  We show the possibility of inducing a superconductive phase transition in
tetrahedrally coordinated semiconductors via field-effect (FET) doping by
taking as an example the hydrogenated (111) silicon surface. We perform density
functional theory computations of the electronic and vibrational properties of
the system in the proper FET geometry, by taking into account the applied
electric field and the induced charge density. Using a simplified
superconductive model at $q=\Gamma$ and the McMillan/Allen-Dynes formula, we
get an estimate of the superconductive critical temperature. We observe that,
by heavily doping with holes at $n_{dop}=6\cdot10^{14}$ cm$^{-2}$, we get an
electron-phonon coupling constant of $\lambda_{Si}=0.98$ and a superconductive
phase transition at $T_{\text{c}}\in[8.94;10.91]$ K, with
$\mu^*\in[0.08;0.12]$.

Superconductivity;Materials Science