Accurate measurements of cross-plane thermal conductivity of thin films by dual-frequency time-domain thermoreflectance (TDTR)

Accurate measurements of the cross-plane thermal conductivity Λ_cross of a high-thermal-conductivity thin film on a low-thermal-conductivity (Λ_s) substrate (e.g., Λ_cross/Λ_s > 20) are challenging, due to the low thermal resistance of the thin film compared with that of the substrate. In principle, Λ_cross could be measured by time-domain thermoreflectance (TDTR), using a high modulation frequency f_h and a large laser spot size. However, with one TDTR measurement at f_h, the uncertainty of the TDTR measurement is usually high due to low sensitivity of TDTR signals to Λ_cross and high sensitivity to the thickness h_Al of Al transducer deposited on the sample for TDTR measurements. We observe that in most TDTR measurements, the sensitivity to h_Al only depends weakly on the modulation frequency f. Thus, we performed an additional TDTR measurement at a low modulation frequency f₀, such that the sensitivity to h_Al is comparable but the sensitivity to Λ_cross is near zero. We then analyze the ratio of the TDTR signals at f_h to that at f₀, and thus significantly improve the accuracy of our Λ_cross measurements. As a demonstration of the dual-frequency approach, we measured the cross-plane thermal conductivity of a 400-nm-thick nickel-iron alloy film and a 3-μm-thick Cu film, both with an accuracy of ∼10%. The dual-frequency TDTR approach is useful for future studies of thin films.