Size effect of out-of-plane thermal conductivity of epitaxial YBa2Cu3O7−δ thin films at room temperature measured by photothermal radiometry

Abstract

The out-of-plane (c-axis) thermal conductivities of high-temperature superconducting thin films (YBa2Cu3O7-δ: YBCO) have been measured by photothermal radiometry (PTR) at room temperature. The YBCO samples are in c-axis-aligned epitaxially grown thin films with thicknesses of 250, 500, and 1000 nm. PTR is a noncontact measurement technique for the thermal conductivity and is based on the detection of infrared radiation emitted from a sample heated by a frequency-modulated laser beam. By changing the modulation frequency up to about 1 MHz, the thermal conductivity of thin film can be determined by a curve-fitting analysis of phase-lag data in the frequency domain. The uncertainty of measured thermal conductivity is estimated to be better than ±7%. The experimental results for thermal conductivity exhibit apparently positive film thickness dependence, and their absolute values are less than half of those for single crystal at the smallest thickness. The results indicate a size effect that cannot be explained by the very short phonon mean free path that the kinetic theory predicts. By employing a simple model taking into account phonon boundary scattering, the possible mean free path to interpret the present results is substantially larger than the prediction. The conclusion supports the validity of quite broad spectral distribution of phonons responsible for the thermal conductivity of YBCO.

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

“…The entire measurement system is arranged on two optical benches with different height in order to avoid the effect of a leak magnetic field from the cryostat on the lasers and optical components such as the Faraday isolators and the balanced detector. The principle and working equations for the experimental technique were essentially consistent with those of photothermal radiometry [19,24], for which we also discussed the uncertainty assessment of the measured thermal conductivity by using this technique. In order to gain sufficiently strong thermoreflectance signals, the YBCO sample surfaces were coated with 159 ± 9 nm sputtering films of platinum as a reflecting layer against the probing laser light.…”

“…In our previous paper [19], we showed that the out-of-plane thermal conductivity of epitaxially grown YBCO thin films exhibited thickness dependence even at room temperature. This result may have been due to the quite broad spectral distribution of phonons responsible for the thermal transport perpendicular to the CuO 2 planes.…”

“…The relative combined standard uncertainties of the thermal conductivity of all samples were estimated to be within ±9 % at 300 K, within ±12 % at 180 K, within ±16 % at 90 K and within ±20 % below 50 K. Figure 3 shows the experimental results for the out-of-plane thermal conductivity of c-axis-aligned epitaxially grown thin films λ c of YBCO with nominal thicknesses of 250 nm, 500 nm and 1000 nm together with the empirical correlations, which will be described later in this section. The films exhibited thickness dependence not only near room temperature [19] but in the entire temperature range from 10 K to 300 K. The absolute values of thermal conductivity in the normal state for thin films are less than half of those for bulk single-crystal values at the smallest thickness. In the superconducting state, on the other hand, the reduction ratio (size effect) reaches less than one-tenth at the maximum.…”

“…For these thermal conductivity results, we evaluated the uncertainties based on the Guide to the Expression of Uncertainty in Measurement (GUM) [26]. Since the working equations of thermal conductivity cannot be expressed explicitly in the measurement principle [19], the uncertainty associated with each measurement component was numerically calculated. This was accomplished by taking the following sources of uncertainty into account: the platinum reflecting layer component (thermal conductivity, thermal diffusivity, and thickness); YBCO sample layer component (specific heat and thickness); thermal conductivity of MgO; heating beam radius; measured phase lag; and temperature.…”

“…In particular, in the case of a high-temperature superconducting magnet, the thermal conductivity of the radial direction (c-axis in YBCO) of the coil structure is critically important and has been reported to be unexpectedly very low in comparison with the estimated values [8]. Table 1 lists previous experimental studies on the thermal conductivity of YBCO in the c-axis direction [9][10][11][12][13]19]. It should be noted here that we have excluded some other studies on thermal conductivity because they measured thermal conductivity in the ab-axis direction [14,15] or because they used ceramic samples produced by the solid-state sintering process [16].…”