In this work, we utilize electron-phonon Monte Carlo simulations of AlGaN/GaN HEMTs to determine the energy loss rate of electrons in the channel of the transistor as a function of bias conditions. Intense energy transfer from electrons to phonons is observed near the gate edge on the drain side of such devices where the peak electric field exists. This intense energy exchange results in nanometer sized hotspots in the vicinity of the gate edge. In order to account for effects of ballistic phonon transport on temperature near the hotspots, a non-gray Discrete Ordinates Method (DOM) is used as a numerical solver for the phonon Boltzmann Transport Equation (BTE). The non-gray model accounts for dispersion effects of GaN by splitting the dispersion curve of GaN into a finite number of frequency bands. The phonons in each frequency band are assumed to have the same properties with the other phonons in the same band and the relaxation times between these bands are calculated. The results show how energy is redistributed among the available phonon bands and demonstrates which modes are most effective at transporting the thermal energy. Finally, the hotspot temperature predictions obtained by the model are compared to temperatures obtained by gray and continuum modeling approaches to show the discrepancies between different techniques.

The description of heat transport at small length scales is very important in understanding a wide range of micro and nanoscale systems. In systems where coherent phonon transport effects are negligible, the Boltzmann transport equation (BTE) is often employed to describe the distribution and propagation of thermal energy in the lattice. The phonon distribution function depends not only on the temporal and spatial coordinates, but also on polarization and wave vector, making fully-resolved simulations very expensive. Therefore, there is a need to develop accurate and efficient numerical techniques for the solution of the BTE. The discrete ordinates method (DOM) and more recently, the lattice Boltzmann method (LBM) have been used for this purpose. In this work, a comparison between the numerical solution of the phonon BTE by the LBM and DOM is made in order to delineate the strengths and weaknesses of these approaches. Test cases are chosen with Knudsen ( Kn ) numbers varying between 0.01–100 to cover the full range of diffusive to ballistic phonon transport. The results show that solutions obtained from both methods converge to analytical results for the 1 dimensional phonon transport in a slab. Solutions obtained by two methods converge to analytical solutions of 2 dimensional problems at low Kn . However, solution accuracy is strongly determined by angular resolution for moderate to high Kn . Since the number of propagation directions in LBM are limited, significant errors are engendered in multi-dimensional acoustically-thin problems. DOM also suffers errors at low angular resolutions for high Kn , but yields accurate solutions when sufficient angular resolution is employed.