Metal-to-Nonmetal Transition in n -Type Many-Valley Semiconductors

We have calculated the critical donor concentration nc for the Mott transition in many-valley semiconductors. Our accurate numerical solution of the Schr\"odinger equation for Mott's model, as extended by Krieger and Nightingale, shows that previously reported good agreement with experiments has been in part the fortuitous result of calculational simplifications. We also find that the model predicts values of nc1/3aH (where aH is the effective Bohr radius in the material) over 45% larger in single-valley semiconductors than in Ge and Si (four and six valleys, respectively) and suggest such experiments as further meaningful tests of the model.