#### Date of Award

Winter 1-2016

#### Embargo Period

4-14-2017

#### Degree Type

Dissertation

#### Degree Name

Doctor of Philosophy (PhD)

#### Department

Mechanical Engineering

#### Advisor(s)

Jon Malen

#### Abstract

Nondiffusive thermal transport occurs when length or time scales of a system are on the order of the mean free paths (MFPs) or lifetimes of the energy carriers. As a result, a local equilibrium temperature cannot be defined and the thermal transport properties of the system can no longer be taken as the bulk values. When system boundaries are decreased below energy carrier MFPs, nondiffusive transport can be described with a reduced, effective thermal conductivity. Heat dissipation in light emitting diodes and transistors is adversely impacted by reductions in thermal conductivity, while thermoelectric energy conversion devices benefit. In my PhD, I studied the physics governing nondiffusive thermal transport. In this dissertation I describe my contributions in nondiffusive thermal transport to the scientific community. First, I describe the development of broadband frequency domain thermoreflectance (BBFDTR), an experimental technique used to observe nondiffusive thermal transport in materials by creating length scales comparable to energy carrier MFPs. I use BB-FDTR to induce nondiffusive thermal transport in Si-based materials at device operating temperatures. I relate my measurements to the thermal conductivity accumulation function, a fundamental physical quantity that describes cumulative contributions to thermal conductivity from energy carriers with different MFPs. Using a first order interpretation of my data I show that 40±5% of the thermal conductivity of crystalline silicon at a temperature of 311 K comes from phonons with MFP > 1 μm. Additional BB-FDTR measurements on a 500 nm thick amorphous silicon film indicate propagating phonon-like modes that contribute more than 35±7% to thermal conductivity at a temperature of 306 K, despite atomic disorder. I also describe the development of multiple models that are used to refine the interpretation of BB-FDTR measurements and better understand nondiffusive thermal transport measurements. First, I the Boltzmann transport equation (BTE) analytically to explain how and why measurements of thermal conductivity change as a function of experimental length scales in BB-FDTR. My solution incorporates two experimentally defined length scales: thermal penetration depth and heating laser spot radius. Comparison of the BTE result with that from conventional heat diffusion theory enables a mapping of MFP-specific contributions to the measured thermal conductivity based on the experimental length scales. The result is used to re-interpret nondiffusive thermal conductivity measurements of silicon with first principles-based calculations of its thermal conductivity accumulation function. Next, I develop a solution to the two-temperature diffusion equation in axisymmetric cylindrical coordinates to model heat transport in thermoreflectance experiments. The solution builds upon prior solutions that account for two-channel diffusion in each layer of an N-layered geometry, but adds the ability to deposit heat at any location within each layer. I use this solution to account for non-surface heating in the transducer layer of thermoreflectance experiments that challenge the timescales of electronphonon coupling. I use the model to refit BB-FDTR measurements of silicon and conclude that spectrally dependent phonon transmission at the transducer/silicon interface affects the shape of the measured accumulation function. Finally, I extend my solution to the BTE to a practical application: resistive-switching memory (RRAM). I model thermal transport in RRAM in the set state where the conductive filament (CF) is approximated by an infinitely long cylinder embedded in crystalline rutile TiO2, a prototypical RRAM material. I determine the phonon MFP spectrum in TiO2 and find that MFPs are similar to the CF radius, indicating thermal transport is nondiffusive. I develop an analytical solution to the BTE to model the nondiffusive thermal transport in the TiO2 and find that the surface temperature rise of the CF predicted by the BTE is larger than that predicted by the heat diffusion equation (e.g., 5× larger for a 1 nm CF radius in a device at a temperature of 300 K). To model thermal transport in RRAM with the heat diffusion equation, I propose a suppressed, effective TiO2 thermal conductivity to more accurately predict the CF temperature.

#### Recommended Citation

Regner, Keith T., "On Nondiffusive Thermal Transport and Phonon Mean-Free-Path-Dependent Contributions to Thermal Conductivity" (2016). *Dissertations*. 615.

http://repository.cmu.edu/dissertations/615