Laser-induced ionization of solids: back to Keldysh

The aim of our consideration is to clarify the influence of band structure of crystalline solids on ionization rate described in the framework of the Keldysh model. In this connection we compare the Keldysh formula with its analogs obtained for several models of band structure. We clearly demonstrate strong dependence of the ionization rate on band model especially in case of the transitional (from multiphoton to tunneling) and the tunneling regimes. An expression for the adiabatic parameter also depends on particular band model, and we present its new definition relating it to lattice constant, electric-field strength and laser frequency. We demonstrate possibility of a new regime of ionization referred to as collective ionization in which conditions for an effective jump of almost all valence electrons over the forbidden band within one period of field oscillations are provided. We present rigorous estimation of the threshold for that effect and show it to be close to 10 TW per square cm for most transparent materials. The influence of band model on multiphoton ionization rate depends on ratio of band gap to photon energy and is the weakest if the ration is slightly below an integer. In this connection we demonstrate that a proper choice of a band model can explain the well-known difference between calculated and measured values of ionization rate.