Multiscale phonon thermal transport in nano-porous silicon

We performed a comprehensive multi-scale phonon-mediated thermal transport study of nano-porous silicon (np-Si) films with average porosities in the range of $φ$ = 30%–70%. This depth-resolved thermal characterization involves a combination of optical methods, including femtosecond laser-based time-domain thermo-reflectance (TDTR) with MHz modulation rates, opto-thermal micro-Raman spectroscopy, and continuum laser wave-based frequency domain thermo-reflectance (FDTR) with kHz modulation rates probing depths of studied samples over 0.5–1.2, 2–3.2, and 23–34 μm, respectively. We revealed a systematic decrease in thermal conductivity (⁠ $k$⁠) with the rise of $φ$⁠, i.e., with the lowering of the Si crystalline phase volumetric fraction. These data were used to validate our semi-classical phonon Monte Carlo and finite element mesh simulations of heat conduction, taking into account disordered geometry configurations with various $φ$ and pore size, as well as laser-induced temperature distributions, respectively. At high $φ$⁠, the decrease in $k$ is additionally influenced by the disordering of the crystal structure, as evidenced by the near-surface sensitive TDTR and Rutherford backscattering spectroscopy measurements. Importantly, the $k$ values measured by FDTR over larger depths inside np-Si were found to be anisotropic and lower than those detected by the near-surface sensitive TDTR and Raman thermal probes. This finding is supported by the cross-sectional scanning electron microscopy image indicating enhanced $φ$ distribution over these micrometer-scale probed depths. Our study opens an avenue for nano-to-micrometer scale thermal depth profiling of porous semiconducting media with inhomogeneous porosity distributions applicable for efficient thermoelectric and thermal management.