A Study of Phonon Transport in Si/Ge Superlattice Thin Films Using a Fast MC Solver

Abstract

We employ a fast Monte Carlo solver, which takes advantage of the geometric symmetry existent in the system to reduce the computational effort, to investigate the phonon transport phenomena in the cross-plane and in-plane directions of Si/Ge superlattice thin films. The simulation results show that the heterogeneous interfaces perpendicular to the heat flow direction create a much stronger thermal resistance than the parallel ones. The cross-plane and in-plane thermal conductivities of a Si/Ge superlattice thin film increase monotonically with the smoothness of the interfaces and the superlattice period. Most of all, a minimum of the in-plane thermal conductivity is observed as the ratio of the layer thicknesses is varied for fixed period. This is due to the effective layer thermal conductivities being determined not only by the phonon intrinsic properties but also by the strong interface scattering. A detailed examination shows that the minimum appears when the effective layer thermal conductivities of the Si and Ge layers are about the same.

Modified series model for cross-plane thermal conductivity of short-period Si/Ge superlattices

“…As displayed in Figure 7, the thermal conductivities increase monotonically with superlattice periods, which agrees well with literatures [25,31,58]. Several causes can interpret this phenomenon.…”

Combined Kinetic Monte Carlo—Molecular Dynamics Approach for Modeling Phonon Transport in Quantum Dot Superlattices

“…Klitsner [15] Peterson [16] Mazumder [30] Lacroix [35] Chen [31], Wang [46] Jeng [23] Randrianalisoa [37] Moore [39] Hao [40,41] Mittal [43] Huang [47,48] Masao [50] Present work: Chen et al [31] extended Mazumder's model and included boundary and isotope scattering, plus a genetic algorithm (GA) to generate and select a set of phonons yielded by 3-phonon processes, while conserving the total energy. Eor the N-processes, the crystal momentum was also globally conserved by the GA. We found that this model did not preserve the Bose-Einstein distribution, had frequency-related statistical biases in its populations, and possible convergence difficulties.…”

“…Their sloped impermeable boundaries permitted both specular and diffuse scattering. Huang et al [47,48] used the MC model of Jeng et al [23] to simulate transport in Si-Ge superlattices via gray-media phonons. They modeled phonon scattering from interfaces using acoustic mismatch equations published by Chen [49], and a spatially variable heat flux at the model boundaries, necessary to prevent cross-plane flux.…”

A Monte Carlo simulation for phonon transport within silicon structures at nanoscales with heat generation

“…However, when the characteristic length of an object is smaller than the mean free path, which is commonly observed at nanoscales, heat conduction no longer obeys the Fourier law, mainly due to the impact of ballistic propagation by the heat carriers. At such scales, thermal conductivity and temperature gradient are reduced while discontinuity in the temperature distribution near the boundary exists [13][14][15][16][17][18][19][20]. Therefore, either the general Boltzmann transport equation (BTE) or the phonon radiative transport equation (PRTE) is required to correctly model the phonon transport [1,2,[21][22][23][24][25][26].…”

“…Among analytical and numerical methods available to solve the BTE [1,2,4,23,26,28], Monte Carlo (MC) simulations are proven to be the most flexible and accurate, yet they can be slow and expensive in terms of computational resources depending on the levels of physics included in the simulation. Many researchers have used MC simulations for phonon transport at nanoscales because of its flexibility in accounting complicated geometries and the correct phonon dispersion relation and different polarization branches [14,[16][17][18][19][20]25,[29][30][31]. While the simulation has been successfully used for predicting thermal conductivities of nanostructures such as nanowires and nanofilms [14,[18][19][20][31][32][33][34], there is plenty of room for improvement in the algorithm, especially for treating the phonon-phonon scattering mechanisms.…”