The calculation of heat transport in nonmetallic materials at small length scales is important in the design of thermoelectric and electronic materials. New designs with quantum dot superlattices (QDS) and other nanometer-scale structures can change the thermal conductivity in ways that are difficult to model and predict. The Boltzmann Transport Equation can describe the propagation of energy via mechanical vibrations in an analytical fashion but remains difficult to solve for the problems of interest. Numerical methods for simulation of propagation and scattering of high frequency vibrational quanta (phonons) in nanometer-scale structures have been developed but are either impractical at micron length scales, or cannot truly capture the details of interactions with nanometer-scale inclusions. Monte Carlo (MC) models of phonon transport have been developed and demonstrated based on similar numerical methods used for description of electron transport [1-4]. This simulation method allows computation of thermal conductivity in materials with length scales LX in the range of 10 nm to 10 μm. At low temperatures the model approaches a ballistic transport simulation and may function for even larger length scales.
Generalized Metropolis dynamics with a generalized master equation: An approach for time-independent and time-dependent Monte Carlo simulations of generalized spin systems