Far-infrared spectra of imperfect YBaCuO films on Si substrates

We have measured the far-infrared (FIR) transmittance of low conductivity, imperfect YBCO films deposited on Si, at both 300 K and 20 K. Test reflectance measurements were also performed at room temperature. Our aim was both to study YBCO phonons by transmission measurements and to check if FIR spectra of imperfect YBCO films can be described in the framework of the BCS theory. In order to describe our measurements, we provide exact expressions for both transmittance and reflectance, averaged with respect to the interference fringes of the substrate. By modelling the complex dielectric constant of the film, we then study the YBCO phonons which are evident in the measured spectra. The comparison between spectra of normal and superconducting phases shows that the superconducting transition affects our spectra only at very low frequencies. By considering a two fluid model in which only a small fraction of electrons becomes superconducting and by assuming an energy gap of the order of 130 cm^-1, we find that our data can be explained in terms of the Mattis-Bardeen theory.