Impact ionization: thresholds, anti-thresholds and proper counting

By defining an 'energy difference function' a simple picture displaying the states involved in an impact ionizing transition is developed. With this picture it can easily be seen how thresholds and anti-thresholds arise and how they can be evaluated and identified. In calculating total transition rates only quantum mechanically distinct transitions should be included in the sum and it is discussed how this can be achieved. The thresholds at 300 K for all 21 possible impact ionizing processes in InSb, InAs and Cd(0.8)Hg(0.2)Te are calculated and also the 18 hole-initiated processes in GaAs, InP and In(0.53)Ga(0.47)As using the anisotropic, non-parabolic four-band k.p band structure with higher and lower lying bands taken into account by perturbation theory.