Delineation of Incoherent and Coherent Phonon Contributions to Thermal Transport in Semiconductor Superlattices

Thermal transport in semiconductor superlattices and other metamaterials with secondary periodicity can be significantly influenced by phonon coherence. In superlattices, which are composed of alternating layers of two or more materials, a minimum thermal conductivity is observed as the period thickness decreases to a few atomic layers. This phenomenon is attributed to a transition between significant phonon-interface scattering and the emergence of wave-like phonons that travel through interfaces unimpeded. This transition is explained by the presence of two distinct types of phonon modes: "incoherent" phonons, which follow the dispersion relations of the superlattice base materials, and "coherent" phonons, which follow the dispersion relation of the superlattice itself. Currently, a spectral analysis of the relative contributions of these two phonon types to the thermal conductivity of superlattices and modified superlattices, such as structures with aperiodically arranged interfaces, is lacking. The atomistic wave-packet method is a powerful tool for directly simulating both incoherent and coherent phonon transport, with a unique capability to specify both wavelength and spatial coherence length. However, previous wave-packet studies on superlattices and other materials have used arbitrary values for coherence length, lacking rigor in finite-temperature physics. In this work, we propose a new methodology using temperature-dependent coherence lengths for the first time in wave-packet simulations to compute phonon transmission spectra at finite temperatures. The results are then correlated with finite-temperature molecular dynamics simulations to estimate thermal conductivity, allowing us to directly delineate the frequency-dependent relative contributions of incoherent and coherent modes to thermal conductivity. Utilizing this technique, we rigorously analyze coherent and incoherent phonon transport in AlN/GaN superlattices at the mode level. The insights gained from our work open avenues for extreme manipulation of the thermal conductivity of semiconductor superlattices, which have critical applications in high-power devices and photonics, through specific control of different phonon modes.