Impact ionisation and Auger recombination involving traps in semiconductors

Four theoretical models have been considered for the discussion of low-field impact ionisation and Auger recombination rates involving a single trap. For shallow levels two hydrogenic models are considered. These are then modified for application to deep levels by the use of the Lucovsky delta -function potential model. It is also shown how atomic results on hydrogen ionisation can be used to compare with the theoretical solid state results. Particular attention is paid to problems induced by the non-orthogonality of approximate wavefunctions, and it is found that the use of orthogonal wavefunctions significantly reduces the impact-ionisation probability per unit time P(2'), for higher energies of the ionising carriers in state 2'. These results are highly model sensitive. When the Auger recombination coefficient is inferred from P(2') by integration, the results obtained are much less model dependent.