  Nonlinear photoionization of dielectrics and semiconductors is widely treated
in the frames of the Keldysh theory whose validity is limited to small photon
energies compared to the band gap and relatively low laser intensities. The
time-dependent density functional theory (TDDFT) simulations, which are free of
these limitations, enable to gain insight into non-equilibrium dynamics of the
electronic structure. Here we apply the TDDFT to investigate photoionization of
silicon crystal by ultrashort laser pulses in a wide range of laser wavelengths
and intensities and compare the results with predictions of the Keldysh theory.
Photoionization rates derived from the simulations considerably exceed the data
obtained with the Keldysh theory within the validity range of the latter.
Possible reasons of the discrepancy are discussed and we provide fundamental
data on the photoionization rates beyond the limits of the Keldysh theory. By
investigating the features of the Stark shift as a function of photon energy
and laser field strength, a manifestation of the transient Wannier-Stark ladder
states have been revealed which become blurred with increasing laser field
strength. Finally, it is shown that the TDDFT simulations can potentially
provide reliable data on the electron damping time that is of high importance
for large-scale modeling.
