Impact ionization rate calculations in wide band gap semiconductors

Abstract

Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-pro t purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. An algorithm for calculating impact ionization rates in the semiclassical Fermi's Golden Rule approximation which is efficient close to threshold is presented. Electron and hole initiated rates are calculated for three semiconductors with particular band structure characteristics, as are the distributions of the generated carriers. Simple analytic expressions of the form RϭA(EϪE 0 ) P are fitted to the calculated rates. The role of the matrix elements in influencing the distribution of final states is investigated. In the direct gap materials, they act to significantly enhance the low-q transitions, while in the indirect gap case they have a lesser effect on the distribution. Results for GaAs obtained here and by several other workers are compared and possible causes of the discrepancies examined, including differences in band structure and approximations made in evaluation of the matrix element. It is found that these differences do not influence the rate sufficiently to account for the wider variation between authors, and so it is concluded that differences in the implementation of the rate integration algorithm are the main cause.

Characteristics of impact ionization rates in direct and indirect gap semiconductors

“…The six-dimensional integral is performed by an algorithm described elsewhere, 19 which is a development of the method of Kane. 20…”

“…Impact ionization rates calculated using the algorithm described in Ref. 19 were approximated by a fit formula of the form…”

Theoretical analysis of breakdown probabilities and jitter in single-photon avalanche diodes

“…19. This full band model employs ionization rates generated from first principles calculations, 24,25 which were in agreement with experimental data. It is important to note that the commonly assumed ionization threshold energies in GaAs of around 2 eV are derived from the Keldysh formula, which is only applicable to parabolic bands.…”

Femtosecond spectroscopy of unipolar nanometer-scale high-field transport in GaAs

“…Additionally, the scattering rate for impact ionization is modelled according to the well-established Keldysh formula 26 : Γ impact = A (E-E th ) P The corresponding values for electrons are taken from Ref. [27]: A e = 1.4 x 10 11 /s, P e = 5.2, E th,e = E Gap + 467 meV. For the case of holes, we use the parameter set: A h = 3.3 x 10 11 /s, P h = 20.4, E th,h = E Gap + 7 meV.…”