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

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2 Theoretical Description of a CPW Resonator2.3.5 Superconducting ResonatorFinally, we will discuss the temperature dependencies of the resonance frequency and thequality factor of superconducting resonators.From (2.24) and (2.21) one can directly observe that superconductivity influences thephase velocity v ph through the kinetic inductance defined by (2.22). The kinetic inductancedepends on the temperature dependent London penetration depth λ L (see (2.23)). In Figure2.12 the temperature dependence of the resonance frequency is shown. One can see thatwith constant length the resonant frequency decreases with increasing temperature.Figure 2.12: Dependence of the resonance frequency calculated with the kinetic inductancemodel for the Yale design on Silicon and Sapphire for a fixed lengthof 8.991 mm.The quality factor Q is also temperature dependent, according to (2.32) it consists of thetemperature dependent quantities β and α. In Figure 2.13 the quality factor dependence ontemperature is shown for Silicon and Sapphire.For Silicon one obtains quality factors of around 260. In our measurements the qualityfactor is one order of magnitude or more larger. The reason for this mismatching qualitiescould be that at lower temperatures the loss tangent is much lower than 0.004 (see Table 2.2).A value of around 0.00007 gives better matching results.22
2.3 Microwave ResonatorsFigure 2.13: Dependence of the quality factor calculated with the kinetic inductance modelfor the Yale design on Silicon and Sapphire for a fixed length of 8.991 mm.23
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: 2.3 Microwave ResonatorsFigure 2.11
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 and 52: 5.2 Measurements - Design 15.2.2 R2
Page 53 and 54: 5.2 Measurements - Design 1Figure 5
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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