Reconstruction of the phonon mean free path spectrum in silicon thin film via transducer-free quasi-ballistic measurements

Abstract

Understanding the phonon mean free path (MFP) spectrum is essential for predicting and engineering heat transport in nanostructured materials, where classical Fourier’s law breaks down. This study reconstructs the MFP spectrum of a 210-nm-thick single-crystalline silicon film using a suspended and transducer-free thermal bridge platform. Quasi-ballistic transport was induced by introducing nanoslit structures with varying widths, and temperature-dependent thermal resistance was measured from 40 to 300 K. The ballistic contribution was extracted by subtracting the diffusive component, and numerical modeling based on the phonon Boltzmann transport equation confirmed the observed trends. The extracted MFP spectrum at room temperature aligns well with previously reported thickness-dependent data, validating the approach. Furthermore, a temperature- dependent contour map of the cumulative MFP spectrum is presented, offering practical design guidance for geometry-driven thermal conductivity control across a wide temperature range.