Mott transition in multivalley semiconductors

We show that the original ideas of Mott when properly extended to the multivalley case to include the effects of intervalley mixing, can still lead to the correct estimate of the critical density at which semiconductor-metal transition should occur in a doped semiconductor. Our treatment does take into account the exact numerical solution for the critical screening of a screened Coulomb potential as pointed out by Martino et al. and the multivalley extension of the Mott model by Krieger and Nightingale. We show that the critical density $n_c$ is given by the formula $n_c^{\frac{1}{3}}{N}^{\frac{2}{3}}\left(\frac{E_c}{E_g}\right)\left(\frac{e^2}{2K{E}_g}\right)=M$. The value of the constant $M$ from the experimental data on Si and Ge appears to be 0.47 ± 0.03. We discuss the possibility of obtaining this value for $M$ by an appropriate theory.