Theory of laser-induced free-electron heating and impact ionization in wide-band-gap solids

A microscopic theory for the interaction of intense laser radiation at visible and near-infrared wavelengths with free electrons in a wide-band-gap solid is presented. We calculate the free-electron mediated energy transfer from the laser field to the solid and the electron-multiplication rate due to band-to-band ionization as a function of laser intensity at wavelengths in the range 250 nm${\mathrm{SiO}}_2$ as an example. The formalism is based on a Monte Carlo integration of the Boltzmann transport equation. The electron interaction with the lattice is described in terms of polar and acoustic-phonon scattering. Band-to-band impact ionization is included using an empirical, Keldysh-type impact ionization rate. The interaction of the laser radiation with the free electrons is treated both within the standard classical approximation and quantum mechanically using second-order perturbation theory. We find that the classical approach to the electron-laser field interaction is valid for λ>2 μm, while reliable results for short wavelengths, λ1 μm. Both methods are inaccurate for λ≃1 μm, yielding only upper and lower bounds for calculated quantities. For λ>2 μm the calculated quantities are found to be close to the values obtained in the dc limit, using a dc field equal to the rms value of the ac field. For λ28, 1039 (1989)].