Thermal boundary resistance predictions from molecular dynamics simulations and theoretical calculations

The accuracies of two theoretical expressions for thermal boundary resistance are assessed by comparing their predictions to independent predictions from molecular dynamics (MD) simulations. In one expression (R₄), the phonon distributions are assumed to follow the equilibrium, Bose-Einstein distribution, while in the other expression (R₍₄), the phonons are assumed to have nonequilibrium, but bulk-like distributions. The phonon properties are obtained using lattice dynamics-based methods, which assume that the phonon interface scattering is specular and elastic. We consider (i) a symmetrically strained Si/Ge interface, and (ii) a series of interfaces between Si and ``heavy-Si, '' which differs from Si only in mass. All of the interfaces are perfect, justifying the assumption of specular scattering. The MD-predicted Si/Ge thermal boundary resistance is temperature independent and equal to 3. 110^-9 m^2-K/W below a temperature of 500 K, indicating that the phonon scattering is elastic, as required for the validity of the theoretical calculations. At higher-temperatures, the MD-predicted Si/Ge thermal boundary resistance decreases with increasing temperature, a trend we attribute to inelastic scattering. For the Si/Ge interface and the Si/heavy-Si interfaces with mass ratios greater than two, R₄ is in good agreement with the corresponding MD-predicted values at temperatures where the interface scattering is elastic. When applied to a system containing no interface, R₄ is erroneously nonzero due to the assumption of equilibrium phonon distributions on either side of the interface. While R₍₄ is zero for a system containing no interface, it is 40%--60% less than the corresponding MD-predicted values for the Si/Ge interface and the Si/heavy-Si interfaces at temperatures where the interface scattering is elastic. This inaccuracy is attributed to the assumption of bulk-like phonon distributions on either side of the interface.