Impact of surface roughness on consistent resonator performance

doi:10.21203/rs.3.rs-5218627/v1

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Impact of surface roughness on consistent resonator performance

https://doi.org/10.21203/rs.3.rs-5218627/v1

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Superconducting circuit-based quantum processors are leading platforms for quantum computing. In these circuits, microwave photons are stored as qubits in ultra-low-loss planar resonators and non-linear inductors formed by Josephson junctions. Resonators are typically made from high-energy-gap superconductors like Nb or Ta, while junctions are made of Al. Resonators occupy much of the circuit, making defect-free fabrication and understanding microwave energy dissipation crucial. Losses arise from noise, two-level systems (TLS), quasi-particles, and impurities. TLS losses dominate at operating temperatures below the critical temperature of the metal, whereas photon loss due to quasi-particles, often stemming from grain boundaries and pinholes in the metal film, becomes more pronounced at higher photon numbers or temperatures approaching the metal's critical temperature. To mitigate these, substrate cleaning, surface control, and non-superconducting film capping prevent oxide formation and reduce impurities. High-frequency drives, coupled with impurities at grain boundaries, lead to nonuniform quality factors among resonators. By controlling oxygen plasma exposure to minimize surface roughness and pinhole depth, we observed an area-dependent quality factor, which we attribute to changes in surface resistivity. This approach minimized variations in quality factors across resonators, improving uniformity in Nb-based devices and more consistent qubit readout performance.

Physical sciences/Materials science/Materials for devices/Electronic devices

Physical sciences/Physics/Electronics, photonics and device physics/Superconducting devices

Superconducting circuit-based qubit platform is one of the front runners in the field of quantum computing, having demonstrated a quantum advantage for the first time¹ and showed a reasonable prospect of scaling the number of qubits.² However, the performance of the quantum gates and the achievable coherence times are the primary limiting factors in demonstrating practical quantum advantage, a goal that is going to disrupt the concept of computing in general.^3,4 Traditionally, these microwave circuits are made of superconducting metals like aluminium (Al), niobium (Nb), and, more recently, tantalum (Ta) that form the planar resonators, waveguides, and transmission lines. However, the Josephson Junction that acts as a non-linear inductor is formed by the Al-Al₂O₃-Al interface. The superconducting energy gap of Nb is ten times that of Al. A single or a few microwave photons that circulate in the quantum circuit largely remain on the Nb or Ta surface (due to the large surface participation ratio⁵). Hence, the quality factor of the resonators, as well as other transmission lines, must be high quality and defect-free to produce a long coherence time.

Niobium is widely used as a superconducting material in cryogenic applications due to its unique properties over other superconducting metals like Al, Ta, In, Pb, and others. These include a high critical temperature (T_c) of 9.25 K for high-quality metal film,⁶ enabling operation at relatively higher temperatures. Furthermore, it demonstrates a significant superconducting energy gap of 1.41 meV associated with lower quasiparticle creation probability,⁷ low kinetic inductance,⁸ and low surface roughness (root mean square (RMS) = ~ 1.0 nm),⁹ leading to reduced device variability. However, the internal quality factor (Qi) of resonators is strongly influenced by various loss mechanisms¹⁰, such as TLS loss associated with surface oxide defects, grain boundaries acting as effective vortex traps¹¹, and quasiparticle loss linked to defects like pinholes¹² and edge roughness of the superconducting metal film.^13,14 A higher resonator Qi is demonstrated when the system is less sensitive to these superconductor metal film surface defects. For example, in a 3D microwave cavity,¹⁵ a Qi of about ∼ 0.5×10⁹ can be achieved due to its lower sensitivity to dielectric and conductor losses at surfaces and interfaces. In opposition, 2D-planar resonators are more sensitive to defects on their surfaces, with the Qi reaching ∼10⁷ at low photon numbers and temperature below 1 K only for selected devices, which are called “hero devices”.¹⁶ However, microwave-induced quasiparticle excitation on the conductor surface leads to non-uniform resonator quality factors on the same chip and variations across different devices. The reason for the nonuniformity of resonator Qi across different resonators on the same chip remains unknown and requires detailed investigation. This uniformity is crucial for achieving consistent performance in quantum devices, particularly in large-scale quantum computing systems where multiple qubits and resonators are interconnected.

In general, superconducting characteristics, such as the T_c and energy gap, are mainly influenced by lattice defects, including grain dislocations, boundaries between the grains on the surface, and impurities like hydrogen that generate hydride impurities.^17,18 These defects are likely to suppress the expulsion of the magnetic field (Meissner state) on the surface and contribute to decoherence, limiting quantum computing performance due to the non-uniformity of resonator Qi even within a single chip. The formation of amorphous oxides or oxygen vacancies at the boundary of the grain and pinholes on the film’s surface leads to generating charge traps and the TLS loss on the film at cryogenic temperature.^19–21 A rich literature is available on minimizing the TLS loss on SC film using various strategies. Some of these efforts directed towards reducing surface oxide defects on the SC film are pre/post cleaning process,^22–24 capping with non-superconducting metal layers,²⁵ and surface passivation using self-assembled organic molecules,²⁶ while these methods have shown significant improvements most often restricted to “hero devices”. This stems from a lack of knowledge of how the quality factor affects the grain boundaries, pinholes, or edge defects, which are microscopic defects that result from various fabrication processes. Investigating the effects of grain boundaries and pinholes on the superconducting film quality and performance is essential at the wafer scale, with enough statistics to improve the repeatability and reliability of the resonator quality factor. Those are important aspects contributing to the performance of SC circuit-based quantum processors.

In the particular case of Nb films, grain boundaries can adversely affect its superconductivity by allowing flux penetration, trapping residual flux, reducing critical current density, decreasing superconductivity and increasing surface resistance, and increasing the effect of the total density of the grain boundaries on the film surface.^27–30 Mitigating these effects requires careful processing techniques, defect density control, optimized growth orientation, and defect structures to improve niobium quality for superconducting applications. Generally, the power loss in a microwave resonator due to TLS or quasiparticle depends differently on the experimental conditions, such as input power, ambient temperature, etc. These exclusive dependencies have quasiparticles exploited to quantify these contributions independently.^1031,32 The TLS loss component is a commonly accepted microwave energy dispersion on a resonator at low power and low photon number, which exhibits a strong power-dependent Qi characteristic of the device. The TLS loss component and quasiparticles are extrinsic properties that may vary depending on the materials and fabrication process involved. Various strategies are used to minimize the strong power-dependent Qi. However, exceptional cases have been reported where quality factors show weak dependence on applied power.¹⁹ Additionally, there are also power-independent but temperature-dependent resonator loss mechanisms due to radiation, magnetic vortices, and quasiparticles originating from stray infrared light and microwave-induced pair-breaking or power dissipation caused by defects such as impurity traps inside the grain boundary and pinholes on the superconductor film surface.^10,33,34 Despite a rich literature on loss mechanisms, controlling the Qi spread of resonators even on a single chip remains challenging, as the total loss in the microwave resonator is a combination of all the above-mentioned loss mechanisms.

Here, we mainly focus on resonator performance at medium photon numbers (~ 10⁸-10¹⁰) and relatively high temperature (~ T_c=1.2 K) to study how surface morphology, such as roughness and pinholes, influence microwave-induced power dissipation and how to minimize these effects to improve the uniformity of the resonator quality factors on a single chip. The primary questions addressed here are (a) the impact of surface roughness on the quasiparticle loss and (b) the impact of metal oxide composition on the quasiparticle loss. Disentangling these two requires careful preparation of samples with quantifiable defects measured in terms of roughness and chemical composition. Furthermore, we obtained our results from a statistically significant randomly chosen samples across three independent wafer-scale processes, not just on a selected single device. The following section introduces the materials and methods used in this work, followed by the results obtained and their significance in the field.

We fabricated a resonator structure on a high resistivity (> 5k ohms. cm) silicon wafer (see experimental section for more details), as shown in Fig. 1A. We characterized the structural properties and chemical composition of the film before and after the device fabrication: a crystalline orientation using an X-ray diffraction (XRD) pattern, surface morphology by atomic force microscopic (AFM) image, and the chemical composition investigated with X-ray photoelectron spectroscopy (XPS). Figure S1A shows XRD patterns of the as-deposited Nb, UV-ozone exposed (Nb-O), and oxygen plasma exposed (Nb-OP) samples. The results reveal two peaks at 38.47^◦ and 82.45^◦, corresponding to the [110] and [220] crystal orientations, indicating that the Nb film contains a plane of [110] structure as the dominant orientation compared to the [220] plane structure. The inset Figure S1A displays an expanded view of the [110] pattern, indicating that the fabrication and plasma cleaning processes do not affect the crystal orientation of the native Nb film. However, there is a small change in the crystallite size, which increases from 21.54 nm to 22.23 nm after the fabrication, indicating that the lithography followed by the dry etching process does not change the lattice strain significantly. The oxygen plasma-exposed samples exhibited a crystallite size of ∼21.82 nm. These results further confirm that the structural characteristics of Nb film are retained after the oxygen plasma exposure.

The surface morphology of the Nb thin film is characterized using tapping mode AFM. Figure 1B&C shows the AFM image of ozone and oxygen plasma exposed. The elongated crystal structure obtained (Fig. 1B) resembles previously reported highly crystalline niobium resonator structures fabricated on sapphire and silicon surfaces.⁹ The Nb thin film with ozone exposure has an RMS value of 0.98 nm over a 1×1 µm² area. After 6 minutes of oxygen plasma exposure, the elongated, densely packed crystal structure disappeared (Fig. 1C), and the Nb surface exhibited an atomically smooth surface with an RMS value of 0.31 nm over the same area. This observation is similar to what was previously reported for the Nb film exposed to an argon milling process,³⁵ which led to smoothening the Nb film surface by increasing valley and peak areas by a factor of 5.6, simultaneously, argon milling causes damage to the surface of niobium.³⁵ Here, the Oxygen plasma exposure partially etches the Nb film surface, making it smoother and significantly reducing the average pinhole depth from 4 nm to 1.5 nm (see Fig. 1D). C.T. Earnest et al.³⁶ demonstrated that surface roughness, specifically horizontal peak-to-valley height, has been linked to the increased loss due to the enhanced participation ratio of the electric fields at the surface while other parameters remaining same. This indicates that it is essential to reduce the overall horizontal peak-to-valley height of the surface, including pinholes, to decrease the electric fields at the surface. We studied the time-dependent oxygen exposure on a Nb film to understand the structural changes (e.g. RMS roughness) of the surface without affecting the internal structure of the film. Figure S1B illustrates changes in the RMS value relative to exposure time, with the RMS value reaching a minimum at approximately 6 minutes of exposure. Upon further exposure time, the roughness value increased, and pinholes were formed on the surface of the Nb film (see Figure S1B). Thus, we confirm that controlled oxygen plasma exposure only alters the surface morphology, resulting in minimized RMS roughness (see Figure S1C&D) and a reduced pinhole on the surface without impacting the Nb film’s crystal structure.

To better understand how oxygen plasma exposure affects the Nb resonator fabricated on a silicon substrate, we investigated the surface chemical composition of the Nb resonator with ozone and oxygen plasma treated chip using the XPS surface characterization. Figure 2A displays a C 1s spectrum with different post-fabrication treatments, clearly showing similar peak positions and shapes. This indicates that any carbon contamination is only attributed to environmental factors and not leftover polymer contamination from the fabrication process. The Si 2p spectrum (Fig. 2B) demonstrates an increase in SiO₂ composition compared to ozone treatment alone, indicating that oxygen plasma increases the SiO₂ concentration at the substrate-air interface. In Fig. 2C, the O 1s spectrum shows an additional peak at 529.85 eV for the Nb-O sample, corresponding to Nb metal hydroxide. This indicates a significant change in the surface metallic oxide composition due to oxygen plasma treatment. Furthermore, Fig. 2D depicts a decrease in the intensity of the low binding energy peak corresponding to the metallic Nb at 201 to 204 eV, indicating that oxygen plasma exposure increases the oxide thickness of the fabricated Nb film. These observations collectively suggest that while oxygen plasma treatment changes the chemical composition of metal surface oxide, it does not have a notable impact on the oxide composition of the bulk Nb film.

A cross-sectional TEM image provides a clear view of the effect of oxygen plasma exposure on the Nb film surface native oxide and bulk interfaces. Figures 3A&B show cross-section images of Nb surfaces treated with ozone and oxygen plasma. These images demonstrate that the native oxide thickness increases by 2.0 nm after exposure to oxygen plasma for 6 minutes, consistent with the XPS results presented earlier. The ozone-treated Nb film showed an interplanar spacing of 2.22 Å, which is smaller than the standard out-of-plane orientation of Nb crystal [110] interplanar spacing of 2.34 Å. This suggests that there is an internal compressed stress present on the patterned Nb-O resonator structure. However, the Nb film sample exposed to 6 minutes of oxygen plasma had an interplanar spacing reaching the standard value of 2.35 Å, indicating that the oxygen plasma treatment slightly released the compressed stress in the Nb film. To further understand the effect of oxygen plasma treatment, we investigated the low-temperature superconducting T_c, as shown in Fig. 4A. The T_c is extracted from the typical phase transition signature in the resistance vs temperature curve. The measured T_c is 9.02 K for Nb-O and 8.98 K for Nb-OP, close to the bulk T_c of 9.35 K,³⁷ and similar to the previously reported high-quality Nb film deposited using the PVD method.³⁸ The observed close and similar T_c for both patterned and exposed ozone and oxygen plasma further confirms that quasiparticle formations are expected to be low, as mentioned in the introduction. We observe a slight decrease in the T_c after exposure to oxygen plasma treatment. This decrease is attributed to a 2.0 nm increase in surface oxide thickness. Additionally, the relative resistance ratio of the Nb-OP films (4.83) slightly increases compared to the Nb-O film (4.67). This confirms that as the film surface roughness decreases, the low-temperature resistance decreases due to less surface scattering. These results confirm that the T_c value depends on the material properties, precisely the difference in oxide thickness. In contrast, the relative resistance ratio may depend on the surface quality of the film.

Figure 4B illustrates the microwave transmission response of the Nb-O sample at 1.2 K, revealing six distinct dips corresponding to the designed resonators at a photon number 10⁹ on the measured chip. However, some chips exhibit inconsistencies in resonator presence, which we attribute to environmental factors such as dust particles adsorbed near the resonator conductor lines during assembly or wire-bonding processes. The yield of working resonators varied for each chip but always exceeded > 90%, the previously reported yield of ≥ 50% by Drimmer et al.³² Before the assembly process, it is crucial to ensure the absence of dust particles and fabrication defects near or around the resonator conductor lines. Through careful investigation and optical inspection of the fabricated chip, we aim to either improve or avoid missing resonators on a single chip. Figure 4C presents a high-resolution view of a single sampled resonator scan and a fitted line using a previously reported fitting procedure³⁹ (see the detailed description in Annexure 1&2 and corresponding Equation S1) to extract each resonator's Qi. To comprehend the variation in quality factor across a single chip, we measured three randomly chosen chips sourced from separate wafers and diverse locations on those wafers. The plot of all the Qi’s, combined with their respective standard deviation obtained from the three independent chips at each specific frequency, reveals a change in the Qi as a function of the frequency. To understand the high-frequency drive couples to the defects on the thin film surface, which are area-dependent, we plotted the Qi as a function of the resonator interface surface area (Fig. 4D). In particular, we are focused on the Nb vacuum/air interface, henceforth called the top interface, while keeping all other interfaces unchanged. The resonators in this study are designed for frequencies between 4 to 6 GHz, corresponding to length variation from 16 to 9 mm, respectively. In the low-frequency (correspondingly larger top-interface area), the smoother samples (Nb-OP) always show higher Qi than their rougher (Nb-O) counterparts. As the top-metal/air interface area becomes smaller (higher frequency), the Qis are independent of the smoothness of the interface. This could be explained by considering the total loss, which is the inverse of the internal quality factor. This is contributed by three components of resistance arising from TLS (R_TLS), QP (R_QP), and a residual (R_res) in an additive manner (see detailed discussion in Annexure 3). The TLS is temperature dependent and only becomes significant for temperatures in the mK range, and at low power, the R_QP is substantial at our operating temperature (1.2 K); however, it is related to the bulk property and hence volume. On the other hand, the R_res originates from the surface resistance originating from different sources, including fundamental residual surface resistivity from boundary states as given by BCS theory, surface defects/grain boundaries, and, more recently, postulated edge boundary states.⁴⁰ The first one is a fundamental limit, but the other two are technical in origin, and it is not easy to distinguish their contribution as they impact the R_res in the same way. The samples, Nb-OP and Nb-O, show different roughness, leading to significantly different residual surface resistances and, consequently, different internal quality factors. Furthermore, for the rough Nb-O samples, we show an area dependence as expected from theory and also observed in our experiment.

In this study, we investigated the influence of surface roughness on the internal quality factor of the resonator. We assessed the impact of microwave-induced loss as a function of frequency, specifically on the area of the microwave conductor. Our findings demonstrate the significant role of surface roughness in microwave-induced quasiparticle loss within microwave resonators. Notably, removing surface roughness significantly reduces quasiparticle loss as a function of frequency, which is directly related to the area of the conductor. These results highlight the critical importance of surface roughness control on the superconductor film to minimize the spread in the resonator quality factor across a single chip. This, in turn, facilitates the integration of uniform quality factor readout in superconductor-based systems, offering valuable insights for improving such devices' overall performance and reliability.

Resonator design and fabrication

We fabricated co-planar waveguide (CPW) resonators by patterning an Nb thin film grown on a high-restive Silicon (Si) with crystalline orientation of [100] substrate. The resonators are designed as λ/2-wave geometry and capacitively coupled to a continuous CPW feedline for transmission power and phase measurements. Specifically, we selected a centerline with a width of 22 µm and a gap of 11 µm with a minimum dielectric loss tangent of a silicon substrate^41–43, and the resonators consist of a capacitively isolated section of a 50Ω transmission line, as illustrated in Fig. 1A. These resonators are designed for resonant frequencies ranging from 4 to 6 GHz. We used aluminium wire bonding on the feedline of the resonators to minimize slot mode effects.⁴⁴ The CPW resonators were fabricated by physical vapor deposition (PVD) grown Niobium with a preferred orientation of [110] on a 4-inch silicon wafer with a resistivity of > 5k ohms.cm followed by a standard fabrication process. First, the Si wafer was cleaned for 60 seconds in buffered hydrofluoric acid solution with a ratio of 7:1 of ammonium fluoride (NH₄F) and hydrofluoric acid, followed by washing deionized water to remove contaminants and native oxides on the Si-wafer surface. The wafer is loaded into the ultrahigh vacuum PVD system with a process chamber base pressure of < 5 × 10^− 8 Torr within 20 min after cleaning. A 100 nm thick layer of Nb thin film was deposited using the TIMARIS cluster tool-deposition system with a source power of 1.4 kW, chamber pressure of 0.003335 mbar, argon gas flow rate of 400 sccm, substrate temperature maintained at 25^◦C, and with this condition we achieved the deposition rate of 10 nm/min. An in-situ argon plasma cleaning was performed on the substrate in a separate pre-cleaning chamber. Subsequently, the cleaned substrate is transferred to the deposition chamber for the Nb deposition process. The resonator structure on the Nb layer was developed by optical photolithography, followed by a dry etching process. First, we spin-coat a positive photoresist (S1818) from MicroChem at 3000 rpm for 70 sec to define the CPW patterns using an MA6 mask aligner. After exposure, the resist is developed using MF-319 developer and gently rinsed with deionized water. Finally, the rinsed wafer is dried using a flow of dry N₂ gas. The ICP-RIE Oxford system is used to etch the unwanted Nb thin film using CH₄ gas before the dry etching process, and the oxygen plasma cleaning process is used to remove photoresist residues from the developed area. This oxygen plasma cleaning step ensures that the following Nb metal etching step was not hindered by residual photoresist on the surface. After the etching process, the wafer was immersed in NMP solution at 80^◦ C for 3 hours to remove the resist. To safeguard the patterned Nb chip from dust generated during the dicing process, a layer of photoresist (S1818) is applied. After dicing, each chip is cleaned with acetone and IPA, followed by a 10-minute UV-ozone cleaning process named Nb-O. The other samples are exposed to oxygen plasma using mini-RIE at 100W power and 50 sccm flow rate at different intervals, referred to as Nb-OP. These samples are further characterized and subjected to cryogenic measurements.

Surface characterization

The surface morphologies of Nb film exposed with ozone and after oxygen plasma exposure were obtained using the Bruker Dimension FastScan AFM with tapping mode tips (FASTSCAN-A). The AFM software NanoScope Analysis (version 1.4) was used to analyze the AFM images to get surface roughness and pinhole depth on the Nb film surface. The effect of change in Nb film's crystal structure and phase formation before and after oxygen plasma exposure was measured using XRD (D8 advance Bruker). The surface chemical composition of the Nb thin film and the change in the surface oxide composition of the Nb film after exposure to oxygen plasma treatment was characterized by XPS. The spectra were measured using a VG ESCA lab-220i XL XPS system equipped with a monochromatic Al Kα X-ray source with a photon energy of 1486.6 eV at 15 kV. High-resolution spectra were collected at a pass energy of 20 eV, with 0.1 eV steps, at a 45◦ takeoff angle. The binding energies were corrected against the Carbon 1s energy of 285.0 eV. The collected XPS high-resolution spectra were analyzed using XPS Peak fit 4.1 software with Voigt function. Shirley-type backgrounds were subtracted from each spectrum to remove most of the extrinsic loss structure.

TEM sample preparation and data collection

The Lamellae samples were prepared with a FEI Helios 600 dual-beam focused-ion-beam. To protect the surface oxide during the ion milling process, the sample was first coated with 50 nm of carbon. The primary Ga + ion beam was operated at 30 kV. The samples were finely polished to a thickness of roughly less than 100 nm using 5 kV Ga⁺ ions to remove surface damage and amorphization in the regions of interest. For final sample cutting, samples were coated with carbon and gold to reduce the charging effect. For transmission electron microscopy (TEM) imaging, we used a 200 kV FEI Tecnai G2 F20 X-Twin system equipped with EDAX Octane Elite TW55 EDS detector with a detection angle of 0.9 srad.

Critical temperature measurement

To determine the transition temperature of the Nb film, we measured the resistance across deposited and patterned Nb films inside an ICE Oxford cryogenic fridge. We used Python code to record the fridge temperature as a function of time as we slowly heated and cooled down the sample across the critical temperature. At the same time, we recorded the resistance vs time values by automatically fitting the current-voltage sweeps measured with a source measure unit (Keithley 2450) controlled by Python software. This was necessary to reduce errors due to environmental voltage offset. By synchronizing both records, we obtain the resistance as a function of temperature.

Resonator quality factor measurements

In this study, all devices were characterized using a vector network analyzer (Rohde & Schwarz ZNL14) connected to a DRY ICE 1.0 K Cryostat from Oxford Instruments with a base temperature of approximately 1K. The measurement setup included a customized PCB for the wire bonding of the sample, and the PCB was connected to fridge RF cables for the measurements. The samples were connected to the VNA through RF cables, and measurements were automated using Python script. A series of S21 transmission measurements were performed to characterize the resonators. Initially, a broad frequency transmission sweep was conducted to identify all the resonators, using the wide frequency scan from 4 to 6 GHz with a step of 20 kHz, a bandwidth of around 100 Hz, and a total integration time of approximately 40 minutes at a constant input power of -40 dBm. For the transmission spectrum of a single resonator, 1001 points were used with a frequency span of 1 MHz and a bandwidth of 500 Hz. The averaging samples/cycles were set to 100 to improve the signal-to-noise ratio. In these experiments, we did not use magnetic shielding.

Supporting Information

Supporting Information is available from the Wiley Online Library.

Acknowledgments

This research was done by the National Research Foundation, Singapore, and A*STAR under its Quantum Engineering Programme (NRF2021-QEP2-02-P10 and NRF2021QEP2-03-P07).

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