Role of Phonon Coherence in 1-D Superlattices Studied Using the Spectral Boltzmann Transport Equation with Ab-Initio Inputs

The effect of phonon coherence on the thermal conductivity of 1-D superlattices has been a topic of debate. Recent measurements on superlattices show a non-monotonic trend of thermal conductivity with respect to period. The Simkin-Mahan model suggests that this behavior is explained by coherent phonon propagation and the folded phonon band-structure of superlattices. However, the model assumes that all phonons have a constant mean free path, an assumption that prior works have shown to be poor. Here, we use numerical solutions of the spectral Boltzmann Transport Equation (BTE) with ab-initio inputs to calculate the thermal conductivity of superlattices assuming a variety of transmission profiles at each interface. We find that the non-monotonic behavior of thermal conductivity versus period cannot be explained with static transmission coefficients, supporting the role of coherence and wave interference. Our work provides further insights into how phonon coherence can alter thermal transport in heterogeneous solids.