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We examine the Coulomb pseudopotential $\mu^*$ in the McMillan equationapplying to the superconductivity of heavily doped semiconductors. Systematiccalculation using the first-principles calculation suggests that $\mu^*$ shouldbe considered as a variable quantity depending on carrier density $n$ insemiconductors, although it is usually considered as a constant about 0.1. Toclarify $n-$dependence of $\mu^*$, we solve the McMillan equation inversely for$\mu^*$ by combining the result of the first-principles calculation and that ofexperiments. It indicates that $\mu^*$ decreases with $n$ and becomes negativeunder $n \sim 5 \times 10^{-21}[{\rm cm^{-3}}]$. This reduction is explained bythe effect of plasmon which may play an important role in the superconductivityof low carrier systems such as heavily doped semiconductors.

Plasmon effect on the Coulomb pseudopotential $\mu^*$ in the McMillan equation