Main

As the detection of single charges has become technically straightforward, it is widely believed7,8,10,11,12 that the realization of spin-to-charge transfer is the key prerequisite for a successful implementation of single spin phosphorus (31P) readout devices, capable of determining the actual spin state (spin up |↑〉 or spin down |↓〉). Different approaches to the electrical spin readout of 31P donor electron spins have been proposed on the basis of spin-dependent transitions between neighbouring 31P atoms7,8,10,11. As the states involved are energetically degenerate, these spin-to-charge transfer schemes are rather difficult to realize. Alternatively, spin-dependent transitions involving dissimilar paramagnetic states might be easier to detect as proposed by Boehme and Lips14. Spin-dependent charge-carrier transport and recombination have been known at least since 1966 (ref. 15), when Schmidt and Solomon observed spin-dependent recombination involving 31P donors in silicon. However, it was not demonstrated until 2003 (ref. 16) that the much more sensitive electrical detection of spins via resonant changes of recombination processes is also able to reflect coherent spin motion, which is necessary for a readout of the spin quantum state as opposed to a mere detection of the presence of spins.

Figure 1a shows the readout scheme on the basis of spin-dependent recombination demonstrated in this paper. To probe 31P donor electron spins, spin-dependent excess charge-carrier recombination through so-called Pb0 centres is used. Pb0 centres are trivalent Si atoms at the interface between crystalline silicon (c-Si) and silicon dioxide (SiO2) that introduce localized, paramagnetic states in the Si bandgap and dominate electron trapping and recombination at the interface17,18. If a neutral Pb0 centre is located in the vicinity of a 31P donor, the electron bound to the 31P and the electron in the Pb0 centre can form a coupled spin pair19,20, whose wavefunction |Ψ〉 can exist in an arbitrary superposition of any of its four energy eigenstates. Two of these states, |T+〉=|↑↑〉 and |T−〉=|↓↓〉 (where the first arrow indicates the state of the 31P electron spin and the second arrow the state of the Pb0 spin) have triplet symmetry and are independent of the strength of the spin–spin coupling. The remaining two states depend on the coupling: For strong spin–spin interaction, they are the pure triplet and the singlet states, whereas in the absence of spin–spin coupling, they are product states |↑↓〉 and |↓↑〉 that can be represented by equal mixtures of |T0〉 and |S〉. For the intermediate coupling regime, the energy eigenbase changes continuously between the two limiting cases. Once a spin pair is generated, it can relax by a transfer of the electron from the 31P donor to the Pb0, forming a negatively charged Pb0−. This relaxation transition depends strongly on the initial symmetry of the two spins within the pair. As the energetically lowest doubly occupied charged state of the Pb0 has to be diamagnetic owing to the Pauli exclusion principle, the relaxation probability is proportional to the singlet content |〈S|Ψ〉|2 of the pair20. After subsequent capture of an excess hole by the Pb0−, and an excess electron by the 31P+, both centres return to their initial uncharged states. This capture of mobile charge carriers, for example, generated by illumination, renders the spin-dependent process detectable by current measurements.

Figure 1: Readout scheme for 31P electron spin quantum states via spin-dependent charge-carrier recombination at Pb0 centres at the crystalline Si/SiO2 interface.
figure 1

a, Band diagram of the Si/SiO2 interface assuming flat band condition. The electrons at the 31P donor and the Pb0 centre form a weakly coupled spin pair |Ψ〉. As the negatively charged Pb0− state is diamagnetic, the recombination probability is proportional to the singlet content |〈S|Ψ〉|2 of the initial pair. ESR of either constituent of the pair can therefore influence the recombination of excess charge carriers. b, Sample structure used for the experiments shown here. To preferentially locate 31P in the vicinity of c-Si/SiO2 states, the active sample is a 15-nm-thick epitaxial layer of 31P-doped c-Si deposited on an intrinsic Si buffer layer. For the electrical measurement, gold contacts are deposited on top of the Si surface.

Full size image

To demonstrate the feasibility of this readout scheme mapping the 31P donor electron spin state on electrical current, pulsed electrically detected magnetic resonance experiments (pEDMR) were carried out on the test structure shown in Fig. 1b. A resonant microwave pulse is used to induce coherent manipulation of the electron spins by electron spin resonance (ESR). The resulting change of the recombination rate is then detected by a transient photoconductivity measurement after the coherent excitation is turned off 20. For the preparation of the initial state of the ensemble of spin pairs, the sample is allowed to attain a low-temperature (T=5 K) steady state in the presence of a strong offset photocurrent I=50 μA, a constant magnetic field B0≈350 mT and illumination with a tungsten light source. In this way, a high density of |T+〉 and |T−〉 spin pairs is generated, as the steady-state recombination leads to a depletion of the short-lived pair states |S〉 and, in the case of intermediate or weak coupling, |T0〉. pEDMR is induced by an intense, coherent ESR microwave pulse generated by a Bruker E580 pulse bridge and amplified by a 1 kW travelling-wave tube amplifier, which imposes a unitary transformation on the spin-pair eigenstates. The final state of this transformation is a coherent non-eigenstate, determined by adjustable pulse parameters such as intensity, pulse length and microwave frequency. If this state has an increased singlet content, the recombination rate after the pulse is also increased and will only gradually return to its steady state, as recombination processes of the charge-carrier pairs typically take place on a much slower timescale than their manipulation by the strong microwave pulse. Figure 2a shows a contour plot of the change ΔI of the photocurrent from its steady-state value as a function of time t after the microwave pulse was turned off. The data shown were obtained for different magnetic fields B0 and represent the measured data after subtraction of non-resonant microwave artefacts. The contour plot shows three resonances at B0=346.2 mT, B0=347.1 mT and B0=350.3 mT, also visible in Fig. 2b, which shows a time slice through the contour plot for t=15.5 μs. The two features indicated by dashed lines have equal amplitudes, are separated by 4.2 mT and correspond to a central g value of 1.9985. This is the characteristic ESR hyperfine signature of the 31P donor electron in silicon21,22. The broader peak at B0=347.1 mT is an unresolved superposition of signal contributions from Pb0 centres that have different orientations with respect to the Si(100) surface, which results in resonances at g=2.0039 and g=2.0081 for the orientation of the sample with respect to the magnetic-field orientation indicated in Fig. 1b (refs 17,18). The current transients at the three resonances exhibit identical dynamics: an initial strong photocurrent decrease caused by the higher singlet content followed by a slower increase of the current originating from the quenching of the number of triplet states that also have a finite recombination probability20. We conclude from the identical time dependence that the electronic transitions that cause the observed signals must belong to the same recombination process, involving 31P donors and Pb0 centres, as illustrated in Fig. 1.

Figure 2: Pulsed electrically detected magnetic resonance of 31P–Pb0 pairs.
figure 2

a, Contour plot of the transient current change after a 480-ns-long microwave pulse with a power PMW=1 W as a function of the magnetic field B0 and after subtraction of microwave artefacts. To protect the amplifier against overload, the detection system is activated only after 3 μs. b, Every time slice has the shape of an ESR spectrum, as exemplarily shown for t=15.5 μs. The spectrum is a superposition of the hyperfine-split resonance of the 31P donors and the resonance of the Pb0 centres.

Full size image

The transient response of the photocurrent after the microwave pulse is proportional to the relative singlet density change induced by the microwave pulse20. Therefore, a current change, integrated over a certain time in a box-car type of experiment for the purpose of noise reduction yielding a charge Q, reflects the spin-state densities directly after the pulse. Because a change of the pulse length τ causes a different nutation angle for the 31P spin on resonance and thus a different singlet content for the 31P–Pb0 spin pair after the pulse, a measurement of Q(τ) must reveal the coherent Rabi nutation of the spins in resonance23.

To observe Rabi flops of the 31P electron spins, the transient current measurement was repeated on resonance with the 31P peak at the magnetic field of B0=350.3 mT under application of microwave pulses with different length τ. Figure 3a shows the measurement of Q(τ) obtained for four different pulse powers PMW under otherwise identical experimental conditions as for the experiments shown in Fig. 2. We clearly see well-developed oscillations that increase in frequency for increasing microwave power. This can be seen more quantitatively in Fig. 3b, which shows the fast-Fourier transform (FFT) of Q(τ). These curves were normalized to the maximum of their respective frequency peaks. With increasing microwave field strength , we observe a clear shift of the characteristic oscillation frequency Ω to higher values. Figure 3c shows that the peak frequency increases linearly with the excitation field B1, as expected for Rabi oscillations. For the integration times used in Fig. 3, a maximum of the recombining charge Q(τ) corresponds to a maximum of singlet states after the pulse. As at low temperatures the electron spins of 31P and Pb0 are in the |↓↓〉 triplet state before the pulse, the maximum of Q indicates |↑〉 of 31P after the pulse, a minimum corresponds to |↓〉. Rabi echo experiments (not shown) reveal that the fast decay of the Rabi oscillations in Fig. 3a is not due to incoherence but is caused by an inhomogeneous B1 field, which leads to a fast coherent dephasing of the spin ensemble.

Figure 3: Electrical observation of Rabi flops of 31P electron spins.
figure 3

a, Photoconductivity change integrated from t1=7 μs to t2=23 μs after a coherent ESR excitation as a function of the applied pulse length τ for four different microwave powers PMW. b, FFT of Q(τ) for the four data sets shown in a, normalized to the intensity of the frequency peak. c, Peak frequencies Ω from b as a function of the microwave field amplitude B1 showing the linear relationship expected for Rabi flops. The typical error bar in c indicates the resolution of the FFT caused by the maximum pulse length τ.

Full size image

On resonance, Ω=γ B1 should hold for isolated spin-1/2 states, where γ=g μB/ħ is the gyromagnetic ratio, μB is the Bohr magneton and ħ is the reduced Planck constant. From the linear fit of the data shown in Fig. 3c, we obtain a proportionality factor of γexp=(1.03±0.08)γ. As the ratio Ω/γ B1 is greater than 1 for strongly coupled systems24, the experimentally observed Ω/γ B1≈1 indicates a weakly coupled spin pair.

Off resonance, the relation between the observed oscillation frequency Ω of Q(τ) and the applied B1 field is described by the Rabi nutation frequency formula in the limit of uncoupled spins20,25. Here, ω is the angular frequency of the microwave radiation and ωL=γ B0 is the Larmor frequency of the spin. To test the Rabi frequency formula for spin-dependent recombination off resonance, Ω was measured with a fixed B1 and varied B0 (or Larmor frequency ωL) near the high-field 31P resonance. Figure 4 shows the results of these measurements in a contour plot of the FFT of Q(τ) as a function of B0. A symmetric increase of Ω with increasing distance from the resonance peak is observed in full agreement with the predictions for Ω at g=1.9985, indicated by the white line. Therefore, the oscillations of Q(τ) shown in Figs 3 and 4 fully meet the predictions of Rabi oscillations of weakly coupled spin-1/2 states.

Figure 4: Detuning-induced shift of the Rabi nutation frequency.
figure 4

The contour plot shows the FFT of Q(τ) as a function of the applied magnetic field B0 in the vicinity of the high-field 31P resonance. The data confirm the predictions for the off-resonance Rabi frequency Ω of a weakly coupled spin-1/2 system with g=1.9985 indicated by the white solid line. The colour scale is in arbitrary units.

Full size image

The experiments shown here have been carried out on ensembles of 31P donors. The charge noise achieved so far is about 104 e, as shown in Fig. 3. As the flip of a single spin approximately leads to one elementary charge detected in the box-car pEDMR experiment20, the detection limit of pEDMR demonstrated here is around 11 orders of magnitude lower than for conventional nuclear magnetic resonance and about 7 orders of magnitude lower than for ESR26. The noise is most likely determined by the shot noise of shunt currents due to excess charge carriers that diffuse into the c-Si bulk. Suppression of these currents via improved sample geometry, for example, using a buried oxide and lateral structuring for confinement should reduce the noise level, resulting in an even higher sensitivity. In fact, continuous-wave EDMR was recently used to successfully detect as few as 100 31P atoms implanted into intrinsic c-Si (ref. 27).

The experimental results shown are an important step towards the realization of an electrical spin readout of donors. The proof-of-principle experiments demonstrate a spin-to-charge transfer mechanism required for 31P electron spin readout via 31P–Pb0 pairs and show that this spin pair is sufficiently weakly coupled so that the 31P hyperfine interaction can be observed, ultimately allowing the electrical detection of the nuclear spin state28. However, although inclusion of this readout scheme into a scalable architecture is in principle conceivable via local gates electrostatically controlling the 31P–Pb0 coupling, there remain a variety of physical and technological issues such as the positioning of Pb0 centres as well as decoherence by the c-Si/SiO2 interface29 or by light-induced charge carriers that have to be addressed before application of the readout scheme to quantum information processing.

Methods

The test structures investigated were grown by low-pressure chemical vapour deposition. The sample consists of a 15-nm-thick layer of c-Si doped with 1017 cm−3 31P atoms on a 5 μm intrinsic buffer. The substrate is a 30-Ω-cm boron-doped Si(001) wafer. A high density of Pb0 centres is achieved by using a native oxide for the formation of the Si/SiO2 interface. The electrical contacts are a grid structure consisting of 10-nm-thick chromium and 100-nm-thick gold films and comprising 112 digits of 2 mm length, 10 μm width and 10 μm spacing.