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Description
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.
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.
ContributorsSabatti, Flavio Francesco Maria (Author) / Saraniti, Marco (Thesis advisor) / Smith, David J. (Committee member) / Wang, Robert (Committee member) / Goodnick, Stephen M (Committee member) / Arizona State University (Publisher)
Created2018