Thermal Modeling of Wide and Ultra-wide Bandgap Materials and Devices Through Cellular Monte Carlo

An efficient thermal solver is available in the CMC that allows modeling self-heating in the electrical simulations, which treats phonons as flux and solves the energy balance equation to quantify thermal effects. Using this solver, thermal simulations were performed on GaN-HEMTs in order to test effect of gate architectures on the DC and RF performance of the device. A Π- gate geometry is found to suppress 19.75% more hot electrons corresponding to a DC power of 2.493 W/mm for Vgs = -0.6V (max transconductance) with respect to the initial T-gate. For the DC performance, the output current, Ids is nearly same for each device configuration over the entire bias range. For the RF performance, the current gain was evaluated over a frequency range 20 GHz to 120 GHz in each device for both thermal (including self-heating) and isothermal (without self-heating). The evaluated cutoff frequency is around 7% lower for the thermal case than the isothermal case. The simulated cutoff frequency closely follows the experimental cutoff frequency. The work was extended to the study of ultra-wide bandgap material (Diamond), where isotope effect causes major deterioration in thermal conductivity. In this case, bulk phonons are modeled as semiclassical particles solving the nonlinear Peierls - Boltzmann transport equation with a stochastic approach. Simulations were performed for 0.001% (ultra-pure), 0.1% and 1.07% isotope concentration (13C) of diamond, showing good agreement with the experimental values. Further investigation was performed on the effect of isotope on the dynamics of individual phonon branches, thermal conductivity and the mean free path, to identify the dominant phonon branch. Acoustic phonons are found to be the principal contributors to thermal conductivity across all isotope concentrations with transverse acoustic (TA2) branch is the dominant branch with a contribution of 40% at room temperature and 37% at 500K. Mean free path computations show the lower bound of device dimensions in order to obtain maximum thermal conductivity. At 300K, the lowest mean free path (which is attributed to Longitudinal Optical phonon) reduces from 24nm to 8 nm for isotope concentration of 0.001% and 1.07% respectively. Similarly, the maximum mean free path (which is attributed to Longitudinal Acoustic phonon) reduces from 4 µm to 3.1 µm, respectively, for the same isotope concentrations. Furthermore, PETSc (Portable, Extensible Toolkit for Scientific Computation) developed by Argonne National Lab, was included in the existing Cellular Monte Carlo device simulator as a Poisson solver to further extend the capability of the simulator. The validity of the solver was tested performing 2D and 3D simulations and the results were compared with the well-established multigrid Poisson solver.