Low microwave loss in deposited Si and Ge thin-film dielectrics at single-photon power and low temperatures

The performance of superconducting microwave resonators used in quantum computing and sensing applications is limited by dielectric and two-level system (TLS) losses in the dielectric and at the metal–air, metal–dielectric, and dielectric–air interfaces.^1–4 Bulk, high-purity single-crystal Si and sapphire (Al₂O₃) are the substrates of choice to minimize these losses.^5–8 

Deposited dielectric layers SiO₂, Si₃N₄, and SiO_xN_y, which are commonly used for isolation, interwiring, and passivation, have high-loss tangents⁵ of 0.1–3 × 10⁻³, making them unsuitable for use in low-loss microwave devices and Josephson junction circuit processes. Furthermore, materials for device isolation and passivation are typically deposited using plasma-enhanced chemical vapor deposition (PECVD), which requires temperatures of ≈350–400 °C to produce electrically insulating low-defect density material. However, for temperature-sensitive devices such as Josephson junctions, temperature limits⁹ (150–175 °C) are imposed to prevent thermally induced changes in the devices. Such temperature limits result in dielectric films with high densities of performance-degrading defects.

In this paper, we will first list potential reasons for considering a couple of specific forms of deposited Si and Ge for low-loss dielectric layers for substrates, isolation, interwiring, passivation, and multi-layer device structures.

1. Several-micron-thick high-purity CVD homoepitaxial silicon layers are considered for the following reasons:

   • They are available in a very pure form with uncompensated carrier concentrations as low as 10¹² cm⁻³ and structural defect densities less than 1 cm⁻².

   • They have proven to exhibit better performance, including higher breakdown fields, in high-power Si device applications than their bulk Si counterparts.

   • They have a different defect composition from float-zone Si wafers, where bulk substrates have an order of 5 × 10¹⁵ cm⁻³ oxygen and carbon contaminants and a significantly higher number of compensated or electrically inactive defects (i.e., defects that do not contribute to conductivity at room temperature).¹⁰ Such bulk Si defects are believed to undergo multi-atom configuration changes at low temperatures and thus contribute to microwave loss and noise in quantum-based computing and sensing applications.

   • They allow for the possibility that metal layers can be deposited in situ in the same system, reducing the losses from interfacial impurity contamination.

2. High-purity low-temperature deposited germanium layers are considered for the following reasons:

   • They can be fabricated with an even higher purity¹¹ source material than Si, with impurity concentrations as low as 10⁸ cm⁻³. If no additional contamination is added during the deposition process, only a few tens of impurity defects would be present in the entire active region of coplanar, microstrip, or stripline structures.

   • They can exhibit high resistivity when evaporated at low substrate temperatures, including at room temperature.

   • They can potentially replace commonly used deposited dielectrics with high-loss in microwave and Josephson junction circuit fabrication.

   • They can enable the use of in situ metal and dielectric deposition processes, which minimize, and may virtually eliminate, interfacial contamination.

In the study reported here, we compare the low-temperature microwave losses in Nb-based coplanar microwave resonators synthesized on (1) molecular-beam evaporated 1 μm-thick amorphous Ge thin-films on Si and (2) chemical vapor deposited (CVD) 9 μm-thick homoepitaxial Si thin-films with (3) high-resistivity bulk Ge substrates (>100 Ω cm) and (4) high-resistivity undoped Si substrates (>10 000 Ω cm). To enhance our sensitivity to the interface and properties of the deposited dielectrics, we designed and built resonators with narrow trace and gap widths and minimal (<20 nm) over-etch. This is in contrast to other studies that focus on maximizing the quality factors by designing resonators with large trace widths and significant over-etch.^12–14 

Nb metal films are sputter-deposited onto the substrates or deposited layers described below. Sputter deposition is performed at room temperature under 4 mTorr of Ar in a UHV system with an unbaked base pressure of <5 × 10⁻⁹ Torr using a 2 in. diameter magnetron sputter source with 99.95%-pure Nb targets. The sputter power is 225 W with a source-film distance of 15 cm, resulting in a deposition rate of ≈0.6 nm/s.

We deposit amorphous germanium (a-Ge) films via thermal evaporation onto undoped float-zone (FZ) Si (100) substrates with resistivities greater than 10 000 Ω cm. The evaporation source material is pieces of undoped crystalline Ge wafers (stated >40 measured >100 Ω cm) broken into small pieces. The Si substrate surface is cleaned in ultrasonic baths of USP-grade acetone and then ethanol for 10 min, followed by etching for 5 min in aqueous 2% HF solution. For Ge deposition, the chamber is evacuated to a base pressure of less than 5 × 10⁻⁹ Torr before slowly warming the Ge evaporation source (SVT High Temperature Effusion Cell) to 1400 °C. The Ge is deposited at ≈0.25 nm/s to a total film thickness of ≈1 µm.

Epitaxial Si films are prepared in a commercial foundry at Lawrence Semiconductor Research Laboratory (Tempe, AZ). The substrate is a (100) orientation Czochralski (CZ)-grown Si wafer (resistivity ρ = 1000–25 000 Ω cm), cleaned using an in situ high-purity HCl etch. The ≈9 µm thick epi-layer was deposited at 900 °C, using 2% silane in H₂, with a deposition rate of ≈300 nm/min. Prior to insertion into the Nb metal layer deposition system, the epi Si/Si film surface is cleaned in ultrasonic baths—first in U.S. Pharmacopeia (USP)-grade acetone and then in ethanol for 10 min each. To remove residual surface contamination, the film is flash-heated in a deposition chamber¹⁵ (<5 × 10⁻⁹ Torr) to 850 °C, and then the temperature was maintained at 650 °C for 1 h before cooling for about 1 h to room temperature before Nb sputter deposition.

Chemical depth profiles are obtained using Time of Flight Secondary Ion Mass Spectrometry (TOF-SIMS). The analysis beam uses Ga⁺ ions with a 1 kV Cs sputter ion beam for depth profiling. Because SIMS sensitivity factors are only reliable for the bulk, and differ greatly from these values for the disordered atomic structures near these Nb/semiconductor junctions, all near-interfacial data presented here will be in secondary ion yield normalized to the relative count rate of the host matrix (the sum of Nb and Ge yields) and are not accurate estimates of atomic concentration.

Coplanar waveguide (CPW) resonators are prepared using standard photolithography and reactive ion etching (RIE) in a CF₄ plasma. We pattern devices into a 50 Ω (on silicon) coplanar waveguide resonator configuration with 2–16 µm trace width, 2–8 µm gap width, and less than 20 nm over-etch to maximize electric field interaction with the interface and dielectric films under study. The quarter-wave CPW resonators are capacitively coupled to the microwave feedline. Transmission measurements (S21) are made at ≈40 mK in a closed cycle dilution refrigerator as a function of applied power. The input signal to the feedline is attenuated by 40 dB at room temperature and 20, 10, and 20 dB on the 4 K, still, and mixing chamber plates, respectively. The output signal is buffered by two isolators in series on the mixing chamber plate and another on the 4 K plate. The signal is amplified by an HEMT amplifier at 4 K and a low-noise amplifier at room temperature. The resonance is fit using the diameter correction method to extract Q_i, the internal quality factor of the resonator, and thus the loss tangent¹⁶ (⁠$tanδi=Qi−1$⁠).

Carrier concentrations determined using room-temperature Hall effect measurements find the deposited a-Ge film is n-type with 6 × 10¹² cm⁻³ net carriers, essentially identical to the original wafer source material. Electron Paramagnetic Resonance (EPR) measurements on these a-Ge films (performed using the in situ parallel plate EPR technique described in our earlier work¹⁷) find that the paramagnetic defect concentration is below the detection limit of ≈10¹⁷ cm⁻³. X-ray diffraction characterization, performed using a PANalytical X’pert MRD Pro, of the a-Ge films do not exhibit any sharp Bragg diffraction peaks, characteristic of amorphous material. Raman spectroscopy, measured with a 532 nm laser at 0.75 mW with 0.5 µm spot size, shows a broad peak near 290 cm⁻¹, similar to that found for electrolytically deposited¹⁸ a-Ge, as would be expected for an amorphous Ge film.

Si films deposited under the same conditions as those used in our study have been measured to be slightly of n-type, with net carrier concentrations less than 10¹² cm⁻³ at room temperature as measured by spreading resistance probe. SIMS measurements find that the impurity concentration within the homoepitaxial Si film is below the detection limit of ≈10¹² cm⁻³.

Table I and Fig. 1 summarize results from low power, low-temperature microwave measurements on Nb-based CPW resonators on the float-zone silicon wafer, homoepitaxial Si films, a high-resistivity Ge wafer, and room-temperature deposited a-Ge. The resonator with the room-temperature deposited a-Ge dielectric exhibits a total dielectric loss comparable to that of the Nb/epi-Si wafer and the lowest single-photon loss in a deposited amorphous dielectric reported to date. Low two-level system loss densities have also been reported in acoustic and thermal measurements on deposited amorphous dielectrics.^19–22 While acoustic measurements are at a much lower frequency and coupled to strain instead of electric fields, TLS spectroscopy measurements in the strain and field find similar spectra and associate these with bulk and surface TLS, respectively.^23,24 Our a-Ge films deposited at room temperature without any post-processing exhibit single-photon loss tangents six times lower than the reported values of internal friction on e-beam and sputtered a-Ge films by Liu and Pohl²⁰ and two times lower than those of a-Ge films reported with post-process annealing (5 h at 350 °C). In those studies, Liu et al. reported that low energy excitations of a-Ge are highly dependent on the preparation method, which they attribute to structural differences in the films. Further enhancement may be possible based on later studies by Liu et al.,²¹ where they reported a-Si films that do not exhibit two-level system loss even without hydrogen passivation by using an optimized 400 °C substrate growth temperature, achieving Q = 5 × 10⁵ (i.e., tan δ = 2 × 10⁻⁶).

Comparing our results to those in the surveys of superconducting coplanar resonators,^5,6,8 we find that our high-purity deposited a-Ge films exhibit loss much lower than that reported for a-Si:H, sputtered a-Si, lumped element a-SiN_x resonators,³ and other deposited dielectric materials.²⁵ The single-photon loss in the a-Ge film is similar in magnitude to early reports of high-quality resonators on single-crystal Si or sapphire but higher than more recent reports, including the CPW resonators on float-zone Si reported here. The loss in a superconducting resonator is sensitive to the cleanliness of the interfaces, and the devices presented here are no exception. Following the technique from Ref. 4, the filling factors of the dielectric film and substrate were calculated using the electric field distributions simulated in Ansys Maxwell for each geometry and material. The simulation assumes that a 2 nm oxide interface layer is present at every surface and interface with dielectric constants of 3.6, 2.5, and 10 for the silicon, germanium, and metal oxides, respectively. Bulk room-temperature dielectric constants were used for silicon 11.9 and germanium 16.0. The effective loss tangents in Table I were calculated by subtracting the interface loss and substrate loss (for the films only) from the measured single-photon loss tangents,

The interface and bulk silicon loss tangents are estimated using values taken from Ref. 26 and scaled to the filling factor of our devices. The effective loss tangent is dominated by the uncertainty in the interface and substrate loss for the films, but the calculated value is useful for comparing resonators of different geometries within a material system. Differences between the effective loss tangents within a single material system are likely due to differences in interface contamination between the devices. More reliable determination of the material and interface losses requires measuring a large number of resonators with varying geometries.²⁶ 

In order to understand the unexpected higher loss in c-Ge than a-Ge, time of flight SIMS depth profiles were collected for the Nb/a-Ge and the Nb/crystalline Ge wafer interfaces. The profiles identify H, C, O, F, and Cl at the interfaces with very low contamination in the a-Ge film or substrate (Fig. 2). The TOF-SIMS data are shown with relative yield instead of concentration to avoid complications associated with matrix effects at and near the metal/semiconductor interface. The a-Ge (which had the Nb deposited in situ) has fewer contaminants near the interface than the Nb deposited directly on the air-exposed, chemically cleaned bulk Ge wafer. On the bulk Ge wafer, we observe contamination of C, F, and Cl peaks extending about 20, 20, and 40 nm into the Ge, respectively. Based on these results, the lower loss in the deposited a-Ge resonator is not unexpected, given the much higher level of chemical purity at the deposited film’s interface.

The smaller difference in the loss tangent between the epitaxial silicon film and the c-Si substrate is likely due to sample-to-sample variation in the interface preparation. However, the loss tangent of the CZ-Si wafer under the homoepitaxial Si was not measured. The effective loss tangent calculation assumes tan δ = 2.6 × 10⁻⁷, but the value of the bulk loss tangent of crystalline silicon at milli-Kelvin temperatures is still an open question as interface losses dominate the measurements.²⁶ Similarly, the differences in low-temperature microwave loss between high-resistivity CZ and float zone (FZ) silicon have not been studied.

The 1 µm thick a-Ge layer evaporated onto Si (100) has an rms roughness of 1.02 Å as measured by atomic force microscopy. Such low roughness topographies are useful for strict device dimensioning and processing in multi-layer structures. These a-Ge films have another advantage for such applications; they have sufficient conductivity at room temperature to protect electronic devices, such as transistors and Josephson Junctions, from electrostatic discharge during fabrication and storage. Room-temperature deposited Ge films exhibit low loss, as shown here, and do not require elevated temperature thermal processing, enabling multi-layer resonator geometries for use in microstrip and stripline microwave devices, as well as interwiring, isolation, and passivation layers. Although the electrical and chemical properties of Ge have many advantages for all the applications discussed here, the natural form that was used in this study does contain a 7.8% abundance of ⁷³Ge, with 9/2 nuclear spin, which could potentially contribute to loss and noise in spin sensitive devices.^27,28 Isotopically enriched ⁷⁴Ge is available and could be used to make thin films if the nuclear spin loss limits device performance.²⁹ 

In summary, we have demonstrated that deposited dielectrics in CPW resonators exhibit low loss when operated at single-photon powers and low (≈40 mK) temperatures. CPW resonators on amorphous germanium films deposited at room temperature have single-photon loss tangents tan δ_eff of 4–5 × 10⁻⁶, and CPW resonators on 9 µm thick high-purity CVD homoepitaxial silicon films have single-photon loss tangents tan δ_eff of 4–14 × 10⁻⁶. Interface losses presumably dominate the resonator performance in these devices.

These results show that room-temperature deposited amorphous Ge layers and CVD Si films exhibit microwave properties suitable for incorporation in quantum computing and sensing applications. These materials exhibit intrinsic loss tangents lower than those at the interfaces and do not limit device performance. The room-temperature deposited amorphous Ge layers could also be used to make co-planar, microstrip, and stripline resonators or could be utilized in place of SiO_x and Si_xN_y for dielectric isolation, wiring, and passivation layers.