Cryogenic On-chip In Situ S-parameter Calibration Using Superconducting Coplanar Waveguides

Description

These data will appear in [1]. The abstract for that paper is given below:This paper presents a new multi-impedance-state line (MISL) in situ scattering parameter (S-parameter) calibration technique using on-chip superconducting transmission lines at 4 K that enables cryogenic calibration in a fixed signal path without the need for cryogenic switches or a cryogenic probe station. The method uses coplanar waveguide (CPW) models based on various impedance states of niobium (Nb), which has zero dc resistance below 9 K and a monotonically increasing resistance from 10 K to room temperature. The different impedance states are accessed by heating the 4 K stage of a cryostat and injecting up to 245 mA of current into the line. Using these states, we solve for the unknowns in an 8-term error model through a least-squares analysis. We first validate the MISL calibration technique by comparing it with short-open-load-reciprocal (SOLR) calibrated measurements in a cryogenic probe station, finding transmission agreement within 0.2 dB and uncertainty overlap for nearly all frequencies up to 26.5 GHz. We then apply the method to calibrate Nb CPWs with and without embedded Josephson junctions (JJs), using a fixed wire bonded connection, and without the use of cryogenic switches or movable probes. Strong agreement with the CPW models is demonstrated, with uncertainty overlap and differences below 0.1 dB up to 4.6 GHz without JJs and up to 2.4 GHz with JJs; resonances cause interruptions beyond these frequencies.[1] Thomas, J. N., Hoffmann, J., Flowers-Jacobs, N. E., Fox, A. E., Jungwirth, N. R., Johnson-Wilke, R. L., Dresselhaus, P. D., & Benz, S. P., "Cryogenic On-chip In Situ S-parameter Calibration Using Superconducting Coplanar Waveguides" submitted to the IEEE Transactions on Microwave Theory and Techniques Journal which if accepted will be published and available on IEEE website at a later date.

Resources

Name Format Description Link
8 Data used in Fig. 7 (bottom) of [1].Setup B, Chip B: Logarithmic magnitude of the transmission coefficients for Chip B's CPW models (|Sn,model,21|, dashed) and the proposed MISL-calibrated measurements (|Sn,MISL,21|, solid), using weights that prioritize transmission accuracy. The uncertainty for each state is represented by a shaded area in different colors. S0,model is shown in white for visual distinction. Bottom: CPW with JJs. S21 for resistive states (n > 0) is decreased compared to without JJs due to higher DC resistance from the JJs and increased use of the 200 nm thick base electrode (see Fig. 3). https://data.nist.gov/od/ds/mds2-3603/Fig7bottom_SetupB_CPWwithJJs.csv
8 Data used in Fig. 5 of [1].Extracted frequency-dependent distributed circuit parameters R′ and L′ for DC resistances of Chip A in Setup A (see Table I), obtained from 2D quasi-static EM simulations incorporating the CPW geometry and material properties, with associated k = 2 uncertainties (shaded areas). C′ = (148.67 ± 2.52) pF/m for the uniform CPWs at all frequencies. https://data.nist.gov/od/ds/mds2-3603/Fig5Resistance_Inductance_Data.csv
8 Data used in Fig. 7 (top) of [1].Setup B, Chip B: Logarithmic magnitude of the transmission coefficients for Chip B's CPW models (|Sn,model,21|, dashed) and the proposed MISL-calibrated measurements (|Sn,MISL,21|, solid), using weights that prioritize transmission accuracy. The uncertainty for each state is represented by a shaded area in different colors. S0,model is shown in white for visual distinction. Top: CPW without JJs. S21 for resistive states (n > 0) is primarily set by the 650 nm Nb wiring layer's DC resistance. https://data.nist.gov/od/ds/mds2-3603/Fig7top_SetupB_CPWwithoutJJs.csv
8 Data used in Fig. 6 (middle) of [1].Setup A, Chip A: Comparison of S-parameters for Chip A's CPW models (Sn,model), SOLR-calibrated measurements (Sn,SOLR), and the proposed MISL-calibrated measurements (Sn,MISL), using weights that prioritize transmission accuracy. Temperature-dependent resistivity variations in the 650 nm Nb wiring layer define seven distinct impedance states. The uncertainty for each state is represented by a shaded area in different colors. For the top and middle plots, S0,model is shown in white for visual distinction. Middle: Linear magnitude of S11. https://data.nist.gov/od/ds/mds2-3603/Fig6middle_SetupA_CPWwithoutJJs.csv
8 Data used in Fig. 8 of [1].Setup B, Chip B: Frequency dependence of the difference in |S21| between two states with nearly identical DC resistance but different heating mechanisms. S21 10K: Cryostat at 10 K with 85 mA DC current, 88.5 Ohms DC resistance. S21 25K: Cryostat at 25 K with 1 mA DC current, 88.47 Ohms DC resistance. https://data.nist.gov/od/ds/mds2-3603/Fig8TempTestData.csv
47 Readme for the navigation, organization, and content for the data in the figures included in the Cryogenic On-Chip In Situ S-Parameter Calibration Using Superconducting Coplanar Waveguides manuscript. https://data.nist.gov/od/ds/mds2-3603/README.txt
8 Data used in Fig. 6 (bottom) of [1].Setup A, Chip A: Comparison of S-parameters for Chip A's CPW models (Sn,model), SOLR-calibrated measurements (Sn,SOLR), and the proposed MISL-calibrated measurements (Sn,MISL), using weights that prioritize transmission accuracy. Temperature-dependent resistivity variations in the 650 nm Nb wiring layer define seven distinct impedance states. The uncertainty for each state is represented by a shaded area in different colors. Bottom: Upper bound of the linear magnitude difference between SOLR- and MISL-calibrated S-parameters for all n. https://data.nist.gov/od/ds/mds2-3603/Fig6bottom_SetupA_CPWwithoutJJs.csv
8 Data used in Fig. 6 (top) of [1].Setup A, Chip A: Comparison of S-parameters for Chip A's CPW models (Sn,model), SOLR-calibrated measurements (Sn,SOLR), and the proposed MISL-calibrated measurements (Sn,MISL), using weights that prioritize transmission accuracy. Temperature-dependent resistivity variations in the 650 nm Nb wiring layer define seven distinct impedance states. The uncertainty for each state is represented by a shaded area in different colors. For the top and middle plots, S0,model is shown in white for visual distinction. Top: Logarithmic magnitude of S21 for states n = 0, 2, 4, 6 (selected for visual clarity). https://data.nist.gov/od/ds/mds2-3603/Fig6top_SetupA_CPWwithoutJJs.csv

Tags

  • s-parameters
  • microwave-metrology
  • superconducting-circuits
  • josephson-junctions-jjs
  • cryogenic-microwave-calibration

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