of shallow impurity states in semiconductors with a non-degenerate and isotropic conduction band minimum. This theory allows us to view collections of impurity sites in semiconductors as hydrogenic clusters, a group of hydrogen-like atoms in a fixed geometric con figuration. Next, we present a generalized Hubbard model which can be used to represent the low-lying energy states of the exact many-body Schrödinger equation of hydrogenic clusters. The parameters of the model are determined by matching quantum chemistry calculations on small clusters, which are essentially exact. We proceed to solve the Hubbard model numerically on a group of clusters with diff erent geometries while varying the size and charge of the clusters. We identify a class of neutral wheel-shaped clusters that have high spin ground states under appropriate conditions. In addition, we see that negatively charged clusters with triangular and square loops and positively charged clusters with square loops attain high spin ground states at sufficiently large sizes. Finally, we present the theory of shallow impurity states in semiconductors with degenerate and anisotropic conduction band minima. We show that it is possible to suppress the electron hoppings between specific pairs of cluster sites in these semiconductors. This phenomenon can be exploited for the creation of clusters with high spin ground states, and we present examples such clusters.