Ballistic heat transport and associated frequency dependence of thermal conductivity in semiconductor alloys

Pump-probe time-domain thermoreflectance is commonly used for thermal characterisation of thin films. Lock-in detection at the pump modulation frequency provides in-phase and out-of-phase components of the temperature oscillations. The thermal conductivity is then obtained by fitting this signal to a diffuse heat spreading model. In 2007, Koh and Cahill reported a significant reduction of thermal conductivity with modulation frequency in semiconductor alloys. They attributed this effect to the assumption that phonons with mean free path longer than the thermal penetration length do not contribute to the measured conductivity. The effect has been successfully reproduced but remained poorly understood. We propose a model that incorporates ballistic transport as internal heat source for the diffusive channel. The results show frequency dependent behaviour similar to the experimental data, even for a given mean free path (MFP). Moreover, the ballistic single pulse response shows accelerated decays compared to the the diffuse one but yet the extracted apparent conductivity is reduced at high modulation frequencies. This strongly suggests that the reduction of apparent conductivity can be mostly attributed to pulse accumulation effects and the fitting procedure.