Device fabrication and charge control
The natSi/SiGe heterostructures are grown on a 300 mm silicon wafer. From bottom to top, the heterostructure comprises a 8 μm strained relaxed buffer (SRB) finished by an unstrained 1 μm Si0.75Ge0.25 layer of constant concentration. This is followed by chemical vapour deposition (CVD) of a tensile-strained natSi quantum well of 9 nm and a Si0.75Ge0.25 buffer layer of 40 nm thickness. To avoid oxidation of the SiGe buffer, a 2 nm thick silicon cap is grown on top of the heterostructure. Ohmic contacts to the natSi quantum well are formed by phosphorus implants. Three overlapping gate layers made of titanium nitride (TiN) and insulated by silicon oxide (SiO2) (From bottom to top: 8 nm SiO2, 30 nm TiN, 5 nm SiO2, 20 nm TiN, 5 nm SiO2, 20 nm TiN) are used for the formation and manipulation of the quantum dots. More details regarding the gate-stack lithography can be found in ref. 21. A cobalt micromagnet (CoMM) module is made in line using a so-called Damascene process, as commonly used in back-end-of-line processing. A full sheet of oxide and photoresist is deposited across the 300 nm wafer. Next, the photoresist is patterned using deep ultraviolet (DUV) lithography. Following this, a gap is etched into the oxide using dry etching techniques. Subsequently, a full sheet of cobalt is deposited on the 300 nm wafer. Finally, the wafer undergoes chemical mechanical polishing (CMP) down to the oxide layer. A SiO2 passivation layer is deposited on top of the whole stack. Vias are etched in this passivation layer to connect the ohmics, gate layers and the CoMM (see Fig. 1a). The gate layout of the device is shown in the false coloured scanning electron microscopy (SEM) picture in Fig. 1b. The architecture is designed to enable the formation of two quantum dots in the single electron regime, later used as qubits, and an adjacent single electron transistor (SET) for readout. The qubit dots are centred below the gap of a C-shaped CoMM, which creates an inhomogeneous external magnetic field at the qubit positions. By applying a microwave signal at the central screening gate (CC), the position of the qubit dot will oscillate, effectively creating an AC magnetic field with the frequency of the applied microwave signal22. Figure 1c shows the measured tunnel current through the right qubit quantum dot over varying voltages applied at the plunger gate PR. Coulomb oscillations of the measured current become visible. It was shown that the charge noise affecting a quantum dot can strongly differ for different working points21. In order to extract a value for the charge noise, we measure the power spectral density at four different working points individually. Figure 1d shows the power spectral density at the marked working point, which follows a 1/f proportionality often observed for charge noise in semiconducting quantum dot devices23,24. The mean charge noise value at 1 Hz from the four working points results to (1.36 ± 0.07) μeV/\(\sqrt{{\rm{Hz}}}\) (for more details see Methods III B). Figure 1e shows the measured sensor current while varying both qubit plunger gate voltages. The sensor current jumps every time the electron occupation of the qubit dots changes. This charge stability diagram enables precise control of the charge state of the qubits, starting from zero electron occupation in the bottom left, up to multiple electrons in both dots in the upper right.
Spin relaxation and valley splitting
By applying an external magnetic field in x-direction, the ground state degeneracy of the electron spin state is lifted via the Zeeman effect. By tuning the quantum dot potential to an energy level between the Zeeman-split spin-down and spin-up states of the electron, a spin selective readout becomes possible. This is demonstrated in Fig. 2a, where the measured sensor current jumps between two distinct values in case of a spin-up event, or stays constant for an electron in the spin-down state. The spin relaxation time can be measured by a three stage pulse scheme25, incorporating the spin selective readout mentioned before. In the first stage the quantum dot is emptied. In the second stage, the quantum dot potential is pulsed deep below the chemical potential of the reservoir to enable the possibility for a tunnelling electron to occupy either the ground or excited spin state. And in the third stage the quantum dot is pulsed to a level where the reservoir lies between the ground and excited spin state, to perform the spin selective readout. By varying the duration of the loading pulse, we increase the available time for a spin relaxation process to occur, which is dominated by spin-phonon interaction26,27,28. Figure 2c shows the measured spin-up fraction of 500 single shot readouts performed for different waiting times in the loading stage, at an external magnetic field of 660 mT, which is later used for qubit manipulations at resonance frequencies of ≈18.5 GHz. The spin-up fraction over waiting time is proportional to \(\exp (-t/{T}_{1})\), and the fit results in a spin relaxation time of T1 = (1.09 ± 0.20) s.
a Measured real time SET current for a spin-up electron (blue) compared to a spin-down electron (orange). b Numerical derivation of the SET current tracking the 1 → 2 electron transition of the qubit dot for external magnetic fields up to 2.5 T. The barrier gate B is used as plunger gate because of the lower lever arm on the dot potential. The change in slope of the tracked transition occurs at the external field, which is equal to the two-electron singlet-triplet splitting. In the regime of strong confinement, this singlet-triplet splitting is almost equal to the valley splitting. Linear fits to the range from 0 T to 0.4 T and 1.3 T to 2.5 T result in a crossing at (0.73 ± 0.08) T which is equal to a valley splitting of (85 ± 9) μeV. c Elzerman pulse sequence for varying waiting times of the loading pulse at an external magnetic field of 0.66 T. The exponential decay corresponds to a spin-relaxation time T1 = (1.09 ± 0.20) s. d Spin relaxation rate 1/T1 over external magnetic field. The black curve shows a fit combining Johnson noise and spin-phonon interaction diverging at the value corresponding to the valley splitting energy. The fit diverges at an external field of (0.76 ± 0.01) T resulting in a valley splitting of (88 ± 1) μeV.
Another important quantity for Si/SiGe heterostructures is the valley splitting energy of the two lowest valley states27,29,30. The conduction band minimum of silicon is normally sixfold degenerate. Straining the Si quantum well between the two SiGe layers splits the degeneracy in two energetically favourable valley states and four excited valley states. The degeneracy of the two lowest valley states gets further lifted by electrical confinement of the electron wave function, and strongly depends on sample geometry and local inhomogeneities31,32. To measure the valley splitting at the position of the qubit quantum dot we performed two different measurements. In Fig. 2b, the plunger gate voltage of the qubit quantum dot is varied for different total external magnetic fields. The colour axis represents the numerical derivation of the measured current through the sensor dot. The gate voltage window required for the transition from 1 to 2 electrons inside the dot is shown. The exact position of the 1 → 2 electron transition shows a change of slope at an external field strength where the Zeeman energy is equal to the two-electron singlet-triplet (ST) splitting. In the strongly confined regime, where the valley triplet has lower energy than the orbital triplet, the measured ST splitting is then nearly equal to the valley splitting33,34. To extract the two slopes, we fit the data in the 0 to 0.4 T interval and the 1 to 2.5 T interval separately and receive a crossing of both lines at (0.73 ± 0.08) T, which corresponds to (85 ± 9) μeV. Another method is by measuring the spin relaxation time over magnetic field. Here we observe a drastic decrease of the T1 time, visible as a peak of the spin relaxation rate 1/T1, at the position where the Zeeman energy is equal to the valley splitting energy. We fit a rate equation that accounts for spin-valley mixing and intra-valley spin-orbit interaction in combination with phonon noise and Johnson noise27,35,36. The fit gives a peak position of (0.76 ± 0.01) T which results in a valley splitting of (88 ± 1) μeV. Both extracted values for the valley splitting are similar and correspond to a frequency above 20 GHz.
We report room-temperature Gate-to-Gate leakage tests conducted on 18 devices per die, across 13 different dies, resulting in a total of 234 tested devices with the gate architecture shown in Fig. 1b. Among these, 13 devices exhibited Gate-to-Gate leakage, resulting in a Gate yield of 94.5%. For quantum dot and qubit yields, characterisation must be performed at low temperatures. However, we currently lack a large-scale testing infrastructure for this purpose. For qubit measurements, we examined four different devices, all selected from those that did not exhibit Gate-to-Gate leakage. All four devices successfully enabled quantum dot formation and coherent spin manipulations. In the following, these four devices are labelled A to D. Device A has a CoMM gap size of 300 nm, Device B has a CoMM gap of 400 nm, and Devices C and D have CoMM gaps of 650 nm. Additionally, Devices A, B, and C originate from the same 300 mm wafer, while Device D stems from a separate wafer. In the following, all shown measurements were performed on the right qubit dot of device A (measurements of Devices B, C, and D are provided in the Supplementary Information).
Cobalt micromagnet magnetisation
Figure 3a shows a SEM image of a C-shaped CoMM with a 300 nm gap, as featured in Device A. The Co layer has a thickness of 250 nm, is encapsulated in SiO2 and connected to a via in order to ground the micromagnet. The quantum dots are positioned in the centre of the gap ~120 nm below the CoMM. Simulations regarding the geometry and field strengths/gradients were performed in ref. 37. To characterise the behaviour of the CoMM, we measure the qubit resonance frequency for different external magnetic fields, as depicted in Fig. 3b. The resonance frequencies are extracted by first ramping the external field to its maximum value to fully saturate the CoMM and then ramping the field down to zero. The two branches corresponding to positive and negative fields are measured independently, and a linear fit of the resonance frequencies between 15 and 20 GHz yields the same y-offset of (129 ± 2) mT for both branches, which corresponds to the external field contribution in the y-direction of the CoMM in saturation.
a Scanning electron microscopy image of a cobalt micromagnet with a 300 nm gap. The image was taken from an angled viewpoint, so the lengths in the y-direction appear smaller than in the x-direction. The blue dots and black arrows indicate the position and oscillation direction of the qubit quantum dots, which are located in the quantum well ~120 nm below the CoMM. b Resonance frequency of the right qubit in Device A as a function of the applied external magnetic field in y-direction. The frequencies are extracted starting from the maximum external field and decreasing to zero. The two branches for positive and negative fields are measured independently. The black lines correspond to a linear fit of all resonance frequencies between 15 and 20 GHz. The contribution of the CoMM field in saturation is extracted from the y-offset of the linear fit and yields a field of (129 ± 2) mT. c Zoom on the positive magnetic field branch shown in (b), to which qubit resonance frequencies extracted from an upward magnetic field sweep have been added. The inset shows a zoom of the lowest measured resonance frequencies. d Difference in qubit resonance frequencies between the upward and downward sweep direction of the external magnetic field.
Figure 3c shows a zoom-in on the positive magnetic field branch, to which qubit resonance frequencies from an upward magnetic field sweep have been added. For external magnetic field values below 0.3 T, the extracted resonance frequencies deviate from the linear fit. Moreover, the extracted qubit resonance frequencies vary depending on the magnetic field sweep direction and the sequence of measurements. The inset shows a zoom of the lowest measured resonance frequencies, where the deviation is greatest. We attribute this deviation to the CoMM magnetisation no longer being fully saturated, which is further evidenced by the hysteretic behaviour of the magnetisation in these magnetic field ranges. We were unable to resolve resonance frequencies below 8 GHz, a limitation we attribute to the decreasing magnetisation of the micromagnet and its field gradient, which is needed for the EDSR drive.
In Fig. 3d, the difference in qubit resonance frequencies between the upward and downward sweep directions is depicted. For external fields of 0.2 T, a resonance frequency difference of approximately 200 MHz is measured, which converges to zero for externally applied magnetic fields above 0.45 T, where the CoMM magnetisation is fully saturated.
Single qubit characterisation
For the measurements displayed in Fig. 4, every extracted spin-up fraction is the result of 200 single shot readouts. Figure 4a shows the spin-up fraction over manipulation pulse duration at qubit resonance frequency of 18.501 GHz. Typical Rabi oscillations become visible. Fitting the oscillations gives a Rabi frequency of 5.2 MHz for an applied RF microwave power of 24 dBm. Figure 4b displays the spin up fractions for different microwave source output powers in dBm over pulse duration, and Fig. 4c shows the extracted Rabi frequency for the respective microwave amplitudes (10 to 23 dBm subtracted by 45 dB inline attenuation and converted to mV). The Rabi frequencies follow a clear linear behaviour over increasing microwave amplitude up to values above ≈14 mV, where a saturation starts to set in. The black line corresponds to a linear fit of the data excluding the resulting Rabi frequencies for the 5 highest amplitudes. Saturation is a sign of a different qubit drive regime, which could be caused by either a lower magnetic field gradient for higher RF amplitudes or a strong quantum dot confinement in the x-direction, dampening larger displacements of the quantum dot position. Figure 4d shows a Ramsey measurement where the waiting time τ between two π/2 pulses is varied. A fixed detuning of 2 MHz creates an additional z-rotation on the Bloch sphere during the waiting time τ at that frequency. Fitting the oscillations with a sine multiplied by a \(\exp (-{(t/{T}_{2}^{* })}^{2})\) term gives a coherence time \({T}_{2}^{* }=(1.05\pm 0.08)\,\mu {\rm{s}}\), similar to the reported values in other natural silicon spin qubit devices38 and consistent for all four measured qubit devices in this work (see Supplementary Information). Figure 4e displays the results for a Hahn echo experiment, fitted with \(\exp (-{(t/{T}_{2}^{{\rm{H}}})}^{\alpha })\). The extracted \({T}_{2}^{{\rm{H}}}\) equals (51.24 ± 1.49) μs with an exponent α = 2.06 ± 0.17 corresponding to a gaussian damped exponential decay, observed in systems where the dominant decoherence mechanism follows a 1/f frequency dependence23,39,40. The comparison between \({T}_{2}^{* }\) and \({T}_{2}^{{\rm{H}}}\) shows the frequency dependence of the dominant decoherence channel, indicating that the noise amplitudes increase to lower frequencies. Considering the abundance of nuclear spins of 29Si isotopes in natural silicon, it was demonstrated that fluctuating nuclear spins in the vicinity of the qubit are the dominant decoherence mechanism4,30. Isotopic enrichment of 28Si can therefore drastically reduce this low-frequency decoherence channel and thus increase the \({T}_{2}^{* }\) time by orders of magnitude12,20,41. To measure the single qubit gate fidelity, we performed randomised benchmarking experiments. For this, starting from a defined initial state, a random sequence of n Clifford gates is performed. A final gate ideally brings the qubit back to a desired final state for readout. With increasing n the probability to reach this desired final state will decrease due to gate errors, and finite qubit lifetimes. By fitting the deviation of the ideal final state over the length n of the random sequence, we can extract the single qubit gate fidelity. To increase the robustness to readout working point deviations, we perform each random gate sequence with a final projection into the spin-up state and a final projection into the spin-down state, and subtract the resulting spin-up probabilities from each other to obtain the difference Pup − Pdown between the two final states. This difference starts at a maximum value for a small n and converges to zero for large n, where the quantum information is completely lost. In the experiment the primitive gate set {I, ± X, ± Y, ± X2, ± Y2} is used to construct all 24 single qubit Clifford gates, where a Clifford gate consists in average of 1.875 primitive gates (for details see supplemental materials). Figure 4f shows the result of the performed randomised benchmarking. Each measured Pup − Pdown value is the result of 40 randomised gate sequences of length n and is fitted with A ⋅ Pn from which we extract the gate fidelity F = 1 − (1 − P)/2. For the primitive gate fidelity, we extract a value of (99.2 ± 0.1)% which converts to a Clifford gate fidelity of (98.5 ± 0.1)%.
a Rabi measurement on resonance with 24 dBm output power up to a pulse length of 1.5 μs. A Rabi frequency of 5.2 MHz is extracted by fitting a sine function to the data. No dampening of the frequency amplitude is visible up to this pulse length. b Same measurement as in a for varying RF output powers. c Extracted Rabi frequencies for all used powers of the measurement shown in b over the applied power converted to the correspinding microwave amplitude in mV. The black line corresponds to a linear fit excluding the 5 data points of highest applied power (marked in red). d Ramsey measurement for a fixed detuning of 2 MHz. The black curve corresponds to a gaussian damped sine and gives a \({T}_{2}^{* }\) value of (1.05 ± 0.08) μs. e Spin-echo measurement fitted with \(\exp (-{(t/{T}_{2}^{{\rm{H}}})}^{\alpha })\), yielding \({T}_{2}^{{\rm{H}}}=(51.2\pm 1.5)\, {\upmu}{\rm{s}}\) with α = 2.06 ± 0.17. f Difference of spin-up and spin-down fraction depending on the length of a randomised gate sequence. The black curve corresponds to a fit of the form A ⋅ Pn which yields the primitive gate fidelity F = 1 − (1 − P)/2 = (99.2 ± 0.1)%.
In conclusion, we demonstrate the formation and operation of EDSR qubits in natural Si/SiGe heterostructures fully fabricated and grown in a 300 mm industrial semiconducting wafer process line. We report a charge noise value of (1.36 ± 0.07) μeV/\(\sqrt{{\rm{Hz}}}\) and valley splitting energies above 84 μeV. We achieve spin relaxation times T1 above 1 s and coherence times \({T}_{2}^{* }\) and \({T}_{2}^{{\rm{H}}}\) of 1 μs and 50 μs respectively. Paired with Rabi frequencies up to 5 MHz we achieve single qubit gate fidelities of 99.2%. Fluctuating nuclear spins of 29Si isotopes in natural silicon are known to limit qubit lifetimes especially in the low frequency regime, and isotopic purification of 28Si in the quantum well is expected to enhance especially the \({T}_{2}^{* }\) time by at least one order of magnitude. In addition, optimisation of the material, geometry and position of the micromagnet could further increase the manipulation speed of the qubit and improve gate fidelity. Overall, these results demonstrate the operation of state of the art spin qubit devices following industrial 300 mm wafer process design rules. This opens the door for the optimisation of qubit metrics on a large scale and the development of much larger and more complex spin qubit architectures required for the realisation of a universal quantum computer.