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

Abstract

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 $$10\, \upmu \hbox {m}$$ , 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 $$\hbox {Al}_2\hbox {O}_3$$ and soda-lime and found agreement both with literature values and with separate measurements obtained with a conventional time-domain thermoreflectance setup.