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Metallic coplanar resonators optimized for low-temperature measurements

“…1 The fundamental frequency of the resonators slightly shifts up by increasing W+2S (from ~2.60 GHz for W=20 µm and S=8 µm to ~3.15 GHz for W=60 µm and S=24 µm). This is due to the decrease of effective permittivity (Ԑ eff ) by increasing W+2S [3,4,22,25]. The fundamental for both W=80 and 100 µm are ~3 GHz.…”

“…The fundamental for both W=80 and 100 µm are ~3 GHz. The thickness in these cases is about 100 nm lower (compared to those with W=20 to 60 µm) which causes Ԑ eff to increase and thus the fundamental mode is below ~3.15 GHz (of W=60 µm) [3,4]. The temperature dependence of the resonance frequency is plotted in figure 1(e); the rightward shift of the resonance frequency upon cooling has several reasons: (i) thermal contraction, (ii) Ԑ eff of CPW decreases in absolute value as the conductivity of the metallic conductor increases [3] and (iii) the relative permittivity of sapphire substrate decreases with lowering the temperature [26].…”

“…In the functionality of a typical planar resonator, the most decisive factors are coupling gaps [16,17], center conductor width [18,19], film quality and edge sharpness [20,21], ground plane size and packaging effects [22], effective permittivity (ε eff ) [4] and meander line dispersion [23,24]. Coplanar resonators can be designed based on these theoretical considerations, but resonator optimization for new applications often involves additional testing and tuning of design parameters of the actually fabricated devices, such as presented in this work.…”

“…Coplanar waveguides (CPWs) from superconducting [1,2] and metallic (non-superconducting) materials [3][4][5] are widely used in microwave transmission lines. Since conductor strip and ground planes are on the same side of the substrate, they can be easily adapted to active/passive components.…”