Fabrication

This section provides a detailed description of our sample fabrication process, which is an adaptation of the recipe described in ref. ¹⁶ to the chemicals and equipment available to us. Notable differences include the choice of CF₄ as the processing gas for Nb etching, which improves the reproducibility of the etch, and the pre-dicing of the sample between the Al evaporation and lift-off, which minimizes the exposure of the sample to the ambient atmosphere. The pieces of equipment used in our process are listed in Supplementary Table 2.

Substrate and niobium patterning

The sample is fabricated using a 675-μs-m-thick 6-inch (100)-oriented high-resistivity ( > 10 kΩcm) intrinsic-silicon wafer sourced from Siegert Wafer. The pre-cleaning of the wafer follows ref. ³¹ and begins with an RCA solvent clean. The wafer then undergoes a dip in dilute hydrofluoric (HF) acid (1:100) for 1 min. After being rapidly transferred to the sputtering tool to minimize exposure to the ambient atmosphere, the wafer is baked at 300 °C under vacuum. The sputtering of a 200-nm Nb film is carried out near room temperature and at 2600-W power. The sputter target has a purity of 99.998%. After the sputtering, the wafer is coated with a protective layer of AZ 5214E photoresist and diced into 25 mm × 30 mm rectangular coupons with a dicing saw.

The resonators, coplanar waveguides, ground plane, and transmon capacitors are patterned as described below. The selected coupon is sonicated in acetone and isopropyl alcohol (IPA) for 3 min each to remove the protective resist layer and dried with a nitrogen gun. The sample is then dehydrated on a hotplate at 110 °C for 1 min, spin-coated with AZ 5214E photoresist at 4000 rpm, and baked at 110 °C for 1 min to achieve a coating thickness of 1.4 μm. The photoresist is exposed using a maskless aligner with a laser wavelength of 405 nm and a dose of 130 mJ/cm². Subsequently, the photoresist is developed in AZ 726MIF for 1.5 min and rinsed in deionized water (DIW) for 1.5 min.

The Nb film is patterned in a plasma processing system by a chemical dry-etching process, clearing the areas revealed by the resist development step. Immediately before the process, the empty plasma chamber is cleaned with a combination of CF₄ and O₂ gases for a total of 5 min. We then load the sample into the chamber and apply oxygen plasma ashing for 10 s at 100-mTorr chamber pressure, 40-sccm gas flow, and 150-W rf source power to remove the post-development residue of photoresist on the sample surface. Then, we pump out the oxygen and introduce CF₄ at 50-mTorr chamber pressure, 20-sccm flow, and 30-W source power. To ensure that the Nb film is fully etched, we carry out an additional etch after unloading, visually inspecting, and re-loading the sample. The etch rate of Si is significantly lower than that of Nb, which helps us to achieve convenient control of the etch depth. The typical total etching time of Nb film is around 10 min. After the etching process, we remove some of the residual chemicals by applying another oxygen plasma ashing for 2 min without breaking the vacuum.

The photoresist is removed by immersing the sample in an N-methylpyrrolidone (NMP)-based solvent Remover PG at 80 °C overnight and sonicating it in the same Remover PG, acetone, and IPA for 3 min each. Subsequently, the sample is dried with a nitrogen gun and plasma-ashed again for 2 min. Using a profilometer, we measure the etch depth to be 250 nm, which implies that the Si substrate is etched by 50 nm.

Electron-beam lithography

In order to remove the oxide layers on the Nb and Si surfaces, we immerse the sample in dilute HF acid (0.5%) for 10 min and rinse it in DIW for 5 min³². The sample is then carried to a spin coater while immersed in fresh DIW to minimize its exposure to the ambient atmosphere. After spin-drying the sample, we immediately spin coat the methyl methacrylate (MMA) EL11 copolymer resist (11% solid content in ethyl lactate) at 4000 rpm, bake it at 180 °C for 5 min, and cool it for 3 min. Then we coat the sample with polymethyl methacrylate (PMMA) 950 A4 resist (950,000 molecular weight, 4% solid content in anisole) at 1000 rpm and bake it at 180 °C for 5 min. This creates a two-layer resist stack with approximately 500 nm of MMA and 400 nm of PMMA.

The resist mask for Manhattan-style Josephson junctions is patterned onto the resist stack using an electron-beam writer with 100-kV acceleration voltage, 300-μm aperture, and 0.5-nA beam current. We use a dose of 1000 μC/cm² to define the junction structure in both the PMMA layer and the MMA layer. In addition, we use a dose of 400 μC/cm² to define an undercut at each end of the line-like structures for the junctions. The undercut serves to separate the aluminum junction evaporated onto the Si substrate from the MMA side walls. We use a mask pattern very similar to that of ref. ¹⁶ to define the Josephson junctions. The electron-beam resist is developed by immersing the sample in methyl isobutyl ketone (MIBK):IPA (1:3) solvent for 5 min, rinsing it in IPA for 1 min, and drying it with a nitrogen gun.

Junction deposition

The Josephson junctions are deposited using an ultra-high-vacuum electron-beam evaporator with separate load-lock, oxidation, and evaporation chambers. After loading the sample, we pump the system for 14 h to reach a load-lock chamber pressure below 10⁻⁷ mbar. Subsequently, we carry out ozone ashing at 10 mbar for 1 min to remove a thin layer of resist residues.

After the ozone cleaning, the load-lock chamber is pumped again to a high vacuum ( < 10⁻⁷ mbar), and the sample is transferred to the oxidation/evaporation chamber. To fabricate the junctions, we evaporate Al at the rate of 0.2 nm/s at tilt and in-plane rotation angles specific for each of the four Al line strips as discussed below. Prior to each Al evaporation step, the oxidation and evaporation chambers are getter-pumped by evaporating Ti with a closed shutter at the rate of 0.1 nm/s for 2 min and waiting for the chamber pressure to decrease below 5 × 10⁻⁸ mbar.

For the bottom layer of the junctions, we deposit 40 nm of Al at θ = 45° tilt and ϕ = − 45° planetary angle. Then we create the insulating aluminum oxide layer by static oxidation at 1.2 mbar for 5 min. During the oxidation, the aluminum source is protected from the oxidation by a valve that blocks the oxygen flow. After the oxidation, we deposit the second Al layer in two steps with θ = 45° tilt and two planetary angles: first 30 nm at ϕ = 45° and then 30 nm at ϕ = −135°. This ensures that both sides of the oxidized bottom strip are covered by the second Al layer.

In order to ensure a galvanic contact between the Josephson junctions and the Nb capacitor pads, we transfer the sample to the load-lock chamber and carry out argon milling with θ = 45° tilt at two planetary angles ϕ = ± 90° for 2 min each at 10-sccm gas flow, 400-V beam voltage, 60-mA beam current, and 80-V acceleration voltage. This removes any Nb surface oxide that has grown in the areas exposed after the electron-beam resist development^33,34. After the argon milling, the sample is transferred back to the oxidation/evaporation chamber, where we deposit the connecting leads between the junction and the Nb pads in three steps with 30/60/60-nm thicknesses, θ = 45° tilt and ϕ = 180°/0°/180° planetary angles.

As the final step, the sample is transferred back to the load-lock chamber and oxidized at 20 mbar for 10 min to create a clean oxide layer on top of the junctions before exposing the sample to the ambient atmosphere.

Dicing and liftoff

After the Josephson junction deposition, we coat the sample with a protective layer of AZ 5214E photoresist and pre-dice the sample with a dicing saw, cutting two-thirds deep of the substrate thickness. Before attaching the sample to the dicing tape, an ionizer fan is applied to the tape to reduce the possibility of electrostatic-discharge damage on the sample. By pre-dicing the sample prior to the liftoff, we can skip one of the resist removal steps carried out in ref. ¹⁶.

The pre-diced sample is immersed in Remover PG at 80 °C for 3 h, after which large Al flakes can be removed from the beaker using a pipette. The sample is sonicated in the same Remover PG, acetone, and IPA for 3 min each. From IPA, the sample is quickly dried with a nitrogen gun and immediately transferred to a vapor prime oven that applies a monolayer of hexamethyldisilazane (HMDS) on the sample surface, which may help to slow down the post-fabrication oxidation of the Nb and Si surfaces. The oven also has the effect of annealing the sample at 150 °C for a total of 20 min under vacuum and nitrogen environments.

The critical currents of the fabricated junctions are estimated by measuring their room-temperature resistances using a probe station. The critical currents for the sample measured in this work are significantly smaller than we had targeted, which led to low E_J/E_C ratios, as low as 20 for qubit Q₂. The sample is then manually cleaved into separate chips utilizing the cuts established with the dicing saw, and selected chips are taken for further characterization.

Setup for qubit measurements

Our experimental setup used for qubit characterization and measurements is presented in Fig. 4, with detailed information on measurement equipment and components provided in Supplementary Table 3. The sample is wire-bonded to the printed circuit board (PCB) of a QCage.24 sample holder and placed inside QCage Magnetic Shielding, both of which are supplied by QDevil (under Quantum Machines). The chip is suspended by four corners inside a cavity and clamped down by the PCB. The assembly is placed inside a light-tight superconducting aluminium enclosure to reject stray microwave and infrared photons before being mounted inside the magnetic shield. The sample is exposed to ambient atmosphere at room temperature for a total of 7 days. It is then cooled down to approximately 10 mK in a Bluefors dilution refrigerator equipped with a tin-plated copper shield at 10 mK and an Amumetal magnetic shield just inside the outer vacuum chamber (OVC). We directly generate the qubit control and readout signals without any analog mixers by using a Xilinx RFSoC evaluation board with QICK firmware^35,36 locked to a Rb frequency standard. The signals then pass through rf attenuators, an Eccosorb infrared filter, and a low-pass filter before reaching the sample. The readout signal coming out of the sample goes through a three-wave-mixing Josephson traveling-wave parametric amplifier (TWPA), a cryogenic high-electron-mobility-transistor (HEMT) amplifier, and a room-temperature HEMT amplifier before being digitized by RFSoC. During the first cooldown, the TWPA is not pumped and therefore does not provide any amplification.

After the first cooldown, we reconfigure the attenuators as described in the caption of Fig. 4 before starting another cooldown. During the second cooldown, we compare measurements with and without a pump signal applied to the TWPA. The 10.5-GHz pump signal passes through a 4–12 GHz circulator, reflects from a 8-GHz low-pass filter, and travels through the circulator again before reaching the TWPA. This configuration allows us to combine the pump and readout signals without the power dissipation of a directional coupler or the impedance mismatch of a diplexer.