Characterization of the low electric field and zero-temperature two-level-system loss in hydrogenated amorphous silicon

Fabien Defrance, Andrew D. Beyer, Shibo Shu, Jack Sayers, and Sunil R. Golwala

Phys. Rev. Materials 8, 035602 – Published 5 March 2024

Abstract

Two-level systems (TLS) are an important, if not dominant, source of loss and noise for superconducting resonators such as those used in kinetic inductance detectors and some quantum information science platforms. They are similarly important for loss in photolithographically fabricated superconducting mm-wave/THz transmission lines. For both lumped-element and transmission-line structures, native amorphous surface oxide films are typically the sites of such TLS in nonmicrostripline geometries, while loss in the (usually amorphous) dielectric film itself usually dominates in microstriplines. We report here on the demonstration of low TLS loss at GHz frequencies in hydrogenated amorphous silicon (a-Si:H) films deposited by plasma-enhanced chemical vapor deposition in superconducting lumped-element resonators using parallel-plate capacitors (PPCs). The values we obtain from two recipes in different deposition machines, $7 \times 10^{- 6}$ and $12 \times 10^{- 6}$ , improve on the best achieved in the literature by a factor of 2–4 for a-Si:H and are comparable to recent measurements of amorphous germanium. Moreover, we have taken care to extract the true zero-temperature, low-field loss tangent of these films, accounting for temperature and field saturation effects that can yield misleading results. Such robustly fabricated and characterized films render the use of PPCs with deposited amorphous films a viable architecture for superconducting resonators and they also promise extremely low loss and high quality factor for photolithographically fabricated superconducting mm-wave/THz transmission lines used in planar antennas and resonant filters.

Received 2 December 2023
Accepted 14 February 2024

DOI:https://doi.org/10.1103/PhysRevMaterials.8.035602

Physics Subject Headings (PhySH)

Defects Dielectric properties Impurities in superconductors Open quantum systems & decoherence Quantum engineering Superconductivity

BCS theory

Quantum Information, Science & TechnologyCondensed Matter, Materials & Applied Physics

Authors & Affiliations

Fabien Defrance ^* and Andrew D. Beyer

Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California 91109, USA

Shibo Shu, Jack Sayers, and Sunil R. Golwala

California Institute of Technology, Pasadena, California 91125, USA

^*fabien.m.defrance@jpl.nasa.gov

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Vol. 8, Iss. 3 — March 2024

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Images

Figure 1
(a) Exploded view, not to scale, showing the geometry of the LC resonators used to measure the loss tangent and internal quality factor of a-Si:H. The CPW feedline is composed of a center conductor on the top Nb layer and ground electrodes on the bottom Nb (“ground plane”) layer separated by the a-Si:H dielectric film to be characterized. The resonator consists of an inductor that runs parallel to the feedline center conductor on the top Nb layer and a series pair of PPCs formed by plates on the Nb top layer and the ground plane. (The a-Si:H layer is only 800 nm thick, while the inductor-top plate gap is 22 $µ m$ and the CPW center conductor and gap are 20 $µ m$ and 12 $µ m$ wide, respectively, so the structure is approximately planar in spite of the vertical separation of the center conductor and ground plane.) A 44 $µ m$ gap separates the ground plane plate from the surrounding ground plane, though this gap is not strictly necessary because this electrode acts as a virtual ground. The inductor couples the CPW feedline to the LC circuit and a gap in the ground plane below the inductor mitigates magnetic screening that would reduce the inductance value and feedline coupling. The gap also limits parasitic capacitance with the ground plane. (b) Lumped element circuit equivalent. The CPW feedline has an impedance $Z_{0} = 50 Ω$ , the two capacitances $C_{0}$ correspond to the two PPCs, $L$ is the inductance, and $k$ represents the mutual inductance with the CPW.
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Figure 2
Schematic showing main device fabrication steps. (1) Deposition and patterning (etchback) of a 190 nm thick Nb film on a 375 µm thick, 100 mm diameter, high resistivity silicon wafer, forming the ground plane (also including the return conductors of the CPW feedline) and the bottom plate of the PPCs. (2) Deposition of a 800 nm thick layer of a-Si:H using plasma-enhanced chemical vapor deposition (PECVD; Caltech KNI) for recipe A and inductively coupled plasma PECVD (ICP-PECVD; JPL MDL) for recipe B. (3) Deposition and patterning (etchback) of a 400 nm thick Nb film on top of the a-Si:H layer, forming the CPW feedline center conductor, the inductor, and the PPC top plates. We deposit all the metal films using rf magnetron sputtering at JPL MDL with a 6-in. target.
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Figure 3
Log-log plot illustrating Eq. (4). $Q_{i}^{- 1}$ converges towards $δ_{other} + δ_{TLS}^{0} tanh [h f_{res} / (2 k_{B} T)]$ at low $| \vec{E} | / E_{c}$ and towards $δ_{other}$ at high $| \vec{E} | / E_{c}$ . The exponent $β$ only changes the steepness of the dependence on $| \vec{E} |$ ; $β = 0.5$ was used here, corresponding to a log-uniform TLS density of states. The different curves correspond to different values of $h f_{res} / (2 k_{B} T)$ . The plot illustrates that taking data in the fully unsaturated (in $T$ and $| \vec{E} |$ ) limit yields the best lever arm on determining the true value of $δ_{TLS}^{0}$ from $Q_{i}^{- 1}$ data and that taking $T$ -saturated data necessitates applying a correction factor $tanh [h f_{res} / (2 k_{B} T)]$ . For reference, $h f_{res} / (2 k_{B} T) \approx 0.96$ [and $tanh (0.96) = 0.74]$ for $f_{res} = 1$ GHz at $T = 25$ mK. Our data probe the range $h f_{res} / (2 k_{B} T) \in [0.08, 0.16]$ , requiring a factor of roughly 6–13 correction for $T$ saturation.
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Figure 4
(a), (b) Data and best-fit TLS model [Eq. (5)] for $[f_{res} - f_{res} (0)] / f_{res} (0)$ as a function of temperature. (c), (d) Data and best-fit TLS model [Eq. (4)] for $Q_{i}^{- 1}$ data as a function of electric field. (a), (c) Devices A(1) and A(2); (b), (d) devices B(1) and B(2). Much of the literature uses photon number instead of $| \vec{E} |$ ; Fig. 6 in Appendix pp2 shows plots (c) and (d) as a function of photon number to facilitate comparison with published results. Table 3 lists the best-fit parameters. Disagreements between the model and the data are discussed in the text; in particular, how we extract $δ_{TLS}^{0}$ and $δ_{other}$ in the presence of such disagreements. The $f_{res} (T)$ data were taken at a readout power (at the device) of approximately $- 100$ dBm ( $| \vec{E} | \approx 500$ V/m). The $Q_{i}^{- 1} (| \vec{E} |)$ data were taken at 246 mK.
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Figure 5
Values of $δ_{TLS}^{0}$ obtained from quality-factor data (orange) and frequency-shift data (blue) for (a) device A(1), (b) device A(2), (c) device B(1), and (d) device B(2). The relative difference between the two fitted values of $δ_{TLS}^{0}$ is indicated in the gray box above.
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Figure 6
(a), (b) Data and best-fit TLS model [Eq. (4)] for $Q_{i}^{- 1}$ data as a function of photon number. The data shown on this plot are the same as in Figs. 4 and 4 but $| \vec{E} |$ has been converted to photon number $N$ using Eq. (B5).
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