  Epitaxial SrTiO$_3$ (STO) on Si is nowadays the benchmark initial platform
for the further addition of functional oxides on Si. Starting the growth of STO
on a Sr-passivated Si substrate with 1/2 monolayer (ML) Sr coverage and a (1
$\times$ 2) reconstructed Si surface with rows of Si dimers, the final
STO/Sr/Si stack exhibits 1 ML Sr coverage and a (1 $\times$ 1) Si surface
without dimer. Using first-principles density functional theory calculations,
we investigate how the interface evolves from 1/2 ML to 1 ML Sr coverage,
concluding that the latter is indeed most stable and that the reconstruction of
the interface takes place during the early stage of the layer-by-layer
deposition. Going further, we determine the band alignment of the final stable
interface and assess its potential interest as photocathode for water
reduction.
