Simulations of ultrafast laser-induced excitation and heating of electron sub-system of semiconductors with the Vinogradov equation and multi-band Keldysh formula

High-intensity laser interactions with band-gap solids are frequently simulated with the Keldysh photoionization-rate formula and the Drude model to describe light absorption and related heating of conduction-band electrons. That approach suffers from several internal contradictions. We fix some of them by combining the Vinogradov equation for energy absorption with multi-band version of the Keldysh equation for the rate of photoionization.