Design, Fabrication and Characterization of a Microwave Resonator ...

2 Theoretical Description of a CPW ResonatorLondon penetration ”normal layerdepth conductivity” thickness frequencyλ 0 σ n (T c = 9.2 K) t f47 ± 5 nm 1.4·10 9 S/m [5] 200 nm 6 GHzTable 2.3: Parameters used for the calculation the of the superconducting conductor losses.London penetration ”normal skin stoppingtemperature depth conductivity” depth distanceT λ L (T ) σ n (T ) δ n ∆4 K 47,86 nm 5·10 7 S/m 2.3 µm 1.4 nm50 mK 47 nm 1.2 S/m 14 µm 1.41 nmTable 2.4: Parameters derived from Table 2.3 used for the calculation of the superconductingconductor losses.conductor loss α c attenuation αdesign Sapphire Silicon Sapphire SiliconYale 0.032 0.034 0.032 0.62design 1 0.017 0.018 0.017 0.61design 2 0.017 0.012 0.011 0.60Table 2.5: Attenuation of resonators α = α c + α d , with α d from Table 2.2.16