Broadband phonon mean free path contributions to thermal conductivity measured using frequency domain thermoreflectance

Non-metallic crystalline materials conduct heat by the transport of quantized atomic lattice vibrations called phonons. Thermal conductivity depends on how far phonons travel between scattering events-their mean free paths. Due to the breadth of the phonon mean free path spectrum, nanostructuring materials can reduce thermal conductivity from bulk by scattering long mean free path phonons, whereas short mean free path phonons are unaffected. Here we use a breakdown in diffusive phonon transport generated by high-frequency surface temperature modulation to identify the mean free path-dependent contributions of phonons to thermal conductivity in crystalline and amorphous silicon. Our measurements probe a broad range of mean free paths in crystalline silicon spanning 0.3-8.0 mu m at a temperature of 311 K and show that 40 +/- 5% of its thermal conductivity comes from phonons with mean free path >1 mu m. In a 500nm thick amorphous silicon film, despite atomic disorder, we identify propagating phonon-like modes that contribute >35 +/- 7% to thermal conductivity at a temperature of 306 K.