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.
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