1 Introduction

Single-photon sources (SPSs) are fundamental elements of quantum communication protocols and play key roles in a number of photonic quantum technologies such as distributed quantum cryptography [1, 2], linear optical quantum computation [3, 4] and quantum teleportation [5]. The strong demand of SPSs in most of envisioned schemes is rooted in the fact that they could provide highly indistinguishable single photons to implement the “Hong-Ou-Mandel” type two-photon interference [6], allowing interfacing stationary qubits to extend the quantum communication over a long distance. Progress has been made in realizing the two-photon interference with indistinguishable photons emitted from atoms [7], trapped ions [8] and single molecules [9]. However, atoms and trapped ions are in vapor phase, molecules are prone to photo-induced chemical reactions [10], and thus they are not suitable for the practical on-chip integration application. Self-assembled quantum dots (QDs) are among the most promising sources of single photons owing to their high brightness and narrow spectral linewidth [11, 12]. Recent experiments have already demonstrated the feasibility of generating high degree of indistinguishable single photons from the remote QDs [13–15]. In particular, the semiconductor QDs are solid-state systems, and they allow for monolithic integration with electronic and photonic elements in mature semiconductor technologies, e. g., embed the QDs into a light-emitting diode (LED) to realize electrically driven SPSs [16, 17]. Despite these advantages, the semiconductor QDs have a large inhomogeneous broadening due to their random shape, strain and composition anisotropy during the Stranski-Krastanov growth in molecular beam epitaxy (MBE). Consequently, the QDs have distinct emission energies of single photons, which becomes the main obstacle hampering the realization of two-photon interference by using the self-assembled QDs systems, especially for the electrically driven QDs. In order to overcome this difficulty, many post-growth tuning techniques have been proposed in order to tune the energy of single photons emitted by QDs, including in situ thermal annealing [18, 19], magnetic field [20] and electric field [21]. However, the thermal annealing is an irreversible coarse tuning technique, while magnetic field always requires complicated setup which renders a practical implementation inconvenient. Although the electric field represents the most promising tuning technique, the main drawback is the difficulty of combining it with electrical excitation at the same time.

Here, we report a strain-tunable quantum LED, in which InGaAs QDs-containing p-i-n nanomembrane is integrated onto a piezoelectric actuator. With this device, we not only realized electrically triggered single-photon emission generated from the quantum LED, but we also achieve a broad tuning range of about 9 meV to the energy of the single-photon emission simultaneously. We further show that the single-photon emission from different QDs can be reliably brought into resonance aiming at obtaining indistinguishable photons for the non-postselective two-photon interference.

2 Results

2.1 Strain-tunable quantum LED and experimental methods

The In(Ga)As QDs-containing nanomembrane in the studied device (see Fig. 1a) was grown on a (001) GaAs substrate by MBE. It consisted of a p-i-n heterostructure diode composed of a 178-nm-thick n-type GaAs layer, a 160-nm-thick intrinsic GaAs layer and a 96-nm-thick p-type GaAs layer. A layer of low density (10\(^6\)–10\(^7\) cm\(^{-2}\)) self-assembled InGaAs QDs was embedded in the middle of the intrinsic GaAs layer. The entire diode structure was grown on a 50-nm-thick AlAs sacrificial layer. In the process of the device, first of all, standard UV photolithography and wet chemical etching were used to fabricate mesa structures with size of 120 \(\times\) 160 \(\upmu\)m\(^2\). The nanomembrane was then released from the substrate and became free-standing by selective etching of the sacrificial layer in diluted hydrofluoric acid. Subsequently, the nanomenbrane was transferred onto a 0.3-mm-thick gold-coated piezoelectric crystal \([Pb(Mg_{1/3}Nb_{2/3})O_3]_{0.72}[PbTiO_3]_{0.28}\) (PMN-PT) via a gold-to-gold thermo-compression bonding technique. The bonded gold layer on the bottom formed the p-contact, while the n-contact was made by bonding a 25-\(\upmu\)m-thick aluminum wire via a wedge bonder on the top of the nanomembrane. The electric contacts for the diode and the piezoelectric crystal are independent, and they share the same ground contact on the gold layer. With this configuration, electric fields can be independently applied to the diode and the PMN-PT crystal without any cross-talk, thereby achieving an all-electrically simultaneous excitation and tuning of the QDs [22, 23].

Additionally, it should be noted that QDs are located at a distance \(\lambda _m\) from the top GaAs/air interface and the total thickness of the structure is 1.67 \(\lambda _m\) (\(\lambda _m\) is the center wavelength of the cavity mode in GaAs matrix). These parameters are chosen to satisfy the standing wave condition, and therefore an optimized total collection efficiency of about 5.3 % is found for a NA of 0.42 in our device, which gives \(\sim\)14-fold enhancement with respect to semiconductor–air interface [23]. It is worth mentioning that further improvement in the out-coupling efficiency of our quantum LED devices is available by integrating the device with microcavities [24] or microlenses [25].

In optical measurements, the electroluminescence (EL) is collected by a 50\(\times\) microscope objective (NA = 0.42), which is placed on the top of the nanomembrane and collects the photon emission from the area close to the metal contact as shown in Fig. 1a. The EL is then directed to a 750-mm focal length monochromator and detected by a liquid-nitrogen-cooled Si-CCD camera, which allows for a spectral resolution of \({\sim }\)20 \(\upmu\)eV. The time-resolved correlation measurements are accomplished by placing a non-polarizing 50:50 beam splitter, dividing the optical paths between two spectrometers. After each spectrometer, a high efficiency single-photon counting avalanche photodiode (SPAD) is used to detect the single-photon emission event and the corresponding electrical signals are sent to a time-correlated single-photon counting module (PicoQuant GmbH, HydraHarp 400), from which a histogram \(g^{(2)}(\tau )\) as a function of the delay time between the two optical paths (\(\tau\)) is recorded. The time-resolved EL is analyzed by a time-correlated single-photon counting technique. The system response time was determined by the data recorded from a 220-femtosecond-long pulse of a Ti:sapphire laser, from which the resolution times of about 495 ps for the \(g^{(2)}(\tau )\) measurements and 280 ps for the time-resolved EL measurements were obtained, respectively.

Fig. 1
figure 1

a n-i-p GaAs nanomembrane-based diode including self-assembled InGaAs QDs integrated onto a piezoelectric crystal, in which the strain field can modify the emission energy of photons emitted from the QDs. b EL spectrum from a single InGaAs QD when only a d. c. bias \(V_d = -2.2\) V is applied. Here the negative indicates a forward bias to the diode due to the reverse flip-chip transferring process of the p-i-n diode nanomembrane. c–e show the results for the second-order time correlation measurements performed between X and X, XX and trion \(X^-\), respectively

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2.2 Electrically driven single-photon emission

By biasing the diode with a d. c. voltage (\(V_d\)), we can electrically address the photon emission from QDs in the device. Figure 1b shows a spectrum recorded from a single QD when a d. c. voltage \(V_d = -2.2\) V is applied to the diode. In the spectrum distinct photon emission peaks are clearly seen. Indeed, these peaks are ascribed to the multi-exciton photon emission from the studied QD, and they can be further identified in the time-resolved correlation measurements. Figure 1c shows the autocorrelation function of the emission line at 1.37532 eV (the brightest line on the right in the spectrum). The autocorrelation function shows an symmetric anti-bunching behavior, together with a suppressed peak at zero delay time [\(g^{(2)}(0)= 0.31\)], indicating that the reduced probability of having two photons emitted simultaneously. This gives an unambiguous indication of the single-photon emission in response to the d. c. power electrical excitation. Furthermore, cross-correlation measurements are performed between the right line and the middle line at 1.37238 eV, and the result is shown in Fig. 1d. An anti-bunching peak at \(\tau <0\) as well as a pronounced bunching peak at \(\tau >0\) is observed. This suggests a biexciton cascade emission dynamics between these two lines. Considering that the right line appears first in response to the increased d. c. pumping power, we are able to identify that these two lines are neutral exciton X (the right line) and biexciton XX (the middle line). Moreover, cross-correlation measurement is carried out between the exciton and the left line at 1.37027 eV, lower than the X by about 5 meV. The correlation function is shown in 1e where an asymmetric anti-bunching dip is observed at zero delay time. This implies that X photon emission and the unknown line do not coexist in the studied quantum dot, which commonly occur between the negative trion exciton (\(X^{-}\)) and the neutral exciton X [26].

Of great importance is electrically pulsed excitation to the QDs within the diode aiming at realization of electrically triggered generation of single photons. This feature is particularly non-trivial for the implementation of on-demand two-photon interference. In our device, the capability of electrically pulsed excitation is achieved by superimposing an ultrafast voltage pulses stream onto the d. c. bias, \(V_d\), via a broadband bias tee [23, 27–29]. The inset in Fig. 2a shows such electrically pulsed excitation scheme, and the spectrum is acquired as only a d. c. bias \(V_d = -2.0\) V is applied. It is noted that this d. c. bias is lower than the EL threshold of the diode and thus no photon counts are recorded at this pump power. Electrically pulsed photon emission is switched on only if a voltage pulses stream is superimposed with appropriate amplitude. As the spectrum shown in Fig. 2b, bright photon emission is observed when a voltage pulse stream with amplitude of \(V_{pp}= -0.8\) V, nominal pulse width of 300 ps and repetition rate of 100 MHz is applied (Picosecond Lab, USA, model 12010). From the spectrum, we can see clear multi-exciton photon emission peaks with high brightness, as in d. c. power electrical excitation. In order to confirm the electrically triggered photon emission, time-resolved EL measurements on X and XX are performed and the results are shown in the inset, from which the lifetime for XX and X is found to be 0.725 \(\pm\) 0.005 and 1.24 \(\pm\) 0.01 ns, respectively. Apart from the time-resolved lifetime measurement, autocorrelation and cross-correlation measurements are carried out and the results are shown in Fig. 2c, d. The periodic autocorrelation peaks together with the absent peak at zero time-delay provides the evidence of the trigged single-photon emission for X. The time separation between the neighboring peaks is 10 ns, which coincides with the repetition rate of 100 MHz. The normalized value of \(g^{(2)}(\tau )\) at zero delay time provides a multi-photon emission probability of \(g^{(2)}(0)= 0.12 \pm 0.04\). This finite probability can be simply described by the expression \(g^{(2)}(0)=(1-\rho ^2)\), where \(\rho =S/(S+B)\). S and B refer to signal and background, respectively, and they can be obtained from the emission spectrum. We find \(\rho = 0.96\) by examining the spectrum shown in Fig. 2b, which gives \(g^{(2)}(0)= 0.078\) and partially explain the nonzero \(g^{(2)}(0)\) value. The residual \(g^{(2)}(0)\) is likely due to recapture processes and the associated multiphoton emission events [24]. In contrast to the absent peak in the autocorrelation measurement for X, a strong bunching peak is observed in the cross-correlation measurement between X and XX, as in d. c. power excitation.

Fig. 2
figure 2

a Electrically pulsed excitation scheme, in which a ultrafast voltage pulse stream is superimposed onto a d .c bias \(V_d\). The spectrum recorded when only the d. c. bias \(V_d = -2.0\) V is applied and there are no photon counts are observed. b Spectrum from the QD when the electrically pulsed excitation is switched on by superimposing a voltage pulses stream on the d. c. bias. The inset shows the time-resolved lifetime measurements on X and XX, respectively. c, d Show the normalized second-order time correlation functions between X and XX

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Fig. 3
figure 3

a Tunable X emission under the in-plane biaxial strain \(\varepsilon _\mathrm{tot}\). Large compressive (\(\varepsilon _\mathrm{tot}<0\)) or tensile strain (\(\varepsilon _\mathrm{tot}>0\)) can be obtained by applying different electric fields to the PMN-PT. The QD is under pulsed electric excitation at 100-MHz excitation repetition rate, 300-ps pulse width and \(V_{pp}=-0.8\) V, \(V_d= -2.0\) V. b–d Autocorrelation measurements demonstrating electrically triggered single-photon emission for X when it is tuned to different energies

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2.3 Energy-tunable electrically triggered single-photon emission

Aside from the capability of electrically triggered single-photon emission, we can achieve dynamically precise energy tuning to the energy of the single photons. In our devices this has been achieved by applying a voltage \(V_p\) to the PMN-PT crystal which induces variable strain fields on the QDs [30–34]. More specifically, the application of \(V_p\) to the PMN-PT results in an out-of-plane electric field \(F_p\) which leads to an in-plane biaxial strain field, \(\varepsilon _\mathrm{tot}\), in the nanomembrane. We record the spectra as a function of the variable \(F_p\) applied on the PMN-PT actuator as shown in Fig. 3a. The shift is expected to be proportional to the opposite of the variation in the volumetric strain at the QD position, which can be estimated as [35]

$$\begin{aligned} \varepsilon _\mathrm{tot}&= 2\times \varepsilon _{yy}\times \frac{S_{11} + 2\times S_{12}}{S_{11}+S_{12}} \nonumber \\&\approx 2.48\times \varepsilon _{yy}\approx 2.48\times d_{32}\times F_p \end{aligned}$$
(1)

where \(S_{yy}\) is one of the two orthogonal in-plane strain components and \(S_{ij}\) is the compliance coefficient of the GaAs material: \(S_{11}= 1.17\) pC/N and \(S_{12}= 0.37\) pC/N [36]. \(\varepsilon _\mathrm{tot}\) is predominantly determined by the piezoelectric coefficient \(d_{32}\), which has a relatively large magnitude of \(-760 \times 10^{-12}\) C/N, and thus we expect a positive \(F_p\) to induce a compressive strain which results in a blueshift of the EL, while a negative \(F_p\) induces a tensile strain, which results in a redshift. We also note that a total energy shift of about 9 meV is achieved as \(F_p\) is varied from \(-\)6.7 to 26.7 kV/cm, corresponding to the total strain field \(\varepsilon _\mathrm{tot}\) from 0.13 to \(-\)0.5 % applied. Noticeably, due to the homogeneous Au-Au bonding on the small QDs-containing nanomembrane, most of the QDs could show the almost same magnitude of the energy shift. Furthermore, the time-resolved autocorrelation measurements are performed on the X at different shifted energy, and the results are shown in Fig. 3. As the X emission line was redshifted to 1.3736 eV at \(F_p\) of \(-\)6.7 kV/cm from 1.37523 eV at \(F_p\) = 0 kV/cm, the \(g^{(2)}(\tau )\) function is measured and plotted in Fig. 3a. The suppressed peak at zero delay time [\(g^{(2)}(0)= 0.13 \pm 0.07\)], as well as the periodic side peaks, proves the triggered single-photon emission and is preserved in response to the applied strain filed. Apart from this, the single-photon emission behavior is also measured as the X emission line is tuned to have higher energy. Figure 3c, d show the \(g^{(2)}(\tau )\) results for the X which is tuned to 1.3774 nd 1.3818 eV by the electric field \(F_p\) at 10 and 26.7 kV/cm, respectively. \(g^{(2)}(0)\) is found to be 0.18 \(\pm\) 0.08, 0.16 \(\pm\) 0.09 for this two tuning energies, suggesting that the electrically triggered single-photon emission remains very well in response to the external strain fields. By comparing the \(g^{(2)}(0)\) at different X emission energies, we do not observe significant changes in the multi-photon emission probability. This finding, together with the demonstrated capability of achieving energy tuning with \(\upmu\)eV precision [22], proves that our technology provides a stable and precise tuning method to the photon emission from an electrically triggered QD-based SPS.

2.4 Tuning the emission energy of single-photon emission from different QDs into resonance

As stated in the previous section, one of the most stringent requirements for the non-postselective two-photon interference is that the triggered single-photon emission generated from distant QDs has to be resonance in energy. Although this has been realized by application of strain fields [13] or electric field [14] in commonly optically excited QD SPSs, this hurdle remains in electrically driven QDs devices and it is still a challenge to be addressed. By combining both of the functionalities demonstrated above, that are, electrically pulsed excitation and energy tunability by strain fields, we are able to overcome the difficulty of bringing the emission energies of different QDs into resonance in our device. Figure 4 shows such tuning capability in our strain-tunable quantum LED devices, where two QDs are tuned into resonance by the strain fields. QD1 has initial photon emission energy at 1.37523 eV when no strain fields applied, while the other QD2 has initial energy at 1.3695 eV. In order to tune their emission energy into resonance, we apply a negative \(F_p\) to the QD1 and a positive \(F_p\) to the QD2. We can see that the emission energy of the QD1 is redshifted, while the QD2 is blueshifted, and they are tuned to have same energy at 1.37324 eV when \(F_p = -4.7\) kV/cm is applied to the QD1 and \(F_p = -17.3\) kV/cm applied to the QD2 (see Fig. 4a, b). Due to the unavoidable creep of piezoelectric actuators and other mechanical-related effects, the emission energy of QDs slightly drifts with a rate of about 10 \(\upmu\)eV min\(^{-1}\), which leads to a difficulty of bringing two remote QDs into resonance. It is noticeable that this can be overcome by employing a closed-loop system in which a fraction of the light is used to provide feedback to the PMN-PT voltage supply, which continuously corrects \(F_p\) in order to lock the energy [22]. After both QDs are stabilized at the same energy, the time-resolved autocorrelation measurements are performed at this resonant energy for the QD1 and QD2, respectively, and the results are shown in Fig. 4c, d. We measure: \(g^{(2)}_{QD1}(0) = 0.14 \pm 0.12\) and \(g^{(2)}_{QD2}(0) = 0.22 \pm 0.06\). These small values are less than 1, verifying the electrically triggered single-photon emission for both QDs. It is worth noticing that the photon emission energies of single photons emitted from different QDs can be tuned and stabilized in the precision of sub-\(\upmu\)eV when an appropriate strain-tuning feedback is used [22]. This would enable the non-postselective two-photon interference by making use of the electrically pulsed single photons with high reliability.

Fig. 4
figure 4

a X emission from two different QDs (Dot 1/2) in the same device (up and bottom panel) is tuned to be in resonance with each other by strain fields. b Energy shifts of the two QDs as a function of the electric field \(F_p\) applied onto the PMN-PT actuator. c, d show the results of electrically puled \(g^{(2)}(\tau )\) for the two dots when they are tuned to degeneracy

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3 Conclusion

In summary, an all-electrically driven single-photon LED has been demonstrated, which allows the generation of triggered, energy-tunable single photons. This device is based on a QD-containing LED nanomembrane integrated onto a 300-\(\upmu\)m-thick PMN-PT piezoelectric crystal. The energy of the QD emission lines can be precisely and stably tuned over a broad range (\({\sim }\)9 meV) by varying the voltage applied to the PMN-PT. We show that the triggered single-photon-emitting characteristic of this diode is well maintained during the strain-controlled wavelength tuning. Together with the ability of tuning the energy of single photons emitted from different QDs into resonance, our device represents a promising way to achieve indistinguishable single-photon emission from two remote single-photon-emitting diodes at high repetition rates. Moreover, our device allows us to employ two-pulse voltage sequence to excite remote QDs, which suppresses multi-photon emission and allows us to carry out a temporal filtering of photons which have undergone dephasing [37]. This peculiar feature might improve the visibility of the quantum interference between remote electrically driven QDs from our devices.