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

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2 Theoretical Description of a CPW ResonatorLondon penetration ”normal layerdepth conductivity” thickness frequencyλ 0 σ n (T c = 9.2 K) t f47 ± 5 nm 1.4·10 9 S/m [5] 200 nm 6 GHzTable 2.3: Parameters used for the calculation the of the superconducting conductor losses.London penetration ”normal skin stoppingtemperature depth conductivity” depth distanceT λ L (T ) σ n (T ) δ n ∆4 K 47,86 nm 5·10 7 S/m 2.3 µm 1.4 nm50 mK 47 nm 1.2 S/m 14 µm 1.41 nmTable 2.4: Parameters derived from Table 2.3 used for the calculation of the superconductingconductor losses.conductor loss α c attenuation αdesign Sapphire Silicon Sapphire SiliconYale 0.032 0.034 0.032 0.62design 1 0.017 0.018 0.017 0.61design 2 0.017 0.012 0.011 0.60Table 2.5: Attenuation of resonators α = α c + α d , with α d from Table 2.2.16
2.2 Including Superconductivity in the CPW2.2.3 Surface ImpedanceFrom the results of the previous sections we get the formula for the surface impedance ofa superconductor by a straightforward calculation. Using the surface impedance of a goodconductor,√ωµ0Z S ≈ (1 + i)2σand inserting σ = σ n − iσ s , a binomial expansion givesZ S =2δ s σ s(λLδ n) 3+ iωµ 0 λ L( ) 3 λL= 2R sδ n} {{ }+iωL S . (2.26)R S fR s denotes the surface resistance of the normal conducting electrons which is reduced by(λ L /δ n ) to the power of three in the superconducting case.17
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: 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 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
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6.2 Simulations Done at the Institu
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7 Conclusion and OutlookThree centr
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A Specimen OverviewDesigns for Rose
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B Masks73
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B.2 Mask for Probing StationB.2 Mas
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Bibliography[1] INFORMATIK: Quanten
Page 83 and 84:
List of Figures2.1 Different realiz
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List of Figures6.6 Forward and back
Page 87 and 88:
List of Tables2.1 Values where (2.1
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DanksagungVor allem möchte ich mic
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