Photoionization rate in wide band-gap crystals

The Keldysh model of the photoionization L. V. Keldysh, Sov. Phys. JETP 20, 1307 1965 is extended by deriving a formula for the photoionization rate of crystals based on the cosine energy-momentum relation. The relation is characteristic of tight-binding approximation and directly takes into account the influence of Braggtype reflections of oscillating electrons at the edges of the first Brillouin zone. Due to the reflections and oscillations, the dependence of the photoionization rate on laser and material parameters takes form of a multibranch function with the branches separated by singularity points with unlimited increasing of the rate. Each of the singularities is coupled to the flattening of the effective-band structure. The laser intensity corresponding to the first singularity is found to be about 10 TW/cm2 for most wide band-gap crystals. We also show that the lowest-order branch of the photoionization rate completely corresponds to the multiphoton regime, and the first singularity takes place before the tunneling regime starts to dominate. Analysis of the ionization-rate asymptotic in the vicinity of the first-singularity point suggests possibility of ionization suppression by high-intensity radiation for certain ranges of laser wavelength.