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Avalanche amplification of a single exciton in a semiconductor nanowire

Interfacing single photons and electrons is a crucial ingredient for sharing quantum information between remote solid-state qubits. Semiconductor nanowires offer the unique possibility to combine optical quantum dots with avalanche photodiodes, thus enabling the conversion of an incoming single photon into a macroscopic current for efficient electrical detection. Currently, millions of excitation events are required to perform electrical read-out of an exciton qubit state. Here we demonstrate multiplication of carriers from only a single exciton generated in a quantum dot after tunneling into a nanowire avalanche photodiode. Due to the large amplification of both electrons and holes (>10^4), we reduce by four orders of magnitude the number of excitation events required to electrically detect a single exciton generated in a quantum dot. This work represents a significant step towards single-shot electrical read-out and offers a new functionality for on-chip quantum information circuits.

Semiconductor quantum dots have been proposed as fundamental elements of a quantum information processor 8 . Quantum bits (qubits) can be stored in either the spin state of a single electron 2,3 , the spin state of a single hole 4 , the dark exciton state 9 or the bright exciton state 7 . Among these, exciton qubits are particularly attractive for long distance quantum communication through the exciton-to-photon and photon-to-exciton transfer of quantum information 10,11 . Coherent optical control of a single exciton qubit in quantum dots has been demonstrated with both optical 7 and electrical 1,5 read-out. However, current readout schemes demand millions of excitation events in order to produce a measurable signal.
To reduce the number of excitation events towards single-shot measurements, an internal pre-amplification of the electrical signal would be desirable. Avalanche photodiodes (APD) ensure this high internal gain and generate a macroscopic current in response to a single photon absorbed 15 . As a result, single photons can be efficiently detected 16 . The avalanche process has been shown at the nano-scale using semiconductor nanowires [12][13][14] and carbon nanotubes 17 , with sensitivity limited to, at best, approximately 100 photons. Importantly, semiconductor nanowires grown via bottom-up techniques offer an unprecedented material freedom in growing advanced heterostructures 18,19 due to reduced strain achieved in the growth of highly mismatched materials 20 , and can additionally include hetero-structured 21 or electrically defined 6 quantum dots for quantum information processing.
In this work, we have integrated a single quantum dot in the avalanche multiplication region of a nanowire photodiode, which features high internal gain and sensitivity to single photons. By spectrally and spatially separating the absorption region from the multiplication region, we can selectively generate a single exciton in the quantum dot that is efficiently multiplied after tunneling in the nanowire depletion region under an applied electric field.
We characterize the nanowire internal gain by photocurrent measurements down to the single photon regime. Finally, we show that only 120 individual excitation events are required to perform electrical read-out of an exciton confined in a single quantum dot. A scanning electron micrograph of our device containing a single quantum dot embedded in a contacted InP nanowire is depicted in Fig. 1A. The InP nanowire has been doped in-situ during vaporliquid-solid growth in order to obtain a p-n junction (see Methods). The depletion region of the p-n junction is used to multiply both electrons and holes as they gain enough energy to initiate the avalanche multiplication process. The operating principle of our nanowire avalanche photodiode is shown schematically in Fig. 1B and Fig. 1C. A single photon inci-dent on the device with a frequency of one of the quantum dot energy levels is absorbed and creates a single exciton. Under reverse bias (V sd < 0), the electron and hole separate and tunnel into the nanowire depletion region. Next, both the electron and hole accelerate under the applied electric field and once the carriers gain enough energy, additional electron-hole pairs are created by impact ionization. These additional electron-hole pairs can further trigger carrier multiplication and strongly enhance the photocurrent. The final result is that each exciton created in the quantum dot is multiplied into a macroscopic current. A unique feature of InP nanowires is that the impact ionization energy is similar for both electrons and holes: 1.84 and 1.65 eV, respectively 22 . Both carriers can thus contribute to the avalanche multiplication process and large gains are obtained. In Fig. 1D we probe the quantum dot and nanowire absorption spectra by tuning the laser excitation wavelength. The measured photocurrent shows a broad absorption peak around 825 nm, originating from InP band-edge transitions and suggests the presence of both wurtzite and zincblende crystal structures confirmed by transmission electron microscopy 23 . Three equally spaced photocurrent peaks are observed at higher excitation wavelengths: at 1007, 986 and 963 nm. By comparison with typical photoluminescence spectroscopy of single quantum dots in intrinsic nanowires (see Supplementary information), we assign these three peaks to absorption in the quantum dot s-, p-, and d-shell, respectively. From photoluminescence spectroscopy of the device at V sd = 0 V, we confirm that the peak at 1007 nm is due to absorption in the quantum dot ground state (s-shell). The observed shell separation of 26 meV corresponds to a diameter of ∼ 27 nm according to calculations that assume an in-plane parabolic confinement in the quantum dot and in agreement with the quantum dot size measured with transmission electron microscopy 24 . Notably, we observe high photocurrent (> 1 nA) for resonant absorption in the quantum dot, which is a direct result of efficient multiplication of charges after tunneling in the nanowire.
We now characterize the photo-response of the nanowire avalanche photodiode. Optical excitation above both InP and InAsP bandgaps is utilized in order to excite the entire nanowire depletion region and measure the resulting multiplication gain. We use a 120 Hz mechanically chopped continuous-wave laser at wavelength λ = 532 nm, that is linearly polarized along the nanowire elongation axis. Inset of Fig. 2A shows the temporal response of the photocurrent (blue line) to the laser trigger (dashed line). We obtain a time constant of 1 ms, which is a direct result of the high resistance of the device (60 MΩ). Current-voltage characterization of the device is shown in the main panel of Fig. 2A as a function of incident optical power on the sample. At V sd = 0, only the p-n junction built-in electric field separates electron-hole pairs to produce a measurable photocurrent without multiplication gain. Here, we measure a linear dependence for the ratio of charge carriers collected at the contacts to the number of photons absorbed by the nanowire, which has been obtained through an estimation of the absorption efficiency (∼ 0.3 %, see Methods). We determine that a single photon absorbed in the nanowire is converted into one electron (hole) worth of current with 96 % probability (see Supplementary information). This remarkable efficiency is comparable to state-of-the-art nanowire solar cells 25 . In the reverse bias region (V sd < 0), the dark current is less than 1 pA until an avalanche breakdown occurs at V sd = −15 V, as shown in the Supplementary information. Under illumination, the photocurrent increases rapidly as the applied reverse bias is larger than V sd ∼ -1 V and reaches saturation set by the nanowire total series resistance. The occurrence of a light-induced avalanche at rather low applied bias is due to the use of a small depletion region (∼ 200 nm) and the low impact ionization threshold in InP. This photo-response is reproducible and similar behavior has been observed on six different devices.
In Fig. 2B, we strongly attenuate the excitation pulses for investigating the multiplication gain in the few-photon regime. The device is operated below breakdown voltage at saturation of the avalanche multiplication (V sd = -8 V) and at a temperature of 40 K in order to optimize the signal-to-noise ratio of the photocurrent (see Supplementary information).
Each experimental data point (black circles) corresponds to the current averaged over 120 excitation pulses and with the dark current subtracted in order to obtain the net photocurrent. From the linear fit (blue line) to the experimental data, we determine an internal gain, G i = 2.3 × 10 4 . This high multiplication factor, combined with the low noise of the device (∼0.2 pA), enables for the detection of a single photon per excitation pulse. We conclude that, for obtaining such high internal gain in an individual nanowire, both electrons and holes contribute to the avalanche multiplication of charges. The sensitivity to single photons is confirmed by measuring the photocurrent after individual excitation pulses. In to the dark current (crosses). We observe that the absorption of a single photon yields a signal well distinguished from the dark current with a signal-to-noise ratio greater than 2.
The detection of single photons from an individual InP nanowire does therefore not require the averaging over multiple excitation events or the use of lock-in amplification. Estimation of the number of photons absorbed per excitation pulse was confirmed by photon counting measurements in the few-photon regime, which are well-described by Poisson statistics.
Measurements are described in the Supplementary information.
In the following, we use the single quantum dot as the only absorption region of the nanowire photodiode. By tuning the excitation energy, we selectively excite only the quantum dot transitions and utilize the nanowire as an efficient multiplication channel for the photo-generated carriers. In Fig. 3A we tune the excitation wavelength to the quantum dot strongest resonance, the p-shell transition at λ = 986 nm, and measure the photocurrent as a function of the laser spot position with respect to the sample. The photocurrent image is superimposed with a laser reflection image to exclude contribution from Schottky contacts.
The photocurrent maximum is reached when the laser spot impinges between the metallic contacts. The same photocurrent maximum position is obtained when exciting the entire nanowire with λ = 532 nm, confirming that, as expected, the quantum dot is positioned within the nanowire depletion region.
A comparison of the photocurrent measured as a function of incident light polarization angle for above bandgap excitation (λ = 532 nm) and resonant quantum dot p-shell excitation (λ = 986 nm) is shown in Fig. 3B. As typically observed in nanowires, the nanowire acts as a dielectric antenna for incoming light and thus photons polarized along the nanowire are favorably absorbed 26,27 . We observe this antenna effect both for excitation in the entire nanowire active area (crosses) and for selective excitation in the quantum dot (circles).
Finally, we estimate the gain obtained after a single photon is resonantly absorbed in the quantum dot p-shell and tunnels into the nanowire multiplication region. Remarkably, we measure a large multiplication gain of 1.3 × 10 4 (Fig. 3C). As a result, the generation of a single exciton in the quantum dot is detected using a low excitation rate of 120 Hz, where only a single photon is absorbed in the quantum dot per excitation pulse. The observed detection efficiency is four orders of magnitude larger than previously reported on selfassembled quantum dots embedded in diode structures 1 and seven orders of magnitude larger with respect to photodetectors based on a single contacted quantum dot in a nanowire 27 .
We have demonstrated that InP nanowires provide an efficient one-dimensional channel for electrical transport, where electrons and holes undergo impact ionization with high probability, thereby achieving large multiplication factors. The significant gain (> 10 4 ) we   Estimations of the absorbed photon rates are confirmed by photon counting measurements in the few-photon regime. We measure the photocurrent after individual excitation pulses and we plot in Supplementary Fig. 3A the statistical distribution of the photocurrent, using a bin size of 0.1 pA, for dark (black) and under laser excitation in the few-photon regime with n = 1.00 (red), 2.14 (blue) and 4.29 (green). Here, n represents the estimated average photon rate. The distribution of the photocurrent under no illumination is fit very well with three equally spaced Gaussian peaks (yellow curves) -the sum is displayed by the black line.
The peak at 0.48 pA is attributed to minority carrier drift across the p-n junction, that constitutes the background current for reverse bias operation of the photodiode. Additionally, we observe a maximum of the photocurrent probability at 0.9 pA and a less pronounced peak  6 and exhibit the sequential s-, p-, and d-shell filling as the excitation power is increased.
The constant energy separation between observed shells, suggests a 2D parabolic in-plane potential as a valid approximation for quantum dots in nanowires. This approximation has been used to calculate the quantum dot diameter (27 nm).

Emission wavelength (nm)
Emission energy (eV) Photoluminescence intensity (counts/s)  Figure 9: Photoluminescence spectroscopy of a single InAsP quantum dot in an InP nanowire.
Typical photoluminescence spectra as a function of laser excitation power exhibit the sequential filling of s-, p-, and d-shell as the laser excitation power is increased. A constant energy splitting is observed between the quantum dot shells.