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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.

Particle-Based Modeling of Electron–Phonon Interactions