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

5 Measurements5.2.3 R27 on SiliconR27 is similar to R25 except for the length. Thus the calculated resonance frequency isincreased by 0.15 GHz in comparison to R25 to 6.156 GHz.name design W S length frequency capacitance substrate[µm] [µm] [mm] [GHz] value materialR27 design 1 10 20 9.555 6.156 overcoupled 24 fF SiliconTable 5.7: Description of the resonator R27 on Silicon.In Figure 5.10 the resonance peaks of R25 and R27 are shown, recorded at 4 K. Thepeaks are separated by 0.18 GHz, the quality factors at this temperature are almost equaland included in the graphs.Figure 5.10: Comparison of transmission S 21 of R25 and R27 on Silicon at 4 K.Figure 5.11 shows the change of resonance frequency and quality factor with increasingtemperature. By coming nearer to the transition temperature, the resonance frequencyand the quality factor decrease (see subsection 2.3.5). The step at 4.3 K, in the resonancefrequency vs. temperature graph can be explained the following way: all measurementsdescribed before were measured at 4 K. For the temperature resolved measurement the liquidHelium is pumped to 1.5 K. Measurements were recorded during warm-up. As soon asthe liquid helium is vaporized we saw the jump, due to a change in the dielectric constantbetween liquid and gaseous Helium. The jump of 15.312 MHz can be explained with adielectric constant of liquid Helium of 1.0047. In the RIE process we always etched intothe Silicon Oxide layer in the gap between the inner strip and the ground plane. This couldpossibly explain the deviation between the experimental value and the value documented inliterature (1.05 [8]) of the dielectric constant of liquid Helium. Theory predicts the measuredresult that the quality factor does not change.48