Advanced quasi self-consistent Monte Carlo simulations of electrical and thermal properties of nanometer-scale gallium nitride HEMTs considering local phonon number distribution

As a means of investigating both the electrical and thermal properties of nanometer-scale electron devices within a reasonable computing time, we previously proposed a quasi-self-consistent Monte Carlo simulation method that used two new procedures: (i) a local temperature determination using the simulated phonon spatial distribution and feedback to update the electron-phonon scattering rates and (ii) a new algorithm which calculates long-time phonon transport by introducing different time increments for the electron and phonon transport. In this paper, to improve the quantitative accuracy and self-consistency of the simulation, we investigate an advanced Monte Carlo method considering (i) spatially dependent electron-phonon scattering rates that are calculated directly using a simulated phonon distribution (not the local temperature) taking into account (ii) the energy dependence of the phonon group velocity and phonon-phonon scattering rate and (iii) positive polarization charges due to piezoelectricity at the AlGaN/GaN interface. Using this advanced Monte Carlo method, we succeeded in simulating the current-voltage characteristics and thermal resistance of GaN HEMTs (High Electron Mobility Transistors), with which a quantitative evaluation could be made using actual devices. We also examined the convergence of this self-consistent Monte Carlo model.