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Electron correlation effects in screened hydrogenic impurity states in many-valley semiconductors.

The critical concentration of donor hydrogenic impurities in a screened Coulomb potential is calculated, considering the effects of exchange, correlations, and mass anisotropy of the bound electron. We used the random-phase approximation and a self-consistent scheme proposed by Singwi, Tosi, Land, and Sj\"olander with variational solutions in the effective mass equation. Our results are compared with other theoretical calculations and with experimental measurements of the metal-semiconductor transition in n-type impurities of silicon and germanium. The agreement with the experimental results let us conclude that in many semiconductor systems the short-range correlations need to be taken into account in a more effective way.