Impact Ionization and Auger effects Involving Traps
In this paper four theoretical models are considered for the discussion of low-field impact ionization and, its inverse process, Auger recombination, involving a single localized level. Four such processes are shown schematically in Table 1, where the corresponding Auger recombination and impact ionization rates are given for non-degenerate statistics. Here, n and p are electron and hole concentrations, nt and pt are concentrations of full and empty traps. The various possibilities are cut down (a) by considering only the process specified by X1 in Table 1, although the present approach can be used for the other processes shown; and (b) by considering the band to be parabolic for energies above the minimum which are of the order of the trap depth, Et. Here the probability P(2’) per unit time per unit volume, that a given energetic electron in a band state 2’ will impact-ionize a bound state of energy -Et, is discussed. The threshold for such a process lies at the electronic kinetic energy E2 =Et. For any band having the probability of finding a vacancy at states 1 and 2 (see Table 1) of order unity, and in particular for a non-degenerate band, P(2) is independent of the statistical electron distribution in the band. One can then obtain the impact ionization coefficient X 1, and the Auger recombination coefficient T1 by an integration over the states 2′.
KeywordsImpact Ionization Auger Recombination Trap Depth Atomic Case Auger Recombination Rate
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