Modeling and simulating a wide band gap semiconductor such as GaN faces some physical effects not encountered in Si or GaAs. The main difference is that GaN crystallizes with a non-cubic symmetry, which results in an increased size and number of atoms per unit cell, thus in a more complex band structure . Accounting for those new complexities Monte Carlo (MC) studies of the transport properties of wurtzite GaN have been conducted. The advantage of this approach is that it does not require extensive experimental input. Earlier works employed analytical two-band conduction band models . Other groups use ensemble Monte Carlo simulation to calculate the transport properties  paying special attention to the band intersection points and their impact on impact ionization. Some studies focus exclusively on the high-field properties of GaN using a microscopic rigid-ion model and focus on the isotropy of the properties and the effects of non-equilibrium hot phonons .
However MC techniques can also be used to calculate GaN based device characteristics. GaN MESFETs with different phases were compared by such a method in . Yamakawa et al. employed a cellular MC approach with quantum corrections , however, the overall current of the device remained nearly unchanged due to the dominant polarization charge. Several works focused on the proper modeling of the piezoelectric polarization effects by using a quasi-two-dimensional model based on a self-consistent charge control [114,115]. Others studied deep levels at the AlGaN surface and their impact on current-slump phenomena: it was found that surface trapping effects may play a major role . A method, which combines MC electronic simulation with an analytical thermal resistance matrix method, was used to investigate the self-heating effects . Accounting for self-heating effects too, the high-frequency noise at different temperatures was studied in . The impact of threading dislocation on the velocity-field characteristics was shown to be small, due to the high carrier concentration screening effects .