The three energy band models used in the simulations of semiconductors with Monte Carlo method are introduced, and comparison among these models has been made. The calculation of scattering rates and the application of band structures, which are two key technologies in the simulations of wurtzite GaN by the full band Monte Carlo method, are also presented. We propose some methods of the determination of the particle's final states after scattering. Depended on the scattering mechanisms and particle's energy, there are 4 methods for the determination of the final states. For the polar optical phonon scattering, the method of the determination of the final states with combination of the analytic band model and the full band model, and with different value of non-parabolic coefficient relating particle's energy, are adopted. With this method the exact results of the final states can be obtained, and the speed of the calculations are also improved.