A finite volume scheme is developed to
solve the phonon Boltzmann transport equation in an energy form accounting
for phonon dispersion and polarization. The physical space and the first
Brillouin zone are discretized into finite volumes and the phonon BTE
is integrated over them. Second-order accurate differencing schemes are
used for the discretization. The scattering term employs a rigorous implementation
of phonon momentum and energy conservation laws in determining the rate
of normal and Umklapp processes. The method is applied to a variety of
bulk silicon and silicon thin-film conduction problems and shown to perform
satisfactorily.
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