Superconducting Microstrip Losses at Microwave and Submillimeter Wavelengths

We present a lab-on-chip experiment to accurately measure losses of superconducting microstrip lines at microwave and submillimeter wavelengths. The microstrips are fabricated from $\mathrm{Nb}\text{−}\mathrm{Ti}\text{−}\mathrm{N}$, which is deposited using reactive magnetron sputtering, and amorphous silicon which is deposited using plasma-enhanced chemical vapor deposition (PECVD). Submillimeter wave losses are measured using on-chip Fabry-Perot resonators (FPRs) 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 $\tan \delta =3.7\pm 0.5\times {10}^{-5}$ at approximately $6\mathrm{GHz}$ and $\tan \delta =2.1\pm 0.1\times {10}^{-4}$ at 350 GHz. These results represent very low losses for deposited dielectrics, but the submillimeter wave losses are significantly higher than the microwave losses, which cannot be understood using the standard two-level system loss model.

Figure 1

(a) Chip schematic. $\mathrm{Nb}\text{−}\mathrm{Ti}\text{−}\mathrm{N}$ CPW structures are given in light blue, the Al/Nb-Ti-N CPW of the hybrid MKIDs is given in white, a-$\mathrm{SI}$ is shown in red, and the Nb-Ti-N microstrip lines are shown in dark blue. One of the CPW microwave resonators ($\mu \mathrm{WR}5$) is also shown in dark blue to highlight the use of the upper $\mathrm{Nb}\text{−}\mathrm{Ti}\text{−}\mathrm{N}$ layer for the CPW center line. (b) FPR coupler schematic with two cross sections $A$-$A^{\prime }$ and $B$-$B^{\prime }$. The schematic is shown top down with semitransparent layers, in order to clearly show the layout of the bottom $\mathrm{Nb}\text{−}\mathrm{Ti}\text{−}\mathrm{N}$ layer which is fully covered by a-$\mathrm{Si}$. (c) Optical microscope image of FP2. (d) Angled scanning electron microscopy (SEM) image of the FPR coupler. (e) High-resolution SEM image of the microstrip open end. Overetch into the a-$\mathrm{Si}$ layer is visible, with the dotted white line indicating the border between $\mathrm{Nb}\text{−}\mathrm{Ti}\text{−}\mathrm{N}$ and a-$\mathrm{Si}$. (f) Picture of the device mounted in the cryostat.

Figure 2

(a) Transmission for $\mu \mathrm{WR}1$ at three different readout powers, with the respective Lorentzian fits shown by the black dotted lines. (b) Measured internal quality factor $Q_i$ as function of $⟨n_{\mathrm{ph}}⟩$ for all $\mu \mathrm{WRs}$ shown as symbols, with fits of Eq. (3) shown by dotted lines with corresponding colors.

Figure 3

(a) Averaged loaded quality factor $Q_L$ as a function of average mode number in the four FPRs. The fit using Eq. (1) is shown by the black line. (b) Measured spectra of the FPRs, offset along the $y$ axis for better comparison. Line colors correspond to the markers in (a).