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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
Description
A model of self-heating is incorporated into a Cellular Monte Carlo (CMC) particle-based device simulator through the solution of an energy balance equation (EBE) for phonons. The EBE self-consistently couples charge and heat transport in the simulation through a novel approach to computing the heat generation rate in the device under study. First, the moments of the Boltzmann Transport equation (BTE) are discussed, and subsequently the EBE of for phonons is derived. Subsequently, several tests are performed to verify the applicability and accuracy of a nonlinear iterative method for the solution of the EBE in the presence of convective boundary conditions, as compared to a finite element analysis solver as well as using the Kirchhoff transformation. The coupled electrothermal characterization of a GaN/AlGaN high electron mobility transistor (HEMT) is then performed, and the effects of non-ideal interfaces and boundary conditions are studied.
The proposed thermal model is then applied to a novel $\Pi$-gate architecture which has been suggested to reduce hot electron generation in the device, compared to the conventional T-gate. Additionally, small signal ac simulations are performed for the determination of cutoff frequencies using the thermal model as well.
Finally, further extensions of the CMC algorithm used in this work are discussed, including 1) higher-order moments of the phonon BTE, 2) coupling to phonon Monte Carlo simulations, and 3) application to other large-bandgap, and therefore high-power, materials such as diamond.
The proposed thermal model is then applied to a novel $\Pi$-gate architecture which has been suggested to reduce hot electron generation in the device, compared to the conventional T-gate. Additionally, small signal ac simulations are performed for the determination of cutoff frequencies using the thermal model as well.
Finally, further extensions of the CMC algorithm used in this work are discussed, including 1) higher-order moments of the phonon BTE, 2) coupling to phonon Monte Carlo simulations, and 3) application to other large-bandgap, and therefore high-power, materials such as diamond.
ContributorsMerrill, Ky (Author) / Saraniti, Marco (Thesis advisor) / Goodnick, Stephen (Committee member) / Smith, David (Committee member) / Wang, Robert (Committee member) / Arizona State University (Publisher)
Created2020