Modeling optical absorption for thermoreflectance measurements
Optical pump-probe techniques based on thermoreflectance, such as time domain thermoreflectance and frequency domain thermoreflectance (FDTR), have been widely used to characterize the thermal conductivity of thin films and the thermal conductance across interfaces. These techniques typically use a transducer layer to absorb the pump light and improve the thermoreflectance signal. The transducer, however, complicates the interpretation of the measured signal because the approximation that all the energy from the pump beam is deposited at the transducer surface is not always accurate. In this paper, we consider the effect of laser absorption in the top layer of a multilayer sample, and derive an analytical solution for the thermoreflectance signal in the diffusion regime based on volumetric heating. We analyze the measurement sensitivity to the pump absorption depth for transducers with different thermal conductivities, and investigate the additional effect of probe laser penetration depth on the measured signal. We validate our model using FDTR measurements on 490 nm thick amorphous silicon films deposited on fused silica and silicon substrates.