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

7 Conclusion and OutlookWe measured resonators with quality factor up to 1.5·10 4 at 1.3 K. The resonator R21,with the highest quality, in Yale design on Silicon, was also measured down to 17 mK wherenot further increase in the quality could be observed. For comparison further resonatorswere fabricated and tested: A resonator with the same geometry, but on a Sapphire substrateshowed a quality factor in the same range as for Silicon. Strangely, the resonance frequencywas shifted in the other direction than predicted by theory. Design 1 was tested with threeresonators. Two resonators with the same substrate material (Silicon) but different lengthshowed a shift in resonance frequency like theoretically expected and had the same qualityfactor. A comparison between the two substrate materials Silicon and Sapphire showed aquality factor for Silicon one order of magnitude larger than the quality factor of Sapphire.Theoretically, these quality factors should be equal. Finally, a resonator in design 2 with verylarge coupling capacitances was measured in order to see how these influence the resonancefrequency and quality factor. Both showed a drastic decrease. The decrease in the resonancefrequency was also predicted by theory, while the quality factor should be larger by twoorders of magnitude. All resonances were analyzed for higher modes and investigatingthe frequency dependance of the phase. The resonators showed a temperature dependenceof resonance frequency and quality factor predicted by theory. Also the power distortiondescribed by Frunzio [6] was verified for Silicon substrates.A number of simulations of resonators were made. At the Walther-Meißner-Institut Sonnetwas used, which is able to simulate a superconducting resonator with a frequency dependentinductance. The best resonator measured in this thesis was simulated at the Institute ofNanoelectronics.Since the measured resonators have quality factors sufficient for the needs of further experiment,the next steps should be an optimization of the coupling capacitors and the lengthof the resonator in order to tune the quality factor and the resonance frequency to the desiredvalues. Therefore, it will be useful to design a mask with a transmission line, where thecapacitances can be written by electron beam lithography, which will also be used for thedefinition of qubits in the cavity. This method is faster because the layout just has to betransferred from the computer to the E-beam machine and the time and costs for the productionof a mask will be avoided. Also, larger values for center strip and gap should befabricated in order to place a qubit with a larger loop area and therefore mutual inductance(which is responsible for the coupling of qubit to the resonator) inside the gap. In orderto have better calibrated measurements which would give a higher accuracy, measurementsshould be done in the probing station. Therefore, new probing tips are available with aresuitable for cryogenic experiments. Preliminary recent experiments on R41 covered by goldhave been done in the probing station, giving promising results. Of course the quality factorwas quite low because of damping in the gold layer.70