  In this article, we report the influence of the interfacial roughness on the
thermal boundary conductance between two crystals, using molecular dynamics. We
show evidence of a transition between two regimes, depending on the interfacial
roughness: when the roughness is small, the boundary conductance is constant
taking values close to the conductance of the corresponding planar interface.
When the roughness is larger, the conductance becomes larger than the planar
interface conductance, and the relative increase is found to be close to the
increase of the interfacial area. The cross-plane conductivity of a
superlattice with rough interfaces is found to increase in a comparable amount,
suggesting that heat transport in superlattices is mainly controlled by the
boundary conductance. These observations are interpreted using the wave
characteristics of the energy carriers. We characterize also the effect of the
angle of the asperities, and find that the boundary conductance displayed by
interfaces having steep slopes may become important if the lateral period
characterizing the interfacial profile is large enough. Finally, we consider
the effect of the shape of the interfaces, and show that the sinusoidal
interface displays the highest conductance, because of its large true
interfacial area. All these considerations are relevant to the optimization of
nanoscale interfacial energy transport.
