Monte Carlo Simulation of Steady-State Microscale Phonon Heat Transport

Abstract

Heat conduction in submicron crystalline materials can be well modeled by the Boltzmann transport equation (BTE). The Monte Carlo method is effective in computing the solution of the BTE. These past years, transient Monte Carlo simulations have been developed, but they are generally memory demanding. This paper presents an alternative Monte Carlo method for analyzing heat conduction in such materials. The numerical scheme is derived from past Monte Carlo algorithms for steady-state radiative heat transfer and enables us to understand well the steady-state nature of phonon transport. Moreover, this algorithm is not memory demanding and uses very few iteration to achieve convergence. It could be computationally more advantageous than transient Monte Carlo approaches in certain cases. Similar to the famous Mazumder and Majumdar’s transient algorithm (2001, “Monte Carlo Study of Phonon Transport in Solid Thin Films Including Dispersion and Polarization,” ASME J. Heat Transfer, 123, pp. 749–759), the dual polarizations of phonon propagation, the nonlinear dispersion relationships, the transition between the two polarization branches, and the nongray treatment of phonon relaxation times are accounted for. Scatterings by different mechanisms are treated individually, and the creation and/or destruction of phonons due to scattering is implicitly taken into account. The proposed method successfully predicts exact solutions of phonon transport across a gallium arsenide film in the ballistic regime and that across a silicon film in the diffusion regime. Its capability to model the phonon scattering by boundaries and impurities on the phonon transport has been verified. The current simulations agree well with the previous predictions and the measurement of thermal conductivity along silicon thin films and along silicon nanowires of widths greater than 22nm. This study confirms that the dispersion curves and relaxation times of bulk silicon are not appropriate to model phonon propagation along silicon nanowires of 22nm width.

Thermal conductivity across nanostructured porous silicon films

“…Once the convergence is achieved, the thermal conductivity across the simulated film can be deduced using the Fourier law knowing the net heat flux per unit area crossing the film and the local pseudo-temperature gradient. More details about the MCM can be found in [4].…”

“…First, the material morphologies are simulated using a 3D model derived from past 2D pore network algorithm for PS [3]. Then, the simulation of thermal conduction through the 3D pore-network using the MCM developed especially for steady-state phonon transport [4] is described. Finally, the results are shown and discussed.…”

Rayleigh waves, surface disorder, and phonon localization in nanostructures

“…Current PMC simulations do not allow for mode conversion or Rayleigh waves. Instead, PMC simulations either have phonons scatter specularly at the surface [3,82,113,116] or have a specularity parameter with the reflected phonon of the same mode as the incident phonon [3,117]. Monte Carlo simulations for chaotic ray-splitting billiards are similar to PMC simulations, and the chaotic ray-splitting billiard simulations have been extended to allow for mode conversion between bulk modes [118].…”

“…Another tool used to study phonon transport in relatively large nanostructures is phonon Monte Carlo (PMC), where a large ensemble of phonons are treated as point particles that drift and scatter [3,82,[114][115][116][117]. Current PMC simulations do not allow for mode conversion or Rayleigh waves.…”

Frequency-Dependent Monte Carlo Simulations of Phonon Transport in Nanostructures

“…To correct this, three-phonon scattering treatment respecting the energy conservation was proposed later (Lacroix et al, 2005;Chen et al, 2005;Hao et al, 2009). Unlimited to thin films, the MC simulations were also carried out for nanowires Lacroix et al, 2006;Randrianalisoa & Baillis, 2008) or 1D transient phonon transport in bulk materials (Lacroix et al, 2005). Among all listed studies, the N process and U process were mostly treated together by a combined scattering rate except for that Chen et al adopted a genetic algorithm to satisfy both energy and momentum conservation for the N process and energy conservation for the U process .…”