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

5 Measurements5.2 Measurements – Design 1This section presents the measurementson overcoupled resonators for design 1.Overcoupled resonators are expected tohave a smaller quality factor, because of alarger coupling to the environment. At firstSilicon was used as substrate material, lateron Sapphire. Therefore, a comparison betweenSilicon and Sapphire is given for theFigure 5.3: overcoupled capacitance of R25resonator R25. After this, R25 is compared to R27, a resonator with the same geometryexcept for the resonator length.5.2.1 R25 on Siliconname design W S length frequency capacitance substrate[µm] [µm] [mm] [GHz] value materialR25 design 1 10 20 9.8 6.003 overcoupled 24 fF SiliconTable 5.5: Description of the resonator R25 on Silicon.The capacitance and the resonance frequency in Table 5.5 are calculated for Silicon. Althoughthe structure was designed for Sapphire, it is also 50 Ω matched for Silicon (seeTable 3.1 on page 28). This matching is valid up to a gap size of 15 µm. Also the taperingis the same, since the taper structures could not be matched to 50 Ω at all and so just thegeometries of the connector and the taper were matched (see section 3.3).When cooling down below the superconducting transition temperature of Niobium, weobserved a very sharp peak in the transmission spectrum at 6.15 GHz (see Figure 5.4) witha quality factor of about 1100.Detailed measurements of reflection, harmonics and phase of the resonator are presentedin the following Figures. In Figure 5.5 one can see the transmission and reflection parametersnear the resonance peak. Surprisingly, the quality factor of reflection is about 10 timeslarger than in the case of transmission.The harmonics in Figure 5.6 are almost exact multiples of the fundamental resonance.The first harmonic mode at 12.3 GHz looks distorted. Perhaps other resonances (e.g. the”gold box mode” at 11.9 GHz) are interfering with this mode. The second harmonic at18.4 GHz is still sharp and has a quality factor of 50.42