We have developed a new technique for accurate measurement of the loss of superconducting microstrips at mm‐wave frequencies. In this technique, we optically couple power to slot antenna, which is connected to one port of a hybrid coupler. One of the output ports of the hybrid delivers power to a series of mm‐wave microstrip resonators which are capacitively coupled to a feedline followed by an MKID (microwave kinetic inductance detector) that measures the transmitted power. Two other MKIDs are connected to the remaining ports of the hybrid to measure the total incident optical power and the power reflected from the mm‐wave resonators, allowing |S21|2 and |S11|2 to be accurately determined and resonance frequency fr and quality factor Q to be retrieved. We have fabricated such a Nb/SiO2/Nb microstrip loss test device which contains several mm‐ wave resonators with fr∼100 GHz and measured it at 30 mK. All the resonators have shown internal quality factor Qi∼500–2000, suggesting a loss tangent of ∼5×10−4−2×10−3 for the SiO2 in use. For comparison, we have also fabricated a 5 GHz microstrip resonator on the same chip and measured it with a network analyzer. The loss tangent at 5 GHz derived from fitting the f0 and Q data to the two‐level system (TLS) model is 6×10−4, about the same as from the mm‐wave measurement. This suggests that the loss at both microwave and mm‐wave frequencies is probably dominated by the TLS in SiO2. Our results are of direct interest to mm/submm direct detection applications which use microstrip transmission lines (such as antenna‐coupled MKIDs and transition‐edge sensors), and other applications (such as on‐chip filters). Our measurement technique is applicable up to approximately 1 THz and can be used to investigate a range of dielectrics.
We present a lab-on-chip experiment to accurately measure losses of superconducting microstrip lines at microwave and sub-mm wavelengths. The microstrips are fabricated from NbTiN, which is deposited using reactive magnetron sputtering, and amorphous silicon which is deposited using plasma-enhanced chemical vapor deposition (PECVD). Sub-mm wave losses are measured using on-chip Fabry-P{é}rot resonators (FPR) operating around $350\ $GHz. Microwave losses are measured using shunted half-wave resonators with an identical geometry and fabricated on the same chip. We measure a loss tangent of the amorphous silicon at single-photon energies of
tanδ=3.7±0.5×10−5 at $6\ $GHz and
tanδ=2.1±0.1×10−4 at $350\ $GHz. These results represent very low losses for deposited dielectrics, but the sub-mm wave losses are significantly higher than the microwave losses, which cannot be understood using the standard two-level system loss model.
We have developed a novel technique for making high quality measurements of the millimeter-wave properties of superconducting thin-film microstrip transmission lines. Our experimental technique currently covers the 75–100 GHz band. The method is based on standing wave resonances in an open ended transmission line. We obtain information on the phase velocity and loss of the microstrip. Our data for Nb/SiO/Nb lines, taken at 4.2 K and 1.6 K, can be explained by a single set of physical parameters. Our preliminary conclusion is that the loss is dominated by the SiO dielectric, with a temperature-independent loss tangent of 5.3±0.5×10−3 for our samples.
Low loss superconducting microstrip is an essential component in realizing 100 kilo-pixel multichroic cosmic microwave background detector arrays. We have been developing a low loss microstrip by understanding and controlling the loss mechanisms. We present the fabrication of the superconducting microstrip, the loss measurements at a few GHz frequencies using half-wavelength resonators, and the loss measurements at 220 GHz frequencies with the superconducting microstrip coupled to slot antennas at one end and to TES detectors at the other end. The measured loss tangent of the microstrip made of sputtered Nb and SiOx is 1-2e-3.
Superconducting resonators provide a convenient way to measure loss tangents of various dielectrics at low temperature. For the purpose of examining the microscopic loss mechanisms in dielectrics, precise measurements of the internal quality factor at different values of energy stored in the resonators are required. Here, we present a consistent method to analyze a LC superconducting resonator coupled to a transmission line. We first derive an approximate expression for the transmission S-parameter S21(ω), with ω the excitation frequency, based on a complete circuit model. In the weak coupling limit, we show that the internal quality factor is reliably determined by fitting the approximate form of S21(ω). Since the voltage V of the capacitor of the LC circuit is required to determine the energy stored in the resonator, we next calculate the relation between V and the forward propagating wave voltage Vin+, with the latter being the parameter controlled in experiments. Due to the dependence of the quality factor on voltage, V is not simply proportional to Vin+. We find a self-consistent way to determine the relation between V and Vin+, which employs only the fitting parameters for S21(ω) and a linear scaling factor. We then examine the resonator transmission in the cases of port reflection and impedance mismatch. We find that resonator transmission asymmetry is primarily due to the reflection from discontinuity in transmission lines. We show that our analysis method to extract the internal quality factor is robust in the non-ideal cases above. Finally, we show that the analysis method used for the LC resonator can be generalized to arbitrary weakly coupled lumped and distributed resonators. The generalization uses a systematic approximation on the response function based on the pole and zero which are closest to the resonance frequency. This Closest Pole and Zero Method is a valuable tool for analyzing physical measurements of high-Q resonators.
Microwave kinetic inductance detectors (MKID) are superconducting broadband direct detectors. If a superconducting thin film patterned into a resonator is illuminated with photons, Cooper pairs break up and the kinetic inductance of the film changes. This shifts the resonance frequency downwards and the dissipation of the resonator increases, which can be detected in the phase and amplitude of a transmitted signal. \n \nIn this thesis, a waveguide coupled MKID is designed and simulated. 350 GHz radiation is coupled into a copper waveguide via a horn antenna. A waveguide probe leads the signal onto a 9 µm silicon membrane where it is absorbed in a 40 nm superconducting aluminum film which is the inductive part of a superconducting resonator. The capacitor of the resonator is made of niobium. Two versions of the device are developed, a transmission line resonator and a lumped element resonator design. The new design will enable an accurate understanding of the optical sensitivity of MKIDs and allow comparison of different resonator materials. Since two different resonator types are used, the direct comparison of transmission line and lumped resonators will also be possible. \n \nA measurement setup is developed including an ADR cryostat to cool MKID devices down to below 40 mK. An analog readout system using either a vector network analyzer or an IQ mixer is designed and built. The necessary software to control the ADR, the temperature monitoring, the readout signal generation and detection and the signal acquisition of the setup is also developed. \n \nThe waveguide coupled MKID design is fabricated in our in-house microfabrication laboratory and measured in the new setup. In my measurements, the devices do not show a resonance feature. The VNA and DC measurements are analyzed to determine a plausible hypothesis of the failure. The devices are diagnosed for critical issues during fabrication which will be addressed in a future iteration. \n \nTo verify the measurement setup, a test device of the IRAM NIKA 2 MKID camera is measured and the complete analysis pipeline is exercised. The quasi-particle lifetime in the aluminum thin films is measured and a dark and optical noise equivalent power are determined. The results are within the uncertainty comparable to measurements of IRAM themselves. \n \nA test chip designed in my master thesis that contains eight NbTiN resonators is measured in the new setup and non-linear effects under strong readout power are studied. Parametric amplification and oscillation of a resonator are shown qualitatively.
An understanding of the origins of power loss in superconducting interconnects is essential for the energy efficiency and scalability of superconducting digital logic. At microwave frequencies, power dissipates in both the superconducting wires and the dielectric and these losses can be of comparable magnitude. We describe an approach to accurately disentangle such losses by exploiting their frequency dependence in a multimode transmission-line resonator. This is supported by the concept of a resonator geometric factor extracted from the Ansys High Frequency Structure Simulator (hfss), a commercial three-dimensional finite-element method (FEM) that we adopt for solving a superconductor interior. Using the technique, we have optimized a planarized fabrication process of reciprocal quantum logic (RQL) for the minimum interconnect loss at 4.2 K and gigahertz frequencies. The microstrip interconnects are composed of niobium (
Nb) insulated by silicon dioxide (
SiO2) made from a tetraethoxysilane (TEOS) precursor. Two process generations use damascene fabrication and the third one uses Cloisonn\'e fabrication. For all three,
SiO2 exhibits a dielectric loss tangent $\mathrm{tan}\phantom{\rule{0.1em}{0ex}}\ensuremath{\delta}=0.0012\ifmmode\pm\else\textpm\fi{}0.0001$, independent of the
Nb wire width over 0.25--4 $\text{\ensuremath{\mu}}\mathrm{m}$. The intrinsic microwave resistance
Rs of
Nb varies with both the process and the wire width. For damascene fabrication, scanning transmission electron microscopy (STEM) and energy-dispersive x-ray spectroscopy (EDS) reveal that plasma oxidation and grain-growth orientation increase
Rs above the Bardeen-Cooper-Schrieffer (BCS) resistance ${R}_{\mathrm{BCS}}\ensuremath{\approx}17\phantom{\rule{0.2em}{0ex}}\text{\ensuremath{\mu}}\mathrm{\ensuremath{\Omega}}$ at 10 GHz. For Cloisonn\'e fabrication, we demonstrate ${R}_{s}=13\ifmmode\pm\else\textpm\fi{}1.4\phantom{\rule{0.2em}{0ex}}\text{\ensuremath{\mu}}\mathrm{\ensuremath{\Omega}}$ down to $0.25\phantom{\rule{0.2em}{0ex}}\text{\ensuremath{\mu}}\mathrm{m}$ wire width, which is below
RBCS and arguably the lowest microwave resistance reported for
Nb at 4.2 K.