Hybrid ballistic–diffusive solution to the frequency-dependent phonon Boltzmann Transport Equation

Solution of the Phonon Boltzmann Transport Equation Employing Rigorous Implementation of Phonon Conservation Rules

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 ...

Semi-analytical solution to the frequency-dependent Boltzmann transport equation for cross-plane heat conduction in thin films

Analytical Green’s function of the multidimensional frequency-dependent phonon Boltzmann equation

Thermal phonon transport at length scales comparable to mean free paths is governed by the Boltzmann equation, which is challenging to solve due to its high dimensionality. Here, we present an analytical Green’s function for the frequency-dependent, multidimensional Boltzmann equation under the relaxation-time approximation. The new analytical solution is valid from diffusive to ballistic trans...

Solution of Time-dependent Boltzmann Equation

The time-dependent Boltzmann equation (BE) is solved in a two-term and a multi-term approximation in order to study the time evolution of the electron energy distribution function (EEDF) in argon plasma in a constant electric field. The initial distribution is taken to be isotropic Gaussian distribution, its center is set to the area of increasing elastic collision cross-section in order to stu...

Boltzmann Solver for Phonon Transport

Boltzmann Transport Equation is solved numerically to model phonon transport in a subcontinuum domain in order to study heat transfer in thin film semiconductors. The phonon distribution function is modified to get an Energy equation from the Boltzmann Transport Equation. Gray form of the Energy equation is solved in the Relaxation time approximation to get the Phonon Energy Density distributio...