Thermal conductivity measurements of non-metals via combined time- and frequency-domain thermoreflectance without a metal film transducer.

The thermoreflectance-based techniques time- and frequency-domain thermoreflectance (TDTR and FDTR, respectively) have emerged as robust platforms to measure the thermophysical properties of a wide array of systems on varying length scales. Routine in the implementation of these techniques is the application of a thin metal film on the surface of the sample of interest to serve as an opto-thermal transducer ensuring the measured modulated reflectivity is dominated by the change in thermoreflectance of the sample. Here, we outline a method to directly measure the thermal conductivities of bulk materials without using a metal transducer layer using a standard TDTR/FDTR experiment. A major key in this approach is the use of a thermal model with z-dependent heat source when the optical penetration depth is comparable to the beam sizes and measuring the FDTR response at a long delay time to minimize non-thermoreflectivity contributions to the modulated reflectance signals (such as free carrier excitations). Using this approach, we demonstrate the ability to measure the thermal conductivity on three semiconductors, intrinsic Si (100), GaAs (100), and InSb (100), the results of which are validated with FDTR measurements on the same wafers with aluminum transducers. We outline the major sources of uncertainty in this approach, including frequency dependent heating and precise knowledge of the pump and probe spot sizes. As a result, we discuss appropriate pump-frequency ranges in which to implement this TDTR/FDTR approach and present a procedure to measure the effective spot sizes by fitting the FDTR data of an 80 nm Al/SiO2 sample at a time delay in which the spot size sensitivity dominates an FDTR measurement over the substrate thermal properties. Our method provides a more convenient way to directly measure the thermal conductivities of semiconductors.