  Traditional models of interfacial phonon scattering, including the acoustic
mismatch model (AMM) and diffuse mismatch model (DMM), take into account the
bulk properties of the material surrounding the interface, but not the atomic
structure and properties of the interface itself. Here, we derive a theoretical
formalism for the phonon scattering at a dislocation grid, or two
interpenetrating orthogonal arrays of dislocations, as this is the most stable
structure of both the symmetric twist boundary and semicoherent
heterointerface. With this approach, we are able to separately examine the
contribution to thermal resistance due to the step function change in acoustic
properties and due to interfacial dislocation strain fields, which induces
diffractive scattering. Both low-angle Si-Si twist boundaries and the Si-Ge
heterointerfaces are considered here and compared to previous experimental and
simulation results. This work indicates that scattering from misfit dislocation
strain fields doubles the thermal boundary resistance of Si-Ge heterointerfaces
compared to scattering due to acoustic mismatch alone. Scattering from grain
boundary dislocation strain fields is predicted to dominate the thermal
boundary resistance of Si-Si twist boundaries. This physical treatment can
guide the thermal design of devices by quantifying the relative importance of
interfacial strain fields, which can be engineered via fabrication and
processing methods, versus acoustic mismatch, which is fixed for a given
interface. Additionally, this approach captures experimental and simulation
trends such as the dependence of thermal boundary resistance on the grain
boundary angle and interfacial strain energy.
