Clustering model inn-doped many-valley semiconductors

We investigate the microscopic structure of the impurity states in $n$-silicon as an example of randomly distributed donor impurities in a diamond-structure many-valley semiconductor. An improved Hartree-Fock-Roothaan scheme with spin-polarized potentials and Kohn-Luttinger donor wave functions associated with each impurity were used in the calculation. It is shown that the many-valley character of the host gives rise to a distribution of impurity clusters of various sizes, quite different from the case of neglecting the valley multiplicity, and that it strongly reduces the self-compensation effect due to the potential fluctuation. The results are in agreement with recent investigations that have appeared in the literature.