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

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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
5.2 Measurements – Design 1Figure 5.11: (a) Transmission S 21 of R27 on Silicon at different temperatures, (b) dependenceof resonance frequency on temperature.49
Page 4 and 5: Contents5.2.3 R27 on Silicon . . .
Page 6 and 7: 1 Motivation and Outlinethe antinod
Page 8 and 9: 2 Theoretical Description of a CPW
Page 14: 2 Theoretical Description of a CPW
Page 19 and 20: 2.2 Including Superconductivity in
Page 21 and 22: 2.2 Including Superconductivity in
Page 23 and 24: 2.3 Microwave Resonators2.3.2 Quali
Page 25 and 26: 2.3 Microwave ResonatorsFigure 2.11
Page 27 and 28: 2.3 Microwave ResonatorsFigure 2.13
Page 29 and 30: 2.4 The Scattering MatrixThe first
Page 31 and 32: 3 Designs Procedure for the Resonat
Page 33 and 34: 3.3 ConnectorsFigure 3.1: Coupling
Page 35 and 36: 4 Fabrication and Measurement Setup
Page 37 and 38: 4.2 Measurement SetupDevelop Resist
Page 39 and 40: 4.2 Measurement SetupFigure 4.3: Me
Page 41 and 42: 4.3 Calibration4.3 CalibrationIn or
Page 43 and 44: 5 MeasurementsThe first part of thi
Page 45 and 46: 5.1 First Experimentsname design W
Page 47 and 48: 5.2 Measurements - Design 1Figure 5
Page 49 and 50: 5.2 Measurements - Design 1The adva
Page 51: 5.2 Measurements - Design 15.2.2 R2
Page 55 and 56: 5.3 Measurements - Yale DesignFigur
Page 57 and 58: 5.3 Measurements - Yale DesignFigur
Page 59 and 60: 5.4 Measurement - Design 2: R36 on
Page 61 and 62: 5.5 Discussion of the Experimental
Page 63 and 64: 5.5 Discussion of the Experimental
Page 65 and 66: 6 SimulationsThis chapter gives a b
Page 67 and 68: 6.1 Simulations in SonnetFigure 6.4
Page 69 and 70: 6.1 Simulations in SonnetFigure 6.5
Page 71 and 72: 6.2 Simulations Done at the Institu
Page 73 and 74: 7 Conclusion and OutlookThree centr
Page 75 and 76: A Specimen OverviewDesigns for Rose
Page 77 and 78: B Masks73
Page 79 and 80: B.2 Mask for Probing StationB.2 Mas
Page 81 and 82: Bibliography[1] INFORMATIK: Quanten
Page 83 and 84: List of Figures2.1 Different realiz
Page 85 and 86: List of Figures6.6 Forward and back
Page 87 and 88: List of Tables2.1 Values where (2.1
Page 89: DanksagungVor allem möchte ich mic

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