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

Abstract

A new kinetic Monte Carlo method for modeling phonon transport in quantum dot superlattices is presented. The method uses phonon scattering phase functions and cross sections to describe collisions between phonons and quantum dots. The phase functions and cross sections are generated using molecular dynamics simulation, which is capable of including atomistic effects otherwise unavailable in Monte Carlo approaches. The method is demonstrated for a test case featuring a Si-Ge quantum dot superlattice, and the model is compared against published experiments. It is found that molecular dynamics-derived cross sections must be weighted by diffuse mismatch model-type weighting factors in order to satisfy detailed balance considerations. Additionally, it is found that thin alloy "base layer" films strongly reduce thermal conductivity in these systems and must be included in the modeling to obtain agreement with published experimental data.

Phonon Boltzmann equation-based discrete unified gas kinetic scheme for multiscale heat transfer

“…[15][16][17][18][19] Generally, the MC method follows a time-splitting algorithm, namely, the dynamics of a simulated particle is decoupled into advection and scattering processes, and thus the time step used is less than the relaxation time, and the grid size is less than the phonon mean-free-path. 20 Consequently, the computational costs of MC method are expensive in the acoustic thick regime, which prohibit its applications for multiscale problems with diffusive region, although it can be quite efficient for ballistic transport. It is also noted that an improved MC method has been developed recently by simulating only the deviation from equilibrium such that the variance can be efficiently reduced in simulating systems with small temperature variations.…”