MONTE carlo simulation of hall effect in N-TYPE GaN

Results of Monte Carlo simulations of electron transport for wurtzite phase GaN in crossed, weak electric and magnetic fields are presented. It is found that the Hall factor, r_H = μ_Hall/μ_drift, decreases monotonically as the temperature increases from 77K to 400K. The low temperature value of the Hall factor increases significantly with increasing doping concentration. The Monte Carlo simulations take into account the electron-lattice interaction through polar optical phonon scattering, deformation potential acoustic phonon scattering (treated as an inelastic process), and piezoelectric acoustic phonon scattering. Impurity scattering due to ionized and neutral donors is also included, with the latter found to be important at low temperature due to the relatively large donor binding energy which implies considerable carrier freeze-out already at liquid nitrogen temperature. The temperature dependences of the electron concentration, drift mobility, and Hall factor are calculated for donor concentrations equal to 5 × 10¹⁶ cm^-3, 10¹⁷ cm^-3, and 5 × 10¹⁷ cm^-3. The Monte Carlo simulations are compared to classical analytical results obtained using the relaxation-time approximation, which is found to be adequate at low temperatures and sufficiently low carrier concentrations so that inelastic scattering effects due to optical phonons and degeneracy effects are negligible. The influence of dislocations on the Hall factor is discussed briefly.