Intriguing transport phenomena of phonons and photons in nanoporous structures have revolutionized the development of materials in recent decades. The particle- and wave-like transport of phonons have respectively demonstrated significant thermal conductivity reduction in thermoelectrics and backscattering-immune waveguiding in topological insulators; the photon transport in nanoporous composites have demonstrated enhanced solar reflectivity for radiative cooling. This doctoral research focuses on understanding phonon and photon transport in nanoporous structures that will guide optimal designs of thermoelectric energy harvesting systems, future phononic circuits, and hierarchical materials for optical and thermal management.

Phonon transport can be viewed in the particle-like picture when the phonon wavelength is much shorter than the structure’s critical dimension. A good example is heat conduction in solids at THz frequencies. Though significant thermal conductivity reduction due to phonon size effect has been observed in nanoporous structures, the presence of various geometric parameters complicates the understanding of governing mechanisms. To investigate phonon-boundary scattering phenomena in Si nanoporous structures with varying pore shapes, alignments, and size distributions, we develop a ray tracing technique that is experimentally validated by bulk Si and Si nanomeshes. The results show that, with identical porosities, asymmetric pore shapes offer a lower thermal conductivity than symmetric ones due to smaller neck sizes that localize heat fluxes; asymmetric pores with fully diffuse surface boundaries show possibilities of realizing a thermal rectification ratio up to 13 by optimally controlling phonon injection angles. Symmetric pore shapes arranged in a hexagonal-lattice provide a lower thermal conductivity than in a squared-lattice due to the limited phonon line of sight; alternating pore size distributions yield a lower thermal conductivity than uniform ones at the same porosity. When phonon wavelength is much longer than the structure’s critical dimension, phonon transport is wave-like. One frequently asked question in condensed matter physics was if the Quantum Spin Hall Effect observed in electrons and photons could be analogously realized for phonons despite their lacking spin-like degrees of freedom and transverse polarizations. Here we numerically demonstrate a six-petal holey Si-based topological insulator, where simple geometric control enables topological edge states for both in- and out-of-plane phonon polarization up to GHz ranges with a submicron periodicity. The unique six-petal geometry induces zone-folding to form a double Dirac cone and breaking discrete translational symmetry leads to the topological phase transition. Our design supports robust backscattering-immune elastic wave transmission up to 90% despite the existence of geometric uncertainties. Though the design has not yet been demonstrated by experiments due to nanofabrication and measurement challenges, the numerical results clearly show the signature of topologically-protected edge transport of phonons, evident by the band inversion and backscattering-immunity. The improved understanding of particle- and like-like phonon transport in Si nanoporous structures regarding phonon-boundary scattering phenomena and phononic topological insulators will pave the way for developing future thermoelectric energy harvesting systems and phononic circuits.

As another bosonic particle, photon’s transport can also be modified by nanoporous structures. Here we focus on understanding the enhanced solar reflection realized by dielectric nanoporous composites, which is important for designing selective emitters that are attractive for radiative thermal management. We employ Mie theory and finite-difference time-domain simulations to study the solar reflectivity of SiO2 and TiO2 microspheres in a polydimethylsiloxane (PDMS) matrix. Our analysis shows that hollow microspheres with a thinner shell are more effective in scattering the light, compared solid microspheres, and lead to a higher solar reflectivity. The high scattering efficiency, owing to the large interface density, in hollow microspheres allows low-refractive-index materials to have high solar reflectivity. The uniform- and varying-diameter design of 0.75 µm and 0.5-1 µm provide the highest solar reflectivity of 0.81 and 0.84, respectively. The effect of varying diameter is characterized by strong backscattering in the electric field. The enhanced solar reflectivity and effectiveness of hollow glass microsphere composites for radiative cooling have been experimentally demonstrated in our recent work. The findings in the current work will guide the optimal designs of microsphere composites and hierarchical materials for optical and thermal management systems.