Soft and hard ionization thresholds in Si and GaAs

We introduce a new simple model of ionization probabilities in semiconductors, which clarifies the origin of softness and hardness of the ionization thresholds observed in Si and GaAs, respectively. It is shown that the ionization probability is, in principle, hard in both materials in the sense that the electrons rapidly ionize when they approach the threshold energies, and that the softness is mainly introduced from the fact that the threshold energies strongly depend upon the wave vectors of the initiating electrons.