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

6 SimulationsThis chapter gives a brief overview of the simulations done to predict the experimental results.For the simulations done at the Walther-Meißner-Institut the software Sonnet Lite wasused. Additional calculations for the resonator R21 were done at the Institute of Nanoelectronics.6.1 Simulations in SonnetFigure 6.1: Structure in the gold plated box withtwo-ports as simulated in SonnetIt is possible to include superconductivityin the simulations done with Sonnetby using the temperate and frequencydependent inductance derived in (2.26)on page 17. In the simulation processthis inductance is multiplied with the frequency1 . All simulations were performedfor three different regimes, first Niobiumas perfect conductor (labeled as nc), secondat temperatures of 4 K and third at a temperature of 50 mK. The results in the superconductingregime do not vary much with temperature, therefore, both results are summarizedin the superconducting (sc) results.The following parameters were used in the simulations:4 K 50 mKλ L 47.9 nm 47 nmL s 0.060 pH 0.059 pHTable 6.1: Inductance inserted in Sonnet to simulate superconductivity.In the simulations we took advantage of the high symmetry of the resonator structure: Asymmetry axis was laid in the middle of the center strip and Sonnet simulated only one halfof the structure, extrapolating the second half. Thus the computer needed less memory andthe necessary calculation time is reduced by a factor of 7. This procedure has been verifiedby comparing it to a simulation of the whole structure.1 See Sonnet manual page 70ff61