Measurement of Out-of-Plane Thermal Conductivity of Epitaxial \(\hbox {YBa}_{2}\hbox {Cu}_{3}\hbox {O}_{7-{\delta }}\) Thin Films in the Temperature Range from 10 K to 300 K by Photothermal Reflectance

We measured the out-of-plane (c-axis) thermal conductivity of epitaxially grown \(\hbox {YBa}_{2}\hbox {Cu}_{3}\hbox {O}_{7-{\delta }}\) (YBCO) thin films (250 nm, 500 nm and 1000 nm) in the temperature range from 10 K to 300 K using the photothermal reflectance technique. The technique enables us to determine the thermal conductivity perpendicular to a thin film on a substrate by curve fitting analysis of the phase lag between the thermoreflectance signal and modulated heating laser beam in the frequency range from \(10^{2}\,\hbox {Hz}\) to \(10^{6}\,\hbox {Hz}\). The uncertainties of measured thermal conductivity of all samples were estimated to be within \({\pm }9\,\%\) at 300 K, \({\pm }12\,\%\) at 180 K, \({\pm }16\,\%\) at 90 K and \({\pm }20\,\%\) below 50 K. The experimental results show that the thermal conductivity is dependent on the thickness of the thin films across the entire temperature range. We also observed that the thermal conductivity of the present YBCO thin films showed \(T^{1.4}\) to \(T^{1.6}\) glass-like dependence below 50 K, even though the films are crystalline solids. In order to explain the reason for this temperature dependence, we attempted to analyze our results using phonon relaxation times for possible phonon scattering models, including stacking faults, grain boundary and tunneling states scattering models.