Anderson localization of thermal phonons : anomalous heat conduction in disordered superlattices

Abstract

In semiconductor devices, thermal energy is carried by phonons, the quantized excitation of atomic vibrations. These phonons scatter with impurities, electrons, grain boundaries, and other phonons. At a sufficiently large scale, phonon dynamics can be approximated as a Brownian random walk, leading to ordinary diffusion described by the heat equation. However, such approximations fail at the scale of the phonon mean free path. In this regime, a proper wave description encoding phonon scattering is required. For sufficiently short thermal systems, the thermal conductivity becomes extrinsic and exhibits linear scaling with system size. This scale is known as the ballistic transport regime. As the system size grows beyond this scale, the thermal conductivity asymptotes into the intrinsic, ordinary diffusive regime. However, there are special circumstances where this transition does not occur. In this Thesis, we demonstrate the anomalous scaling of thermal conductivity. The source of this anomaly is the Anderson localization of thermal phonons. Anderson localization is the spatial trapping of waves due to extreme levels of elastic disorder. The hallmark of Anderson localization is an exponential decay law of conductance with increasing system size. Since thermal transport is a broadband process, this exponential suppression leads to a thermal conductivity maximum as a function of system size. Our numerical study of GaAs/AlAs superlattices with ErAs nanoparticles exhibits this thermal conductivity maximum, yielding quantitative agreement to experiments. We then generalize our elastic model to allow for the incorporation of finite-temperature effects. The inclusion of phonon-phonon scattering decoheres phonons, resulting in phonon delocalization. Counterintuitively, the additional inelastic scattering increases conductance for originally localized phonons. This localization to diffusive transition as a function of temperature is captured in our model at low temperatures (~20K).