Optimal basis sets for deep levels. II. Defect-molecule approximation.

Abstract

We test the ``defect-molecule'' model of Coulson and Kearsley by calculating s- and p-type bound-state energies in silicon for attractive and repulsive Gaussian substitutional impurity potentials with exponential coefficients \ensuremath{\alpha}=0.2 and 1 a.u. The model is shown to work surprisingly well, which justifies its widespread use in the interpretation of experimental and computational results. The leading correction is found to be a d-state wave function on the impurity site. This enters for p states only and is much more important for repulsive than for attractive potentials. The basis set of the wave functions is much smaller than the nonorthogonal basis of the Green's function. In order to treat this problem properly we have developed a least-squares method of approximating the Green's-function equation. The method should be applicable to other problems also.