Abstract
Silicon, the main constituent of microprocessor chips, is emerging as a promising material for the realization of future quantum processors. Leveraging its wellestablished complementary metal–oxide–semiconductor (CMOS) technology would be a clear asset to the development of scalable quantum computing architectures and to their cointegration with classical control hardware. Here we report a silicon quantum bit (qubit) device made with an industrystandard fabrication process. The device consists of a twogate, ptype transistor with an undoped channel. At low temperature, the first gate defines a quantum dot encoding a hole spin qubit, the second one a quantum dot used for the qubit readout. All electrical, twoaxis control of the spin qubit is achieved by applying a phasetunable microwave modulation to the first gate. The demonstrated qubit functionality in a basic transistorlike device constitutes a promising step towards the elaboration of scalable spin qubit geometries in a readily exploitable CMOS platform.
Introduction
Localized spins in semiconductors can be used to encode elementary bits of quantum information^{1,2}. Spin qubits were demonstrated in a variety of semiconductors, starting from GaAsbased heterostructures^{3,4,5}. In this material, and all III–V compounds in general, electron spins couple to the nuclear spins of the host crystal via the hyperfine interaction resulting in a relatively short inhomogeneous dephasing time, (a few tens of nanoseconds in GaAs^{6}). This problem can be cured to a large extent by means of echotype spin manipulation sequences and notch filtering techniques^{7,8,9}. In natural silicon, however, the hyperfine interaction is weaker, being due to the ≈4.7% content of ^{29}Si, the only stable isotope with a nonzero nuclear spin. Measured values range between 50 ns and 2 μs (refs 10, 11, 12, 13, 14). Experiments carried out on electron spin qubits in isotopically purified silicon (99.99% of spinless ^{28}Si) have even allowed extending to 120 μs (ref. 15). Following these improvements in spin coherence time, siliconbased spin qubits classify among the best solidstate qubits, at the singlequbit level. Recently, the first twoqubit logic gate with controlNOT functionality was also demonstrated^{16}, marking the next essential milestone towards scalable processors.
Surfacecode quantum computing architectures, possibly the only viable option to date, require large numbers (eventually millions) of qubits individually controlled with tunable nearestneighbour couplings^{17,18}. Their implementation is a considerable challenge since it implies dealing with issues such as devicetodevice variability, multilayer electrical wiring and, most likely, onchip classical electronics (amplifiers, multiplexers and so on) for qubit control and readout. This is where the wellestablished complementary metal–oxide–semiconductor (CMOS) technology becomes a compelling tool. A possible strategy is to export qubit device implementations developed within academicscale laboratories into largescale CMOS platforms. This approach is likely to require significant process integration development at the CMOS foundry.
Here we present an alternative route, where an existing process flow for the fabrication of CMOS transistors is taken as a starting point and is adapted to obtain devices with qubit functionality. More precisely we define at low temperature, a double quantum dot (QD) inside the channel of a ptype silicon transistor with two gates. One QD encodes a hole spin qubit while the other one is used for qubit readout. We achieve electric fieldmediated twoaxis coherent control of the hole spin qubit by applying a microwave modulation on one gate of the transistor. Characteristic spin lifetimes ( and T_{echo}) are revealed by means of Ramsey and spin echo manipulation sequences.
Results
Device description
We use a microelectronics technology based on 300 mm silicononinsulator wafers. Our qubit device, schematically shown in Fig. 1a, is derived from silicon nanowire fieldeffect transistors^{19}. It relies on confined hole spins^{20,21,22,23,24}, and it consists of a 10 nmthick and 20 nmwide undoped silicon channel with pdoped source and drain contact regions, and two ≈30 nmwide parallel top gates, side covered by insulating silicon nitride spacers (further details on the spacers are given in Supplementary Note 1). A scanning electron microscopy top view and a transmission electron microscopy crosssectional view are shown in Fig. 1b,c, respectively. At low temperature, hole QDs are created by charge accumulation below the gates^{25}. The doublegate layout enables the formation of two QDs in series, QD1 and QD2, with occupancies controlled by voltages V_{g1} and V_{g2} applied to gates 1 and 2, respectively (Supplementary Fig. 2 and Supplementary Note 2). We tune charge accumulation to relatively small numbers, N, of confined holes (we estimate N≈10 and ≈30 for QD1 and QD2, respectively, as discussed in Supplementary Note 2). In this regime, the QDs exhibit a discrete energy spectrum with level spacing δE in the 0.1–1 meV range, and Coulomb charging energy U≈10 meV.
In a simple scenario where spindegenerate QD levels get progressively filled by pairs of holes, each QD carries a spin S=1/2 for N=odd and a spin S=0 for N=even. By setting N=odd in both dots, two spin1/2 qubits can be potentially encoded, one for each QD. This is equivalent to the (1, 1) charge configuration, where the first and second digits denote the charge occupancies of QD1 and QD2, respectively. In practice, here we shall demonstrate full twoaxis control of the first spin only, and use the second spin for initialization and readout purposes. Tuning the double QD to a parityequivalent (1, 1)→(0, 2) charge transition, initialization and readout of the qubit relies on the socalled Pauli spin blockade mechanism^{5,26}. In this particular charge transition, tunnelling between dots can be blocked by spin conservation. Basically, for a fixed, say ‘up’, spin orientation in QD2, tunnelling will be allowed if the spin in QD1 is ‘down’ and it will be forbidden by Pauli exclusion principle if the spin in QD1 is ‘up’, that is, a spin triplet (1, 1) state is not coupled to the singlet (0, 2) state. This charge/spin configuration can be identified through characteristic experimental signatures^{27,28,29} associated with the Pauli blockade effect discussed above (Supplementary Fig. 4 and Supplementary Note 3). (We note that deviations from pairwise filling of the hole QD orbitals can occur, especially beyond the fewhole regime^{30}, resulting in more complex spin configurations.)
Electricdipole spin resonance
We now turn to the procedure for spin manipulation. In a recent work on similar devices with only one gate, we found that hole gfactors are anisotropic and gatedependent^{25}, denoting strong spin–orbit coupling^{29}. This implies the possibility to perform electricdipole spin resonance (EDSR), namely to drive coherent holespin rotations by means of microwave frequency (MW) modulation of a gate voltage (Supplementary Note 4). Here we apply the MW modulation to gate 1 to rotate the spin in QD1. Spin rotations result in the lifting of spin blockade. In a measurement of sourcedrain current I_{sd} as a function of magnetic field B (perpendicular to the chip) and MW frequency f, EDSR is revealed by narrow ridges of increased current^{28}. The data set in Fig. 2a shows two of such current ridges: one clearly visible, most likely associated with QD1 (strongly coupled to the rfmodulated gate); and the other one rather faint, most likely arising from the spin rotation in QD2 (which is only weakly coupled to gate 1). Both ridges follow a linear f(B) dependence consistent with the spin resonance condition hf=gμ_{B}B, where h is Planck’s constant, μ_{B} the Bohr magneton and g the hole Landé gfactor (absolute value) along the magnetic field direction. From the slopes of the two ridges we extract two gfactor values g_{1}=1.63 and g_{2}=1.92 comparable to those reported before^{25}. In line with our plausible interpretation of the observed EDSR ridges, we ascribe these gfactor values to QD1 and QD2, respectively. We have observed similar EDSR features at other working points (that is, different parityequivalent (1, 1)→(0, 2) transitions) and in two distinct devices (Supplementary Figs 5 and 6 and Supplementary Note 4).
Coherent spin control
To perform controlled spin rotations, and hence demonstrate qubit functionality, we replace continuouswave gate modulation with MW bursts of tunable duration, . During spin manipulation, we prevent charge leakage due to tunnelling from QD1 to QD2 by simultaneously detuning the double QD to a Coulombblockade regime^{4} (Fig. 2b). Following each burst, V_{g1} is abruptly increased to bring the double dot back to the parityequivalent (1, 1)→(0, 2) resonant transition. At this stage, a hole can tunnel from QD1 to QD2 with a probability proportional to the unblocked spin component in QD1 (that is, the probability amplitude for spinup if QD2 hosts a spindown state). The resulting (0, 2)like charge state ‘decays’ by emitting a hole into the drain, and a hole from the source is successively fed back to QD1, thereby restoring the initial (1, 1)like charge configuration. The net effect is the transfer of one hole from source to drain, which will eventually contribute to a measurable average current. (In principle, because not all (1, 1)like states are Pauli blocked, the described charge cycle may occur more than once during the readoutinitialization portion of the same period, until the parityequivalent (1, 1)→(0, 2) becomes spin blocked again and the system is reinitialized for the next manipulation cycle.)
We chose a modulation period of 435 ns, of which 175 ns are devoted to spin manipulation and 260 ns to readout and initialization. Figure 2c shows an EDSR resonance recorded on a second device taken with the previously described gate 1 modulation and a MW burst of 20 ns (a wider f−B range of the EDSR spectrum is shown in Supplementary Fig. 6a). Figure 2d shows I_{sd} as a function of MW power P_{MW}, and at the resonance frequency for B=144 mT (see white arrow in Fig. 2c). The observed current modulation is a hallmark of coherent Rabi oscillations of the spin in QD1, also explicitly shown by selected cuts at three different MW powers (Fig. 2e). As expected, the Rabi frequency f_{Rabi} increases linearly with the MW voltage amplitude, which is proportional to P_{MW} ^{1/2} (Fig. 2f). At the highest power, we reach a remarkably large f_{Rabi}≈85 MHz, comparable to the highest reported values for electrically controlled semiconductor spin qubits^{31}. Figure 3a shows a colour plot of I_{sd}(f, ) revealing the characteristic chevron pattern associated to Rabi oscillations^{13}. The fast Fourier transform of I_{sd}, calculated for each f value, is shown in the upper panel. It exhibits a peak at the Rabi frequency with the expected hyperbolic dependence on frequency detuning Δf=f−f_{0}, where f_{0}=9.68 GHz is the resonance frequency at the corresponding B=155 mT (working point indicated by a black arrow in Fig. 2c).
Dephasing and decoherence times
To evaluate the inhomogeneous dephasing time during free evolution we perform a Ramsey fringeslike experiment, which consists in applying two short, phase coherent, MW pulses separated by a delay time . The proportionality between the qubit rotation angle θ and is used to calibrate both pulses to a θ= rotation (see sketch in Fig. 3c). For each f value, I_{sd} exhibits oscillations at frequency Δf decaying on a timescale ≈60 ns (Fig. 3b). Extracted current oscillations at fixed frequency are presented in Fig. 3c. At resonance (Δf=0), the two pulses induce rotations around the same axis (say the x axis of the rotating frame). The effect of a finite Δf is to change the rotation axis of the second pulse relative to the first one. Alternatively, twoaxis control can be achieved also at resonance (Δf=0) by varying the relative phase Δφ of the MW modulation between the two pulses. For a Ramsey sequence , the first pulse induces a rotation around x and the second one around x, y, −x and −y for Δφ=0, , π and , respectively. The signal then oscillates with Δφ as shown in the insets to Fig. 4a, and the oscillation amplitude vanishes with on a timescale (Fig. 4a).
Spin echo techniques can extend spin coherence if the source of dephasing fluctuates slowly on the timescale of the hole spin dynamics. We performed a Hahn echo experiment, where a π pulse is introduced half way between the two pulses, as sketched in Fig. 4b. The amplitude of the oscillations in Δφ (insets to Fig. 4b)) decays on a coherence time T_{echo}=245±12 ns.
Discussion
The relatively short and T_{echo} (not limited by spin relaxation, see Supplementary Note 5) can hardly be explained by dephasing from Si^{29} nuclear spins. In fact, even if little is known about the hyperfine interaction strength for confined holes in silicon, we would expect it to be even smaller than for electrons^{32}. Alternative decoherence mechanisms could dominate, such as paramagnetic impurities, charge noise or the stronger hyperfine interaction with boron dopants diffused from the contact regions. To the best of our knowledge, no relevant magnetic phases should be present in our devices. (Both the nitridebased spacer layers and the silicide contacts are nonmagnetic. Magnetic defects may possibly exist in the gate dielectric at the interface between SiO_{2} and HfSiON but their density should be very low.) Further studies will be necessary to establish statistically relevant values for the coherence timescales and to identify their origin.
In essence, we have shown that a ptype silicon fieldeffect transistor fabricated within an industrystandard CMOS process line can exhibit hole spin qubit functionality with fast, allelectrical, twoaxis control. In the prospect of realizing largescale quantum computing architectures, this result opens a favourable scenario with some clear followup milestones. The next step is to advance from the simple, yet limited transistorlike structures studied here to more elaborate qubit designs, incorporating additional important elements such as singleshot qubit readout (for instance based on rfgate reflectometry^{33}), and enabling scalable qubittoqubit coupling schemes. (We refer the reader to Supplementary Note 6 for a more detailed discussion.) In addition, a systematic investigation of qubit performances, including the benchmarking of hole qubits against their electron counterparts has to be performed in the short term. The use of stateoftheart CMOS technology, with its wellestablished fabrication processes and integration capabilities, is going to be a clear asset in all these tasks. At a later stage, it should also favour the cointegration of classical cryogenic control hardware.
Methods
Device fabrication
The entire device fabrication process was carried out in a 300 mm CMOS platform. A detailed description is provided in Supplementary Note 1.
Experimental setup
All measurements were performed in a dilution refrigerator with a base temperature of T=10 mK. The direct sourcedrain current providing qubit readout was measured by means of a current/voltage amplifier with a gain of 10^{9}. All lowfrequency lines are lowpass filtered at base temperature with twostage RC filters. Highfrequency signals on gate 1 are applied through a 20 GHz bandwidth coaxial line with 36 dB attenuation distributed along the dilution fridge for thermalization. A homemade bias tee mounted on the sample board enables simultaneous application of microwave and lowfrequency signals on gate 1. One channel of an arbitrary wave generator (Tektronix AWG5014C) is used to generate the twolevel V_{g1} modulation driving the device between Coulomb blockade (qubit manipulation phase) and Pauli blockade (qubit readout and initialization). Two other channels of the AWG define square pulses to control the I and Q inputs of the MW source. MW bursts and the twolevel gate modulation are combined by means of a diplexer before reaching the dilution fridge.
Data availability
The data that support the findings of this study are available from the corresponding authors on reasonable request.
Additional information
How to cite this article: Maurand, R. et al. A CMOS silicon spin qubit. Nat. Commun. 7, 13575 doi: 10.1038/ncomms13575 (2016).
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Acknowledgements
We thank D. Estève, M. Hofheinz, F. Kuemmeth, T. Meunier, J. Renard, N. Roch and D. Vion for their help, as well as G. Audoit and C. Guedj for the transmission electron microscopy sample preparation and imaging. The research leading to these results has been supported by the European Union through the research grants No. 323841, No. 610637 and No. 688539, as well as through the ERC grant No. 280043.
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X.J., M.S., S.D.F., R.L., S.B. and M.V. designed the devices; R.L., L.H., S.B. and M.V. followed their fabrication process; R.L., D.K.P., A.C. and H.B. characterized the basic electronic properties of the devices; R.M. performed the experiments with input from S.D.F., R.M., X.J., M.S. and S.D.F. analysed the results; R.M. and S.D.F. wrote the manuscript, with input from all authors; S.D.F., X.J. and M.S. initiated the project.
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Supplementary Information
Supplementary Figures 18, Supplementary Notes 16 and Supplementary References (PDF 1228 kb)
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Maurand, R., Jehl, X., KotekarPatil, D. et al. A CMOS silicon spin qubit. Nat Commun 7, 13575 (2016). https://doi.org/10.1038/ncomms13575
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DOI: https://doi.org/10.1038/ncomms13575
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