A novel Monte Carlo rejection technique for solving the phonon and electron

Boltzmann Transport Equation (BTE), including full many-particle interactions, is

presented in this work. This technique has been developed to explicitly model

population-dependent scattering within the full-band Cellular Monte Carlo (CMC)

framework to simulate electro-thermal transport in semiconductors, while ensuring

the conservation of energy and momentum for each scattering event. The scattering

algorithm directly solves the many-body problem accounting for the instantaneous

distribution of the phonons. The general approach presented is capable of simulating

any non-equilibrium phase-space distribution of phonons using the full phonon dispersion

without the need of the approximations commonly used in previous Monte Carlo

simulations. In particular, anharmonic interactions require no assumptions regarding

the dominant modes responsible for anharmonic decay, while Normal and Umklapp

scattering are treated on the same footing.

This work discusses details of the algorithmic implementation of 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 approach

is then extended with a technique based on the multivariable Hawkes point process

that has been developed to model the emission and the absorption process of phonons

by electrons.

The simulation code was validated by comparison with both analytical, numerical,

and experimental results; in particular, simulation results show close agreement with

a wide range of experimental data such as the thermal conductivity as function of the

isotopic composition, the temperature and the thin-film thickness.