The foundations of Shockley's equation for the average electron–hole-pair creation energy in semiconductors

Energetic carriers in semiconductors thermalize by impact-ionization, which generates electron–hole pairs (EHPs), and energy losses to phonons. The average EHP creation is typically about three times the gap. In 1960, Shockley derived a simple equation for with single free parameter that fits experimental values wide range of materials, but underlying assumptions, as stated, have been widely criticized lacking justification. Modified expressions improved approximations proposed do not fare better. Here, we revisit foundations Shockley's provide robust justification kinetic-energy component model averaging procedure then apply similar phonon equation. result retains form, interpretation are now on par those term. single-parameter fit data remains unchanged, i.e., present analysis accounts exceptional applicability