Application of Diffuse Mismatch Theory to the Prediction of Thermal Boundary Resistance in Thin-Film High-T_c Superconductors

Thermal boundary resistance (R_b) plays an important role in the design and performance of thin-film high-temperature superconducting devices, such as infrared detectors and optical switches, which rely upon the temperature rise of the film as the basis for their operation. Although there is general agreement on the magnitude of R_b from experimental data, there is at present no generally accepted theory capable of predicting R_b for these films, particularly at the intermediate cryogenic temperatures where they are likely to be used. Here, the Diffuse Mismatch Model (DMM), which considers that all phonons reaching the interface between the film and substrate scatter diffusely, is applied to the calculation of R_b. The results indicate that when employing the Debye model for the phonon density of states, the DMM yields results slightly more in agreement with data than the Acoustic Mismatch Model (AMM). Considering the measured phonon density of states, however, greatly increases R_b over that calculated assuming the Debye model, thus bringing the DMM results in relatively good agreement with the experimental data.