A Monte Carlo rejection technique for numerically solving the complete, nonlinear phonon Boltzmann transport equation (BTE) is presented in this work, including three particles interactions. The technique has been developed to explicitly model population-dependent scattering within a full-band cellular Monte Carlo (CMC) framework, to simulate phonon transport in semiconductors, while ensuring conservation of energy and momentum for each scattering event within gridding error. The scattering algorithm directly solves the many-body problem accounting for the instantaneous distribution of the phonons. Our general approach is capable of simulating any nonequilibrium phase space distribution of phonons using the full phonon dispersion without the need of approximations used in previous Monte Carlo simulations. In particular, no assumptions are made on the dominant modes responsible for anharmonic decay, while normal and umklapp scattering are treated on the same footing. In this work, we discuss details of the algorithmic implementation of both the three-particle scattering for the treatment of the anharmonic interactions between phonons, as well as treating isotope and impurity scattering within the same framework. The simulation code was validated by comparison with both analytical and experimental results; in particular, the simulation results show close agreement with a wide range of experimental data such as thermal conductivity as function of the isotopic composition, the temperature, and the thin-film thickness.

In order to assess the underlying physical mechanisms of hot carrier-related degradation such as defect generation in millimeter-wave GaN power amplifiers, we have simulated the electron energy distribution function under large-signal radio frequency conditions in AlGaN/GaN high-electron-mobility transistors. Our results are obtained through a full band Monte Carlo particle-based simulator self-consistently coupled to a harmonic balance circuit solver. At lower frequency, simulations of a Class AB power amplifier at 10 GHz show that the peak hot electron generation is up to 43% lower under RF drive than it is under DC conditions, regardless of the input power or temperature of operation. However, at millimeter-wave operation up to 40 GHz, RF hot carrier generation reaches that from DC biasing and even exceeds it up to 75% as the amplifier is driven into compression. Increasing the temperature of operation also shows that degradation of DC and RF characteristics are tightly correlated and mainly caused by increased phonon scattering. The accurate determination of the electron energy mapping is demonstrated to be a powerful tool for the extraction of compact models used in lifetime and reliability analysis.

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An important challenge in particle-based modeling of electron–phonon interactions is the large difference in the statistical weight of the particles in the two simulated populations. Each change in the state of a simulated phonon during scattering is statistically representative of an interaction with multiple simulated electrons, which results in a large numerical burden accurately represent both populations. We developed two stochastic approaches to mitigate this numerical problem. The first approach is based on Poisson modeling of the scattering processes coupled with a thinning algorithm, which works effectively at steady-state, but it is prone to statistical errors in the energy during the transient regime. The second approach is based on point process (PP) modeling of the scattering, allowing stochastical book-keeping, which corrects the energy error. Here, we present a mathematical description of the problem and the two stochastic approaches along with the numerical results we obtained for the synchronous transient simulation of the electron and phonon populations.