A three-valley Monte Carlo simulation approach was used to investigate electron transport in wurtzite GaN such as the drift velocity, the drift mobility, the average electron energy, energy relaxation time, and momentum relaxation time at high electric fields. The simulation accounted for polar optical phonon, acoustic phonon, piezoelectric, intervalley scattering, and Ridley charged impurity scattering model. For the steady-state transport, the drift velocity against electric field showed a negative differential resistance of a peak value of 2.9×105 m/s at a critical electric field strength 180×105 V/m. The electron drift velocity relaxes to the saturation value of 1.5×105 m/s at very high electric fields. The electron velocities against time over wide range of electric fields are reported.

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The non-local nature of impact ionisation is modelled using lucky-drift theory with the assumption that the relevant electric field is the average field, but that the relevant drift velocity is that associated with the local field. The carrier density relevant for impact ionisation is also taken to be non-local. The model is applied to the case of a thin film insulator, with Fowler-Nordheim injections of electrons at the cathode. For clarity's sake, the authors avoid considering the excitation of holes and limit attention to the ionisation of a set of occupied deep-level states present in high concentration. Further simplifying assumptions include the neglect of diffusion, overshoot and non-parabolicity. The authors show that the non-local nature of the ionisation process reduces the local field markedly, resulting in a pile-up of free electrons to maintain current continuity in the rest of the film. This is contrasted with the prediction of local impact ionisation theory in which the field is reduced merely to that necessary to sustain a small level of ionisation. Under certain circumstances space-charge striations are produced-this is analogous to the situation in gas discharge-and for some film thicknesses a negative differential resistance occurs.

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