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

## Abstract

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<λ<10 μm, using SiO2 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, λ<1 μm, can only be obtained by using the quantum approach. Second-order perturbation theory is found to fail at long wavelengths, λ>1 μm. Both methods are inaccurate for λ1 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 λ<1 μm the electron-multiplication rates decrease dramatically as wavelengths become shorter indicating that multiphoton absorption becomes the dominant mechanism for free-electron generation at visible wavelengths. At all wavelengths the theory predicts efficient free-electron mediated energy transfer from the laser field to the lattice. It is therefore possible to observe significant lattice heating caused by free electrons generated via multiphoton absorption in the prebreakdown regime. These findings are shown to be consistent with recent laser experiments [S. Jones, P. Braunlich, R. Casper, X. Shen, and P. Kelly, Opt. Eng. 28, 1039 (1989)]. © 1992 The American Physical Society.