Electrically-driven single-photon sources based on colloidal quantum dots with near-optimal antibunching at room temperature

Photonic quantum information requires high-purity, easily accessible, and scalable single-photon sources. Here, we report an electrically driven single-photon source based on colloidal quantum dots. Our solution-processed devices consist of isolated CdSe/CdS core/shell quantum dots sparsely buried in an insulating layer that is sandwiched between electron-transport and hole-transport layers. The devices generate single photons with near-optimal antibunching at room temperature, i.e., with a second-order temporal correlation function at zero delay (g (2)(0)) being <0.05 for the best devices without any spectral filtering or background correction. The optimal g (2)(0) from single-dot electroluminescence breaks the lower g (2)(0) limit of the corresponding single-dot photoluminescence. Such highly suppressed multi-photon-emission probability is attributed to both novel device design and carrier injection/recombination dynamics. The device structure prevents background electroluminescence while offering efficient single-dot electroluminescence. A quantitative model is developed to illustrate the carrier injection/recombination dynamics of single-dot electroluminescence.


Supplementary Figure 2. Atomic force microscope images of samples. a, A typical
Atomic force microscope (AFM) image of isolated quantum dots on Poly-TPD (1um 1um). Inset: Zoom-in scan of a 150 nm 150 nm area with one dot in this region. b, A typical AFM image of the same sample after depositing a 12-nm thick PMMA layer (5um 5um). Inset: Zoom-in scan of a 0.8 um 0.8 um area from this region. No dots can be found in multiple measurements, indicating that all the isolated dots were buried in the 12-nm PMMA layer. 6 0.11, 0.12, 0.14 and 0.14 respectively. c, Histograms of the g (2) (0) values measured from 30 isolated electroluminescence spots in the devices with approximately 36% of the data points below 0.07 (I), and 26 isolated photoluminescence spots on bare quartz substrates with all of the data points higher than 0.07 (II). Regarding the statistical results for the g (2) (0) of all electro-excited single dots (0.08±0.04), the standard deviation is relatively large. One of the major reasons for such spread distribution of g (2) (0) is due to fluctuation of the thicknesses of PMMA layer, which modulates electron injection rates and thus affects charge balance. At optimal conditions, the EL intensity from single quantum dot shows non-blinking-like time trace at low applied voltages, as shown in Supplementary Fig. 4. In such cases, the g (2) (0) values are generally smaller than the lower limit of g (2) (0) value (~0.07) from photo-excited quantum dots. We would like to note that the uncertainty of the g (2) (0) values has been taken into consideration in such comparison (e.g., the g (2) (0) value shown in Fig. 1e is 0.045 ± 0.005 without any background subtraction). At non-optimal conditions, the unbalanced charge injection results in long-lived charged states in the quantum dots which reduce the average intensity. As a consequence, the signal to noise (mainly from dark counts of APD) ratio is diminished. Considering that the coincident counts at τ = 0 are almost zero, the diminished signal to noise ratio degrades the g (2) (0) values, which brings wide distributions of the statistical results. The red and blue curves are the same as those plotted in Fig. 4c. Orange and green curves present two conditions which deviate from balanced charge injection, i.e., p h =0.5p e and p h =2p e respectively. The simulation results reveals that g (2) (0) for single-dot electroluminescence at all conditions are lower than that for the corresponding single-dot photoluminescence (at identical pumping rates). where = , 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15is a column vector consisting of the 15 states in consideration, and A is the coefficient matrix given by:

Supplementary
Here p e (p h ) stands for the electron-injection (hole-injection) rate of at a certain voltage when the quantum dot is at its neutral state. This charge-injection rate is modified by a coefficient γ when a net negative (positive) charge exists in the quantum dot due to Coulomb blockade effect.
While a positive (negative) charge is presented in the quantum dot, Coulomb attraction is taking into account the electron-injection rate modified by 1/γ as a first order approximation. The coefficients , , , , , in the matrix denote the decay rates (including radiative and non-radiative decays) of six states as X, X + , X -, BX, X 2+ , and X 2-, respectively. Finally, to make the charge circulation a closed loop, we assume that the four-hole (four-electron) state will spontaneously decay to the three-hole (three-electron) states with a rate of p e (p h ), as we only consider states with up to four carriers. This assumption shall not impact the general conclusion, since the 11 (probability distribution of the four-hole state) and 15 (probability distribution of the four-electron state) are negligibly small in the simulation.

Estimation of γ constant
The modification coefficient γ is estimated by following the model described (Poly-TPD) layer is ~5 nm, and is ~7 nm to the surface of the ZnO layer with the existence of a ~12-nm thick PMMA layer. The capacitance C is then calculated as 2.33 aF. Therefore, the energy shift is calculated to be 68.6 meV when adding an additional net charge. This result means that a voltage rising of 68.6 mV is required to keep the injection rate constant. Equivalently, from the experimental data shown in Fig. 1f, we get a reduction of EL count rate of ~0.63 times with the decease of applied voltage by 68.6 mV at a driven voltage of ~2.5 V. Therefore, we estimate the modification coefficient γ due to the Coulomb blockade to be 0.63 assuming that the EL count rate has a linear relation with the carrier injection rate.

Numerical simulation of g (2) (τ)
The second order correlation function g (2) (τ) is proportional to the probability density J(τ) of detecting a photon at time τ provided that a photon has been detected at time zero. With the rate equation mentioned in Section 1, we are able to calculate J(τ) based on the dynamics of six emissive states, i.e., X, X + , X -, BX, X 2+ , and X 2-.
are the emission intensities from these six states at steady state and equals to the sum of six items. The coefficients X , + , − , 2+ and 2− are quantum yield of X, X + , X -, BX, X 2+ , and X 2states, respectively.

Determination of other coefficients
The exciton decay rate is reciprocal to the lifetime of an exciton which was measured from isolated single quantum dots on quartz substrates by the standard TCSPC method. A typical figure is shown in Supplementary Fig. 9d. Lifetime can be acquired by fitting this data with a single exponential decay function. For the decay trace shown in Supplementary Fig. 9d, the exciton lifetime is determined to be 40 ns.

:
For single quantum dot spectroscopy, the single exciton quantum yield is considered as 100% for our non-blinking quantum dots.
k BX : The bi-exciton decay rate is reciprocal to the lifetime of a bi-exciton. Under higher optical pumping power, we can observe the existence of a fast decay channel in single-dot lifetime measurements ( Supplementary Fig. 10a). By fitting data with a bi-exponential decay function, we can get the lifetime for the two decay channels. The coefficient of the fast term increases quadratically with the pumping power which is a signature of bi-exciton decay ( Supplementary   Fig. 10b). Thus, the fast channel with a lifetime of 0.76 ns is attributed to the bi-exciton recombination.

:
The radiative decay rate of a bi-exciton should be four times faster than that of an exciton 29 , namely ~10 ns -1 for our dots. Using the equation of k total =k r +k nr , we estimate that k nr for a bi-exciton is ~9 ns -1 , which is dominated by Auger process. Finally, BX = = 0.076 is calculated. This value is very close to that from the second-order correlation measurements by pulsed laser excitation ( Supplementary Fig. 12, 0.078).
The QY of the positive and negative trion state (|X : ⟩, |X ; ⟩) can be determined from the measured (10 ms time bin, low-power pulsed optical excitation) intensity histograms of single-dot blinking trace ( Supplementary Fig. 9). Following the method used in Supplementary Ref parameters used in our theoretical model.