Theoretical Prediction of Zinc Blende Phase GaN Avalanche Photodiode Performance Based on Numerically Calculated Electro
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45 Mat. Res. Soc. Symp. Proc. Vol. 423 01996 Materials Research Society
measured in terms of low noise and high bandwidth operation, occurs under single carrier ionization conditions [4]. Though few materials are known to exhibit single carrier-type ionization, satisfactory noise performance can still be attained provided the ionization rate of the secondary carrier species is very much less, by more than an order of magnitude, than the primary carrier species ionization rate. It is the purpose of this paper to present the first determination of the electron and hole ionization rates in bulk zinc blende phase GaN. The rates are determined theoretically using an ensemble Monte Carlo calculation. The Monte Carlo simulators for the electrons and holes contain the full details of the conduction and valence bands covering the full energy range of interest. Results are presented for the electron and hole ionization rates, average carrier energy and originating band as a function of applied electric field strength. MODEL DESCRIPTION The calculations are performed using ensemble Monte Carlo simulators for electron and hole transport which include the full details of the first four conduction and first three valence bands respectively. These bands cover the full energy range of interest. The band structure is obtained from an empirical pseudopotential calculation [8] using an expansion set of 113 reciprocal lattice vectors. All of the relevant phonon scattering mechanisms, as well as ionized impurity scattering are included into the simulators. The parameters used to determine the electron scattering rates, i.e., phonon energies, dielectric constants, deformation potential constants, etc. have been reported in reference [8]. In the hole simulator, owing to the very anisotropic nature of the valence bands, the phonon scattering rates are all calculated numerically by integrating over the actual pseudopotential band structure and incorporated into the simulations following the approach of Hinckley and Singh [9]. In both the electron and hole simulators, the high energy phonon scattering rates are assumed to be dominated by deformation potential scattering. In this regime, the phonon scattering rate is calculated through use of a time dependent perturbation theory expansion by integrating the transition rate over the final, numerically determined, density of states including collision broadening effects [10]. The wavevector dependent interband impact ionization transition rate is calculated numerically using the empirical pseudopotential band structure. The transition rate is determined by integrating Fermi's golden rule for a two-body, screened Coulomb interaction over the possible final states using a numerically generated wavevector dependent dielectric function [11] and pseudowavefunctions. The usual first order umklapp processes as well as those processes arising from the pseudowavefunction expansion as described by Sano and Yoshii [12] are included in the evaluation of the direct and exchange terms which comprise the f
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