Measuring Thermal Conductivity with Magnitude-Dependent Frequency–Domain Thermoreflectance Using Modulated CW Lasers

We demonstrate a minimally invasive optical pump–probe technique for measuring thermal conductivity. Like time-domain thermoreflectance, the version of frequency–domain thermoreflectance demonstrated here relies on a non-zero thermo-optic coefficient in the sample, but uses moderate cost continuous wave lasers modulated at kHz or MHz frequencies rather than a more expensive ultrafast laser system. The longer timescales of these frequency ranges enable this technique to take measurements of films with thicknesses ranging from 100 nm to 10 m , complimentary to time-domain thermoreflectance. This method differentiates itself from other frequency–domain methods in that it is also capable of simultaneous independent measurements of both the in-plane and out-of-plane values of the thermal conductivity in anisotropic samples through measurements of relative reflective magnitude rather than of phase. We validated this alternate technique by measuring the thermal conductivity of Al_2O_3 and soda-lime and found agreement both with literature values and with separate measurements obtained with a conventional time-domain thermoreflectance setup.