Contributions to the theory of impact ionization in semiconductors
Contributions to the theory of impact ionization in semiconductors
A joint calculation of the phonon-assisted and phononless Auger recombination rates is given for any parabolic band structure in a constant matrix element approximation, by a modification of the approach of Hill and Landaberg to the calculation of the Auger rate in indirect materials. An analogy is drawn between the impact ionization probability integrals so obtained and joint density-of states integrals in radiative processes. The critical point concept in radiative transitions is extended to thee impact ionization probability in six (phononless) and nine (phonon-assisted)dimensions. Explicit expressions for the impact ionization probability and the phonon-assisted Auger recombination rate are discussed. The Auger rate calculation is adapted to the calculation of impact ionization thresholds, and explicit expressions are given from which the results of earlier workers may be obtained as special cases. Two classes of thresholds are identified. In class a , thresholds arise away from the extrema due to energy and momentum constraints. In class 9 , thresholds occur at the band extrema. The analogy between radiative and Auger processes is extended by the identification of the generalised van Hove singularity with theclass a 'threshold' (in the general sense of thresholds, anti-thresholds and saddle thresholds). The classification is completed by the identification of two further subgroups of transitions, the critereon being whether or not there is an impact ionization 'window' in terms of energies. A simple example of an anti-threshold is constructed, and further examples in indirect materials considered.In the presence of trapping, the usual electron and hole ionization coefficients a and 6 are inadequate to describe the multiplication process. The usual theory has to be generalised and four ionization coefficients introduced. It is shown here how this may be achieved. The key results of earlier workers, who assumed no trapping, are obtained as special cases. By the development of a result for the band-trap ionization coefficients the conditions under which atrapping effect may become important are predicted. Some evidence for a trapping effect is seen in low-field ionization measurements.
University of Southampton
1978
Robbins, David James
(1978)
Contributions to the theory of impact ionization in semiconductors.
University of Southampton, Doctoral Thesis.
Record type:
Thesis
(Doctoral)
Abstract
A joint calculation of the phonon-assisted and phononless Auger recombination rates is given for any parabolic band structure in a constant matrix element approximation, by a modification of the approach of Hill and Landaberg to the calculation of the Auger rate in indirect materials. An analogy is drawn between the impact ionization probability integrals so obtained and joint density-of states integrals in radiative processes. The critical point concept in radiative transitions is extended to thee impact ionization probability in six (phononless) and nine (phonon-assisted)dimensions. Explicit expressions for the impact ionization probability and the phonon-assisted Auger recombination rate are discussed. The Auger rate calculation is adapted to the calculation of impact ionization thresholds, and explicit expressions are given from which the results of earlier workers may be obtained as special cases. Two classes of thresholds are identified. In class a , thresholds arise away from the extrema due to energy and momentum constraints. In class 9 , thresholds occur at the band extrema. The analogy between radiative and Auger processes is extended by the identification of the generalised van Hove singularity with theclass a 'threshold' (in the general sense of thresholds, anti-thresholds and saddle thresholds). The classification is completed by the identification of two further subgroups of transitions, the critereon being whether or not there is an impact ionization 'window' in terms of energies. A simple example of an anti-threshold is constructed, and further examples in indirect materials considered.In the presence of trapping, the usual electron and hole ionization coefficients a and 6 are inadequate to describe the multiplication process. The usual theory has to be generalised and four ionization coefficients introduced. It is shown here how this may be achieved. The key results of earlier workers, who assumed no trapping, are obtained as special cases. By the development of a result for the band-trap ionization coefficients the conditions under which atrapping effect may become important are predicted. Some evidence for a trapping effect is seen in low-field ionization measurements.
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Published date: 1978
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Local EPrints ID: 459984
URI: http://eprints.soton.ac.uk/id/eprint/459984
PURE UUID: 162d71cb-a574-40d4-9e39-02b0e7398456
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Last modified: 04 Jul 2022 17:32
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Author:
David James Robbins
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