ATOMS Laboratory | Advanced Thermal/Fluid Optimization, Modelling and Simulation Laboratory

Thermal Transport in Bulk and Nanostructured Homogeneous Systems

As engineers, we typically use the thermal conductivity to describe thermal energy transport in bulk solids. In solids, thermal energy is carried by electrons and/or phonons (i.e., a quanta of energy associated with lattice vibrations). In materials with low electrical conductivity, such as semiconductors and insulators, phonons dominate thermal transport. In our research, we use a combination of the Boltzmann transport equation and atomistic modeling techniques (e.g., molecular dynamics simulations and lattice dynamics calculations) to simulate phonon transport. As an example of our work, in the figures on the right we plot phonon transport properties for bulk silicon at a temperature of 300 K predicted using lattice dynamics calculations and the Stillinger-Weber (SW) interatomic potential. Each red dot represents an individual phonon mode. The near-right plot is phonon dispersion data for all phonons in the first Brillouin zone, the slope this data corresponds to the phonon group velocity. The frequency-dependence of phonon-phonon relaxation times is potted in the far-left plot. The phonon-phonon relaxation time is defined as the average time between successive phonon-phonon scattering events.

For bulk systems, these phonon properties can be used in the steady-state solution to the Boltzmann transport equation, combined with Fourier law, to predict the thermal conductivity. For nanostructures, the Boltzmann transport equation can be used to model these structures (i) directly using an appropriate geometry and boundary conditions (we use the lattice Boltzmann method, see Exact BTE in figure) or (ii) indirectly by correcting the bulk phonon-phonon relaxation times to account for appropriate phonon-boundary scattering corresponding to the nanostructure of interest (e.g., by using the Matthiessen rule, see BTE + Matthiessen rule in figure). Using both of these methods we plot the length-dependence of thermal conductivity for thin silicon films in the figure to the right. Also plotted is experimental data from Hopkins et at. Nano Letters 11 107 (2011). The agreement of our cross-plane thermal conductivity data with the one available experimental measurement is good, although more data is needed to fully assess its performance.

For more details on the results presented here, please see:
D. P. Sellan, J. E. Turney, A. J. H. McGaughey, and C. H. Amon, "Cross-plane phonon transport in thin films." Journal of Applied Physics 108 (2010) 113524.