Studies of non-diffusive heat conduction through spatially periodic and time-harmonic thermal excitations

Abstract

Studies of non-diffusive heat conduction provide insight into the fundamentals of heat transport in condensed matter. The mean free paths (MFPs) of phonons that are most important for conducting heat are well represented by a material's thermal conductivity accumulation function. Determining thermal conductivity accumulation functions experimentally by studying conduction in non-diffusive regimes is a recent area of study called phonon MFP spectroscopy. In this thesis, we investigate nondiffusive transport both experimentally and theoretically to advance methods for determining thermal conductivity accumulation functions in materials. We explore both spatially periodic and time-harmonic thermal excitations as a means for probing the non-diffusive transport regime, where the Fourier heat diffusion law breaks down. Boltzmann transport equation calculations of one-dimensional (1D) spatially sinusoidal thermal excitations are performed for gray-medium and fully spectral cases. We compare our calculations to simplified transport models and demonstrate that a model based on integrating gray-medium solutions can reasonably model materials with a narrow range of dominant heat-carrying phonon MFPs. We also consider the inverse problem of determining thermal conductivity accumulation functions from experimental measurements of thermal-length-scale-dependent effective thermal conductivity. Based on experimental measurements of Si membranes of varying thickness, we reproduce the thermal conductivity accumulation function for bulk Si. To investigate materials with short phonon MFPs, we developed an experimental approach based on microfabricating 1D wire grid polarizers on the surface of a material under study. This work finds that the dominant thermal length scales in polycrystalline Bi 2Te3 are smaller than 100 nm. We also determine that even small amounts of direct sample optical excitation, which occurs when light transmits through the grating and directly excites electron-hole pairs in the substrate, can appreciably influence the measured results, suggesting that an alternate approach that prevents all direct optical excitation is preferable. To study thermal length scales smaller than 100 nm without the need for microfabrication, we develop a method for extracting high frequency response information from transient optical measurements. For a periodic heat flux input, the thermal penetration depth in a semi-infinite sample depends on the excitation frequency, with higher frequencies leading to shallower thermal penetration depths. Prior work using frequencies as high as 200 MHz observed apparent non-diffusive behavior. Our method allows for frequencies of at least 1 GHz, but we do not observe any deviation from the heat diffusion equation, suggesting that prior observations attributed to non-diffusive effects were likely the result of transport phenomena in the metal transducer.