Statistics of the Occupation of Dislocation Acceptors (One-Dimensional Interaction Statistics)

Abstract

It is known that dislocations in semiconductors can act as acceptors. This effect has been explained by noting that dislocations with edge components can have unpaired electrons at the terminating half‐plane which act as acceptors; thus a dislocation contains a line of uniformly spaced acceptors only a few angstroms apart. In n‐type materials the dislocation line becomes negatively charged and a positive space charge develops around the line. The occupation statistics are strongly modified by the electrostatic energies involved. Certain approximate solutions to this problem have already been given by W. T. Read. This paper derives improved statistics which, in addition, explicitly take into account interactions between nearest‐neighbor electrons; the results are valid over the complete range of occupation. The statistics are given in terms of two functions which occur in the form of infinite series; the series have been evaluated over a considerable range of occupation and are herein tabulated. Techniques for use of the results are presented. Our theory was applied to a specific problem originally chosen by Read. The results fall between his most accurate approximations for this problem. Statistics have also been derived which take into account the proper spin degeneracy of acceptor states.