Silicon, the main constituent of microprocessor chips, is emerging as a promising material for the realization of future quantum processors. Leveraging its well-established complementary metal–oxide–semiconductor (CMOS) technology would be a clear asset to the development of scalable quantum computing architectures and to their co-integration with classical control hardware. Here we report a silicon quantum bit (qubit) device made with an industry-standard fabrication process. The device consists of a two-gate, p-type 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 read-out. All electrical, two-axis control of the spin qubit is achieved by applying a phase-tunable microwave modulation to the first gate. The demonstrated qubit functionality in a basic transistor-like device constitutes a promising step towards the elaboration of scalable spin qubit geometries in a readily exploitable CMOS platform.
Localized spins in semiconductors can be used to encode elementary bits of quantum information1,2. Spin qubits were demonstrated in a variety of semiconductors, starting from GaAs-based heterostructures3,4,5. 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 GaAs6). This problem can be cured to a large extent by means of echo-type spin manipulation sequences and notch filtering techniques7,8,9. In natural silicon, however, the hyperfine interaction is weaker, being due to the ≈4.7% content of 29Si, the only stable isotope with a non-zero 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 28Si) have even allowed extending to 120 μs (ref. 15). Following these improvements in spin coherence time, silicon-based spin qubits classify among the best solid-state qubits, at the single-qubit level. Recently, the first two-qubit logic gate with control-NOT functionality was also demonstrated16, marking the next essential milestone towards scalable processors.
Surface-code quantum computing architectures, possibly the only viable option to date, require large numbers (eventually millions) of qubits individually controlled with tunable nearest-neighbour couplings17,18. Their implementation is a considerable challenge since it implies dealing with issues such as device-to-device variability, multi-layer electrical wiring and, most likely, on-chip classical electronics (amplifiers, multiplexers and so on) for qubit control and read-out. This is where the well-established complementary metal–oxide–semiconductor (CMOS) technology becomes a compelling tool. A possible strategy is to export qubit device implementations developed within academic-scale laboratories into large-scale 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 p-type silicon transistor with two gates. One QD encodes a hole spin qubit while the other one is used for qubit read-out. We achieve electric field-mediated two-axis coherent control of the hole spin qubit by applying a microwave modulation on one gate of the transistor. Characteristic spin lifetimes ( and Techo) are revealed by means of Ramsey and spin echo manipulation sequences.
We use a microelectronics technology based on 300 mm silicon-on-insulator wafers. Our qubit device, schematically shown in Fig. 1a, is derived from silicon nanowire field-effect transistors19. It relies on confined hole spins20,21,22,23,24, and it consists of a 10 nm-thick and 20 nm-wide undoped silicon channel with p-doped source and drain contact regions, and two ≈30 nm-wide 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 cross-sectional view are shown in Fig. 1b,c, respectively. At low temperature, hole QDs are created by charge accumulation below the gates25. The double-gate layout enables the formation of two QDs in series, QD1 and QD2, with occupancies controlled by voltages Vg1 and Vg2 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 spin-degenerate 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 spin-1/2 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 two-axis control of the first spin only, and use the second spin for initialization and read-out purposes. Tuning the double QD to a parity-equivalent (1, 1)→(0, 2) charge transition, initialization and read-out of the qubit relies on the so-called Pauli spin blockade mechanism5,26. 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 signatures27,28,29 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 few-hole regime30, resulting in more complex spin configurations.)
Electric-dipole 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 g-factors are anisotropic and gate-dependent25, denoting strong spin–orbit coupling29. This implies the possibility to perform electric-dipole spin resonance (EDSR), namely to drive coherent hole-spin 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 source-drain current Isd as a function of magnetic field B (perpendicular to the chip) and MW frequency f, EDSR is revealed by narrow ridges of increased current28. The data set in Fig. 2a shows two of such current ridges: one clearly visible, most likely associated with QD1 (strongly coupled to the rf-modulated 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=gμBB, where h is Planck’s constant, μB the Bohr magneton and g the hole Landé g-factor (absolute value) along the magnetic field direction. From the slopes of the two ridges we extract two g-factor values g1=1.63 and g2=1.92 comparable to those reported before25. In line with our plausible interpretation of the observed EDSR ridges, we ascribe these g-factor values to QD1 and QD2, respectively. We have observed similar EDSR features at other working points (that is, different parity-equivalent (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 continuous-wave 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 Coulomb-blockade regime4 (Fig. 2b). Following each burst, Vg1 is abruptly increased to bring the double dot back to the parity-equivalent (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 spin-up if QD2 hosts a spin-down 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 read-out-initialization portion of the same period, until the parity-equivalent (1, 1)→(0, 2) becomes spin blocked again and the system is re-initialized 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 read-out 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 Isd as a function of MW power PMW, 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 fRabi increases linearly with the MW voltage amplitude, which is proportional to PMW 1/2 (Fig. 2f). At the highest power, we reach a remarkably large fRabi≈85 MHz, comparable to the highest reported values for electrically controlled semiconductor spin qubits31. Figure 3a shows a colour plot of Isd(f, ) revealing the characteristic chevron pattern associated to Rabi oscillations13. The fast Fourier transform of Isd, 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−f0, where f0=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 fringes-like 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, Isd 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, two-axis 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 Techo=245±12 ns.
The relatively short and Techo (not limited by spin relaxation, see Supplementary Note 5) can hardly be explained by dephasing from Si29 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 electrons32. 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 nitride-based spacer layers and the silicide contacts are non-magnetic. Magnetic defects may possibly exist in the gate dielectric at the interface between SiO2 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 p-type silicon field-effect transistor fabricated within an industry-standard CMOS process line can exhibit hole spin qubit functionality with fast, all-electrical, two-axis control. In the prospect of realizing large-scale quantum computing architectures, this result opens a favourable scenario with some clear follow-up milestones. The next step is to advance from the simple, yet limited transistor-like structures studied here to more elaborate qubit designs, incorporating additional important elements such as single-shot qubit read-out (for instance based on rf-gate reflectometry33), and enabling scalable qubit-to-qubit 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 state-of-the-art CMOS technology, with its well-established 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 co-integration of classical cryogenic control hardware.
The entire device fabrication process was carried out in a 300 mm CMOS platform. A detailed description is provided in Supplementary Note 1.
All measurements were performed in a dilution refrigerator with a base temperature of T=10 mK. The direct source-drain current providing qubit read-out was measured by means of a current/voltage amplifier with a gain of 109. All low-frequency lines are low-pass filtered at base temperature with two-stage RC filters. High-frequency 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 home-made bias tee mounted on the sample board enables simultaneous application of microwave and low-frequency signals on gate 1. One channel of an arbitrary wave generator (Tektronix AWG5014C) is used to generate the two-level Vg1 modulation driving the device between Coulomb blockade (qubit manipulation phase) and Pauli blockade (qubit read-out 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 two-level gate modulation are combined by means of a diplexer before reaching the dilution fridge.
The data that support the findings of this study are available from the corresponding authors on reasonable request.
How to cite this article: Maurand, R. et al. A CMOS silicon spin qubit. Nat. Commun. 7, 13575 doi: 10.1038/ncomms13575 (2016).
Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Kane, B. E. A silicon-based nuclear spin quantum computer. Nature 393, 133–137 (1998).
Loss, D & Divincenzo, D. P. Quantum computation with quantum dots. Phys. Rev. A 57, 120–126 (1998).
Petta, J. R. et al. Coherent manipulation of coupled electron spins in semiconductor quantum dots. Science 309, 2180–2184 (2005).
Koppens, F. H. L. et al. Driven coherent oscillations of a single electron spin in a quantum dot. Nature 442, 766–771 (2006).
Hanson, R., Kouwenhoven, L. P. & Petta, J. R. Spins in few-electron quantum dots. Rev. Mod. Phys. 79, 1217–1265 (2007).
Koppens, F. H. L., Nowack, K. C. & Vandersypen, L. M. K. Spin echo of a single electron spin in a quantum dot. Phys. Rev. Lett. 100, 236802 (2008).
Bluhm, H. et al. Dephasing time of GaAs electron-spin qubits coupled to a nuclear bath exceeding 200/μs. Nat. Phys. 7, 109–113 (2010).
De Lange, G., Wang, Z. H., Dobrovitski, V. V. & Hanson, R. Universal dynamical decoupling of a single solid-state spin from a spin bath. Science 330, 60 (2010).
Malinowski, F. K. et al. Notch filtering the nuclear environment of a spin qubit. Nat. Nanotechnol.http://dx.doi.org/10.1038/nnano.2016.170 (2016).
Pla, J. J. et al. A single-atom electron spin qubit in silicon. Nature 489, 541–545 (2012).
Maune, B. M. et al. Coherent singlet-triplet oscillations in a silicon-based double quantum dot. Nature 481, 344–347 (2012).
Wu, X. et al. Two-axis control of a singlet-triplet qubit with an integrated micromagnet. Proc. Natl Acad. Sci. USA 111, 11938–11942 (2014).
Kawakami, E. et al. Electrical control of a long-lived spin qubit in a Si/SiGe quantum dot. Nat. Nanotechnol. 9, 666–670 (2014).
Takeda, K. et al. A fault-tolerant addressable spin qubit in a natural silicon quantum dot. Sci. Adv. 2, e1600694 (2016).
Veldhorst, M. et al. An addressable quantum dot qubit with fault-tolerant control-fidelity. Nat. Nanotechnol. 9, 981–985 (2014).
Veldhorst, M. et al. A two- qubit logic gate in silicon. Nature 526, 410–414 (2015).
Bravyi, S. B. & Kitaev, A. Y. Quantum codes on a lattice with boundary. Preprint at https://arxiv.org/abs/quantph/9811052 (1998).
Dennis, E., Kitaev, A., Landahl, A. & Preskill, J. Topological quantum memory. J. Math. Phys. 43, 4452 (2002).
Barraud, S. et al. Performance of omega-shaped-gate silicon nanowire MOSFET with diameter down to 8 nm. IEEE Electron Device Lett. 33, 1526–1528 (2012).
De Greve, K. et al. Ultrafast coherent control and suppressed nuclear feedback of a single quantum dot hole qubit. Nat. Phys. 7, 872–878 (2011).
Higginbotham, A. P. et al. Hole spin coherence in a Ge/Si heterostructure nanowire. Nano Lett. 14, 3582–3586 (2014).
Brunner, D. et al. A coherent single-hole spin in a semi- conductor. Science 325, 70–72 (2009).
Hu, Y., Kuemmeth, F., Lieber, C. M. & Marcus, C. M. Hole spin relaxation in Ge-Si core-shell nanowire qubits. Nat. Nanotechnol. 7, 47–50 (2012).
Pribiag, V. S. et al. Electrical control of single hole spins in nanowire quantum dots. Nat. Nanotechnol. 8, 170–174 (2013).
Voisin, B. et al. Electrical control of g-factor in a few-hole silicon nanowire MOSFET. Nano Lett. 16, 88–92 (2016).
Ono, K., Austing, D. G., Tokura, Y. & Tarucha, S. Current rectification by Pauli exclusion in a weakly coupled double quantum dot system. Science 297, 1313–1318 (2002).
Danon, J. & Nazarov, Y. V. Pauli spin blockade in the presence of strong spin-orbit coupling. Phys. Rev. B 80, 041301 (2009).
Nadj-Perge, S. et al. Disentangling the effects of spin-orbit and hyperfine interactions on spin blockade. Phys. Rev. B 81, 201305 (2010).
Li, R., Hudson, F. E., Dzurak, A. S. & Hamilton, A. R. Pauli spin blockade of heavy holes in a silicon double quantum dot. Nano Lett. 15, 7314–7318 (2015).
Zwanenburg, F. A., Van Rijmenam, C. E. W. M., Fang, Y., Lieber, C. M. & Kouwenhoven, L. P. Spin states of the first four holes in a silicon nanowire quantum dot 2009. Nano Letters 9, 1071–1079 (2009).
van den Berg, J. W. G. et al. Fast spin-orbit qubit in an indium antimonide nanowire. Phys. Rev. Lett. 110, 066806 (2013).
Testelin, C., Bernardot, F., Eble, B. & Chamarro, M. Holespin dephasing time associated with hyperfine interaction in quantum dots. Phys. Rev. B 79, 195440 (2009).
Betz, A. C. et al. Dispersively detected Pauli spin-blockade in a silicon nanowire field-effect transistor. Nano Lett. 15, 4622–4627 (2015).
Koppens, F. H. L. et al. Universal phase shift and nonexponential decay of driven single-spin oscillations. Phys. Rev. Lett. 99, 106803 (2007).
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.
The authors declare no competing financial interests.
About this article
Cite this article
Maurand, R., Jehl, X., Kotekar-Patil, D. et al. A CMOS silicon spin qubit. Nat Commun 7, 13575 (2016). https://doi.org/10.1038/ncomms13575
Effect of valley, spin, and band nesting on the electronic properties of gated quantum dots in a single layer of transition metal dichalcogenides
Physical Review B (2020)
Nature Nanotechnology (2020)
Semiconductor Science and Technology (2020)
Optical properties of silicon and germanium determined by high-precision analysis of reflection electron energy loss spectroscopy spectra
Physical Review B (2019)