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

List of Figures2.1 Different realizations of CPW: (a) the conventional CPW, (b) the conductorbacked CPW. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42.2 Structure of a CPW, a conducting strip and two ground planes are placed ona substrate. The CPW is shielded on top and bottom by conducting layer. . 42.3 Configuration of the air capacitance of a CPW. . . . . . . . . . . . . . . . . 52.4 Configuration of the dielectric capacitance of a CPW. . . . . . . . . . . . . 62.5 Configuration of the dielectric capacitance of a CBCPW. . . . . . . . . . . 72.6 Schematic of a CPW on a double-layer dielectric substrate. . . . . . . . . . 82.7 Frequency dependent effective dielectric constant ε e f f for all designs realizedin this thesis. The cut-off frequencies are indicated by vertical lines foreach substrate material. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.8 Comparison of normal and superconducting (@ 4 K) CPW impedance forSilicon and Sapphire with a fixed gap width W of 5 µm. . . . . . . . . . . 142.9 (a) parallel and (b) series lumped element resonant circuits . . . . . . . . . 182.10 Z in for a parallel resonant circuit . . . . . . . . . . . . . . . . . . . . . . . 182.11 Ilustration of CPW resonators (a) λ/2 resonator (b) λ/4 resonator. . . . . . 212.12 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. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222.13 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. 232.14 A two-port device illustrating incident, reflected and transmitted waves. . . 243.1 Coupling capacitors used in the paper of Frunzio el al [6]. . . . . . . . . . . 294.1 Overview of the Niobium CPW fabrication process. . . . . . . . . . . . . . 314.2 Connecting with silver glue (a) on connector (b) grounding on edges. . . . . 344.3 Measurement setup with the cryostat. . . . . . . . . . . . . . . . . . . . . 354.4 Picture of the measurement setup with PC (with LabView) on the left, heliumcan on the right and RT measurement devices in between. . . . . . . . 365.1 Transmission S 21 of R20 and R22 at 4 K in the hybrid box. Since therecorded data from R22 was uncalibrated a level of 20 dB is added to thedata. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405.2 Coupling Capacitance of R20 (same as Figure 3.1 on page 29) . . . . . . . 405.3 overcoupled capacitance of R25 . . . . . . . . . . . . . . . . . . . . . . . 4279