Device and setup

In this work, the lateral n-i-p junction is made in a conventional undoped 15 nm GaAs quantum well using standard lithography techniques (see the “Methods” section). Electrons and holes are induced in the regions under the electron and hole surface gates, which are separated by an intrinsic region (Fig. 1a). A source-drain (S-D) bias less than the GaAs bandgap is applied across the n-i-p junction to create a finite potential difference between the electron and hole regions. A SAW is generated by applying a radio-frequency (RF) signal to an interdigitated transducer (IDT) at its resonant frequency f SAW = 1.163 GHz. Electrons are trapped in SAW potential minima and pushed towards the hole region (Fig. 1b).

Fig. 1: SAW-driven lateral n-i-p junction, and its electrical and optical properties. a Schematic of the device. Electron and hole surface gates induce electrons (n-region) and holes (p-region) in a GaAs quantum well, forming a lateral n-i-p junction along an etched 1D channel. A SAW is generated by applying an RF signal to a transducer (placed 1 mm from the n-i-p junction). b Schematic diagram showing the band structure of the n-i-p junction modulated by the SAW potential, for an applied forward bias less than the bandgap. A single electron is carried in each SAW minimum, creating a single photon when it recombines with a hole. c S-D current (top) and EL intensity (bottom) as a function of applied RF frequency at an RF power of 9 dBm. They both show a significant enhancement around 1.163 GHz, which is the resonant SAW frequency of the IDT. d SAW-driven EL intensity as a function of time. The 860 ps periodic feature corresponds to the applied SAW frequency of 1.163 GHz. e Energy spectrum of the SAW-driven EL. The spectrum shows a peak at 1.531 eV (FWHM ~ 1 meV), which matches the exciton energy in the quantum well (see Supplementary Note 1). Full size image

To achieve SAW-driven single-electron transport, lateral confinement is provided by etching the region connecting the electron and hole regions into a 1D intrinsic channel. In addition, a pair of side gates is placed on either side of the channel to adjust the electrostatic potential in the intrinsic region. The physical length of the channel is made to be similar to the SAW wavelength of 2.5 μm. In this case, any current flow will be caused by the SAW carrying electrons up the potential slope linking the conduction band in the regions of electrons and holes, not by the SAW reducing the height of the potential barrier in the intrinsic region at a certain part of its cycle. All measurements were carried out at 1.5 K.

SAW-driven electron transport and electroluminescence

In order to test the effect of a SAW on the induced lateral n-i-p junction, a S-D bias, V SD , <1.45 V is applied to the junction. This is at least 90 mV below the voltage required to align the conduction band in the n and p regions so that a current can flow at cryogenic temperature if any intermediate barrier is overcome. In this case, due to the conduction-band offset between the n and p regions, electrons cannot reach the p region to recombine with holes unless a SAW carries them there. Therefore, a S-D current and electroluminescence (EL) signal will only appear when an RF signal is applied to the IDT at f SAW .

The SAW-driven current and EL are shown in Fig. 1c. The S-D current (Fig. 1c top panel) is greatly enhanced around f SAW ~ 1.163 GHz with an RF power of 9 dBm (quality factor \(\frac{{f}_{{\rm{SAW}}}}{\Delta f} \sim 390\)). This SAW-driven current is close to 1 ef SAW = 0.186 nA. It means that the number of electrons carried in each SAW minimum is roughly one on average, a single-electron regime which will, in principle, generate single photons. These electrons driven by the SAW arrive at the hole region and recombine, causing a SAW-driven EL signal, as seen in Fig. 1c (bottom panel). The EL signal is emitted from the p region as electrons recombine with holes there.

The internal quantum efficiency, η, defined as the ratio of the number of photons actually collected to the number of photons that can theoretically be collected by the optics, is about 2.5% (see the “Methods” section). This low η may be caused by trapping and non-radiative recombination in surface states around the etched edges32, or due to electrons being carried away without recombining near the junction. The time-resolved measurement of the SAW-driven EL, shown in Fig. 1d, exhibits periodic peaks with a period of 860 ps. Hence, it is evident that electrons are injected into the hole region by the SAW, leading to photon emission with the period of the SAW.

The spectrum of the SAW-driven EL is shown in Fig. 1e. The spectral peak corresponds to the neutral-exciton transition from the conduction band to the first heavy-hole subband in the quantum well (see Supplementary Note 1)33. The full width at half maximum (FWHM) of the peak is about 1 meV, which can be attributed to acoustic-phonon scattering (ΔE ~ 0.2 meV at 1.5 K) and interface roughness (atomic monolayer fluctuations in the quantum-well thickness give ΔE ~ 0.5 meV)34. The lower-energy tail of the peak may be due to localised exciton states or a Stark shift in the hole region. Unlike conventional single-photon emission based on self-assembled quantum dots, which usually have an extra peak in the spectrum due to biexciton states, this device shows only one peak (neutral exciton) without any spectral filtering or optical cavity.

Time-resolved SAW-driven electroluminescence

The dynamics of the SAW-driven generation of single photons from single electrons can be studied using a time-resolved EL measurement technique. A 350 ns-long pulsed RF signal is applied to the IDT to generate a pulsed SAW (Fig. 2a top). The SAW-driven current is close to the single-electron regime. Because the SAW velocity on GaAs is ~2800 m/s and the distance from the IDT to the n-i-p junction is ~1.1 mm, it will take about 400 ns for the SAW to arrive at the junction, and for its amplitude to build up so that it transports electrons which then recombine with holes. Therefore, compared with the RF signal, the SAW-driven EL is delayed by about 400 ns, as can be seen in Fig 2a (bottom). This confirms that the EL signal is indeed caused by the SAW, rather than by electromagnetic crosstalk generated by the RF signal, which should have an effect without any noticeable delay since the speed of light is five orders of magnitude faster than the SAW.

Fig. 2: Time-resolved measurement of the SAW-driven EL. a A 350 ns-long pulsed RF signal (top, shown at a low frequency for clarity) is applied to the IDT to create a pulsed SAW. The SAW-driven EL signal (bottom) is delayed by roughly 400 ns owing to propagation of the SAW from the IDT to the n-i-p junction. b Averaged SAW-driven EL and the best fit using H(t) (see Supplementary Note 2). Full size image

In order to understand more detailed dynamics, data points three SAW periods apart are averaged across a large part of the region where the EL signal is observed, in Fig. 2a (bottom), to give three periods that are the combination of every third period of the data. The resulting data is shown in Fig. 2b. The shape of an individual peak can be understood from the injection of electrons by the SAW. When an electron is pumped across the n-i-p junction by the SAW, the probability of electron-hole recombination suddenly steps up and causes a rapid enhancement of the EL signal. The signal then decays exponentially as the probability that the electron has already recombined rises. The peaks in Fig. 2b are broadened by the temporal uncertainty (jitter) of the single-photon avalanche photodiode (SPAD) and of the SAW-driven electron transport itself, originating from a slight uncertainty about the position of an electron in a SAW minimum. Note that each peak in Fig. 2b does not decay to zero by the time the next peak appears. The reason for this non-zero background level may be due to after-pulsing of the SPAD35 or to slowly decaying secondary-exciton states (lifetime ~0.2–1.5 ns)36,37. These slowly decaying exciton states may be the localised excitons seen in the small lower-energy tail in Fig. 1e.

Dynamical parameters, including carrier lifetime, τ, background offset, BG EL , and jitter, w, are quantified by fitting the data to a function, H(t), describing the SAW-driven EL (see Supplementary Note 2). The best fit, plotted along with the data in Fig. 2b, gives τ = 94 ps, w = 33 ps, and BG EL = 7% of the peak height. The short carrier lifetime of 94 ps is likely to be caused by non-radiative recombination at surface states, which also gives rise to the observed low quantum efficiency η. On the other hand, a propagating electron only spends a few hundred ps in the junction area, which would also lead to the observed short lifetime. This carrier lifetime is short compared with the 860 ps SAW period, so photons driven by consecutive SAW minima do not overlap significantly in the time domain.

Photon antibunching in the single-electron regime

In this device, quantised SAW-driven current cannot be observed, meaning that there is some variation in the number of electrons in each SAW minimum. However, the probability distribution of electron occupation numbers can still be affected by the discrete nature of SAW-driven charge transport, causing a reduced variance in electron number. The probability distribution should thus become a sub-Poissonian distribution, which will lead to photon antibunching after recombination.

Photon antibunching in the SAW-driven EL is tested by measuring an autocorrelation histogram using a Hanbury Brown and Twiss (HBT) setup (see the “Methods” section). A continuous SAW is used to drive the n-i-p junction in the single-electron regime (with an average number of electrons in a SAW minimum of 0.89) stabilised by a feedback control loop. Coincidences occurring outside the optimum single-electron regime (SAW-driven current above 1ef or below 0.8ef) are removed from the dataset after acquisition (see the “Methods” section). The autocorrelation histogram as a function of time delay, Δt, in Fig. 3a shows periodic peaks with the 860 ps SAW period, indicating that coincidences in the histogram are indeed caused by the periodic SAW-driven photon emission. In the single-electron regime, the peak at Δt = 0 is suppressed to 58% of the average peak value (69% for the raw data, see Supplementary Note 6). The suppression at Δt = 0 is clear evidence of photon antibunching in the SAW-driven EL (a reduced probability of two photons arriving at the same moment).

Fig. 3: Photon antibunching in the SAW-driven EL. a Normalised autocorrelation histogram of the SAW-driven EL. The coincidence at Δt = 0 is suppressed to 58% of the average peak value, indicating photon antibunching, i.e., that there is a reduced probability of two photons arriving simultaneously. b Averaged autocorrelation histogram and the best fit using G(Δt) (see Supplementary Note 3). Full size image

Second-order correlation function

Although photon antibunching is observed in Fig. 3a, the second-order correlation function g(2)(Δt), which confirms the presence of single-photon emission if g(2)(0) < 0.5, cannot be simply obtained from the peak heights. This is because coincidence at a peak can have a contribution from the two neighbouring peaks if they have significant overlap, and also because an effective background (BG EL ) in EL can give rise to a background, BG g2 , in the autocorrelation histogram. Therefore, the actual shape of individual peaks and the background BG g2 have to be considered in order to extract the real g(2)(Δt). The peak shape and the background can be estimated by fitting the autocorrelation histogram to a function, G(Δt), describing the autocorrelation of SAW-driven EL (see Supplementary Note 3). To have a better fit, points from every third peak in the histogram are averaged together. The averaged histogram and the best fit are plotted in Fig. 3b. The fit shows that the autocorrelation histogram is caused by a SAW-driven EL signal with τ = 99 ps, w = 33 ps and BG EL = 8% of the peak height. These parameters are consistent with those obtained in fitting the time-resolved data (Fig. 2b). With these parameters, the actual shape of individual peaks and the background BG g2 are known. Hence, the real g(2)(Δt) can now be extracted from the autocorrelation histogram.

g(2)(Δt) of the SAW-driven EL is obtained by finding the real contribution from each peak in the autocorrelation histogram (see Supplementary Note 4). The result is shown in Fig. 4a. In the single-electron regime, the suppressed photon-antibunching peak at Δt = 0 gives g(2)(0) = 0.39 ± 0.05 (g(2)(0) = 0.63 ± 0.03 for the raw data), showing that the SAW-driven n-i-p junction can indeed produce single-photon emission from single-electron transport. In addition, since the average number of electrons, N avg , in a SAW minimum is 0.89, the probability distribution of photon-number states can be estimated. The wave function of electrons in a SAW minimum can be expressed in the Fock basis

$$\left|\psi \right\rangle =\sqrt{{P}_{0}}\left|0\right\rangle +\sqrt{{P}_{1}}\left|1\right\rangle +\sqrt{{P}_{2}}\left|2\right\rangle +\sqrt{{P}_{3}}\left|3\right\rangle +\cdots$$

where \(\left|n\right\rangle\) and P n denote the electron-number states and their respective probabilities. N avg is thus a function of the probability distribution {P n }. When n electrons (electron-number state \(\left|n\right\rangle\)) arrive at the hole region, each of these electrons may recombine with a hole and produce a photon according to the internal quantum efficiency η. Hence, up to n photons are produced from \(\left|n\right\rangle\). These photons then cause coincidences in an autocorrelation histogram. As a result, g(2)(0) is also a function of the probability distribution {P n }. Assuming that \(\left|\psi \right\rangle\) has no projection on to \(\left|m\right\rangle\) with m ≥ 4 (meaning that a SAW minimum can carry only up to three electrons) and given that N avg = 0.89 and g(2)(0) = 0.39, the probability distribution {P 0 , P 1 , P 2 , P 3 } of electron-number states (and photon-number states) in the single-electron regime is estimated to be {25 ± 3%, 63 ± 7%, 10 ± 6%, 2 ± 2%} (see Supplementary Note 5 for the analysis). This probability distribution is shown in Fig. 4b, along with the distribution expected for a classical Poissonian light source (with the same average number N avg = 0.89) for comparison. It can be seen that, in the SAW-driven n-i-p junction, the single-photon probability is greatly enhanced compared with the classical case. Based on this estimated probability distribution, when a detector receives a light signal from this SAW-driven n-i-p junction, the signal has a probability of P 1 ∕(P 1 + P 2 + P 3 ) = 79–90% to actually be a single photon.