Microwave properties of dielectric single crystals, ceramics and thin films

The nonlinear effects in hts films are strongly temperature dependent, in particular close to Tc. Therefore, operation temperature of 50 to 65 K are more favourable than 77 K. Temperatures in this range can be attained by low-power closed-cycle cryocoolers. 

Apart from ybco, thin films with reasonable microwave properties have been prepared from the thallium-based compounds Tl2Ba2CaCu208 (Tc 105 K) and Tl2Ba2Ca2Cu30io (Tc 115 K) [10], hts films with reasonable and qualified microwave properties nowadays can be grown on wafers up to more than 4 in diameter, the most common size are 2 and 3 for microwave applications. A very important step was the preparation of double-sided coating, which have turned out to be essential for planar microwave devices, where the metal ground plane needs to be superconducting in order to achieve high quality factors. 

5 Microwave properties of dielectric single crystals, ceramics and thin films 

The most simple model of dielectrics in the microwave and near infrared regime is based on classical harmonic oscillators with damping [2]  

The quantity eoo represents the optical permittivity, which is determined by the electronic polarizability. The second term represents the ionic crystal lattice as a sum of N classical harmonic oscillators with eigenfrequencies ujj, damping constants Tj and oscillators strengths Sj. In order to fit Equation (5.7) to the observed far infrared spectra, these parameters are used 

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