In this dissertation, the phonon size effect in the experimental and theoretical studies of random and periodic porous media are reported. First, a literature review on the past modeling studies on porous media are presented that covers both the earlier works that use the traditional effective medium approach and the few existing recent works that consider the low-dimensional effects. Next, the experimental characterization of the cross-plane thermal conductivity of randomly nano-porous bismuth thin films is presented. Fabricated in search for more efficient thermoelectric materials, the nanoporous bismuth films use nano-scale pores to impede phonon transport more than electron transport. Their cross-plane thermal conductivity characterization using the differential 3ω technique revealed an order-of-magnitude reduction in the thermal conductivity values of the porous bismuth over those of non-porous bismuth films and a potential for the independent tuning of their electrical conductivity and thermal conductivity, but the defect-laden structure was difficult to model. Therefore, a new study was undertaken that focused on simpler periodic micro-porous single-crystal silicon membranes. A batch of such membranes were fabricated from both a plain silicon wafer and a silicon-on-insulator wafer using MEMS techniques, including bulk chemical etching and deep-reactive ion etching. The resulting samples contained periodically arranged pores of controlled dimension and orientation, but the pore dimension and orientation was varied from sample to sample to experimentally isolate the phonon size effect due to pore boundary scattering. The in-plane thermal conductivity of the microporous silicon membranes is characterized by a modified version of Völklein's DC method. The resulting thermal conductivity reduction in porous films compared to the solid silicon film strongly suggest phonon size effect. The three-dimensional phonon transport in porous silicon membranes were modeled using the Monte Carlo method to yield an equivalent solution to the three-dimensional Boltzmann transport equation. Since the focus of the modeling is the effect of pore boundary scattering on phonon transport, a simplified view of gray-body medium is studied. The thermal conductivity result predicts a thermal conductivity reduction in porous silicon films compared to solid silicon films by an amount beyond that predicted from porosity and comparable to that observed in experiments.
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