Single-photon sources with quantum dots in III–V nanowires

1 Introduction

Quantum photonics employs semiclassical and quantum mechanical properties of photons in the generation, manipulation, and detection of light. Among the various applications for quantum photonics [1], perhaps the most impactful ones are in quantum information science including secure communications via quantum cryptography [2], quantum communication with the realization of the quantum internet [3], [4], and optical quantum computation and simulation to solve classically intractable computational problems [5], [6], [7]. All of these applications deal with quantum light fields, including single and entangled photons. Indeed, photons are well suited to operate as decoherence-resistant carriers of quantum information, as they interact only weakly with optically transparent media and can be transmitted by means of free space or fiber optics without interaction among themselves. Photons also have suitable degrees of freedom, like polarization, for the encoding of quantum information [6].

Realizing most of these prospective applications requires efficient single-photon generation, manipulation, and detection. Ideally, all of these functions could be integrated on a chip using nanophotonics fabrication techniques. In addition to well-known linear optical components, highly efficient superconducting nanowire single-photon detectors [8] have emerged that can also be integrated with planar waveguide designs [9]. However, some applications would additionally employ components, such as nontrivial two-qubit quantum gates, which require interaction between two photons in a medium with optical nonlinearity at the single-photon level [1]. Such components are still a major challenge, although, e.g. a two-photon phase shift close to the ideal value of π has been demonstrated for fiber-guided photons [10]. On the other hand, efficient single-photon sources (SPSs) would be immediately useful in applications such as quantum key distribution [12] (using, e.g. the standard BB84 protocol [13]) and linear optical quantum computation [5], [6], [11] (if the emitted single photons are indistinguishable).

Ideally, an SPS deterministically emits exactly a single, indistinguishable photon at a time to a given optical mode. Single-photon generation for quantum photonics has typically been realized by employing (heralded) spontaneous parametric downconversion. However, the spontaneous conversion process is probabilistic, making the sources nondeterministic and hence reducing their usefulness [14], [15]. Increasing the pump intensity improves the generation rate but also increases the chance of generating multiple photons at a time in the output [15]. Another technique for obtaining single photons, which is mostly used in current quantum key distribution demonstrations, is to attenuate a laser such that the average power corresponds to less than that of a single photon. Such single-photon emission is also probabilistic and fundamentally limited compared to a high-efficiency true SPS [16].

These shortcomings of the aforementioned SPSs have, in part, motivated the research on alternative SPSs. Significant progress has been made in this area, and single-photon emission has been demonstrated from, e.g. trapped atoms or ions [17], [18], defect sites in various materials [19], [20], [21], [22], and semiconductor quantum dots (QDs) [23], [24]. Out of these, semiconductor QDs are among the most promising for on-demand SPSs and can employ a wealth of well-known top-down fabrication techniques and processes from integrated electronics and photonics. For example, this fabrication path offers a promising platform for the realization of entire integrated quantum photonic systems with various semiconductor materials [25], [26].

As a platform, bottom-up-grown semiconductor nanowires can have high aspect ratios with smooth sidewalls and form both axial and radial heterostructures, especially axial QDs, with considerable freedom in choosing the materials and compositions [27], [28], [29]. Growth processes of nanowires with embedded QDs are starting to mature and offer a way for fully deterministic positioning of the QDs [30], [31]. Furthermore, nanophotonic structures are often employed to enhance the emission and light extraction from embedded semiconductor QDs, and nanowires can themselves operate as photonic structures that enhance light extraction [32], [33]. Most notably, nanowire growth can be tuned to form a photonic nanoantenna structure [33] for this purpose, which has sparked interest in bottom-up-grown nanowire SPSs as an alternative to top-down-fabricated designs (although the top-down approach currently has attracted more attention).

Here, we review the development and current state of the art in semiconductor SPSs with QDs in bottom-up-grown nanowires and compare them with other semiconductor-QD-based sources obtained via top-down fabrication methods. We will also identify the current challenges with nanowire SPSs and discuss the prospects and possible future research directions. We focus specifically on group III–V QDs, as most of the high-performance SPS demonstrations have been achieved with these materials. SPSs based on colloidal QDs [34] are not considered here. Other recent reviews concerning QD SPSs [16], [24], [35], [36] have not discussed nanowires in detail, and this review will therefore help elucidate the advantages and disadvantages of the bottom-up nanowire growth compared with the top-down approaches to direct future research efforts. Note that, although entanglement plays a major role in many of the aforementioned applications, we focus on single-photon emission; the generation of entangled photon pairs is only briefly mentioned. A recent review on the topic of entangled photon pair generation with semiconductor devices can be found in Ref. [37] and specifically with QDs in Ref. [38].

First, in Section 2, we discuss the characterization of SPSs and the relevant performance metrics, while in Section 3 we introduce the basic principles of single-photon emission from semiconductor QDs. Then, in Section 4, we discuss the emission and extraction enhancement by nanophotonic structures, specifically cavities and nanowires, and in Section 5 we consider the differences in SPS fabrication via top-down methods and bottom-up nanowire growth. In Section 6, we discuss the state of the art in demonstrated performance. Lastly, in Section 7, we discuss the current challenges and prospects for nanowire SPSs, and in Section 8 we present the conclusions.

2 Characterizing single-photon sources

The performance of an SPS can be quantified by considering the following metrics: single-photon purity, indistinguishability of the emitted photons, source efficiency, and source brightness. Single-photon purity is defined as the probability of emitting a single photon instead of multiple photons and is therefore the most fundamental metric. Indistinguishability, on the other hand, concerns the quantum states of successive single photons, with perfect indistinguishability meaning that the photons are emitted to identical quantum states. Many applications require indistinguishability in addition to purity. For example, in linear optical quantum computing, the requirement of indistinguishability is needed to make use of quantum interference between separately generated single photons [6]. Source efficiency states the fraction of applied triggers with which a single photon was collected from the source and is equal to unity in the ideal case. High efficiency is required to obtain deterministic operation. Source brightness is not well defined, but is often used to indicate the maximum rate at which the source can emit single photons (i.e. without degrading the other metrics). However, there exists a discrepancy in the adopted nomenclature such that source efficiency is sometimes referred to as source brightness (see, e.g. Ref. [24]). In the following, we describe briefly the characterization of single-photon purity and indistinguishability, while a more detailed discussion can be found, e.g. in Ref. [39] and the references therein.

Single-photon purity is typically quantified statistically via the second-order coherence g⁽²⁾(τ), where τ is the time delay between two photons in the emitted light field. At zero time delay, in the case of a single mode and a stationary source, the second-order coherence can be expressed with the photon number operator n^(t) as [39]

where t is time, and the angle brackets denote ensemble average. This also means that the g⁽²⁾(0) value is related to the probability P(n) of the source emitting n photons to the mode. In the case of coherent light (photon number probability following Poissonian statistics), g⁽²⁾(τ)=1, and for any classical light field, g⁽²⁾(τ)≥1 [39]. On the other hand, it can be seen from Eq. (1) that a single-photon state yields g⁽²⁾(0)=0 and an n-photon state yields g⁽²⁾(0)=1−1/n. Therefore, the condition g⁽²⁾(0)<0.5 is often considered as the signature of single-photon emission in experiments. Pulsed measurements are not stationary and lead to a modified expression for g⁽²⁾(τ), but the value at zero time delay still equals zero with single photons [39].

Single-photon purity can be experimentally estimated with the so-called Hanbury Brown–Twiss (HBT) interferometer setup [40]. The HBT setup is schematically illustrated in Figure 1A and consists of a beamsplitter, two single-photon detectors, and electronics for coincidence counting and readout. Note that it is also possible to realize the setup with fiber-optic components rather than free-space optics [41]. A single photon passing through the beamsplitter exits in a superposition state of the two output modes. However, the event of detection collapses the superposition and the photon is registered by only one of the detectors. Therefore, single photons result in zero coincidence counts at zero time delay. The second-order coherence between the beamsplitter outputs g34(2)(τ) is the same as for the input g11(2)(τ) and, conveniently, single-photon detectors can be used to obtain g34(2)(τ) approximately, even if a detector with low efficiency and without photon number resolving capabilities is used (the result can still be accurate if the condition P(1)≫P(2)≫P(n>2) is satisfied) [39]. Additionally, coincidence counts with high enough τ values are used for normalization, as g⁽²⁾(τ)→1 for τ→∞, regardless of the type of photon statistics [39]. Experimentally, background light and detector dark counts can lead to false coincidence counts, skewing the statistics, and the raw data is often processed to correct for this (see, e.g. Ref. [42]). Finite time response of the detectors can obscure the g⁽²⁾(0) dip and may also be corrected for (see, e.g. Ref. [43]), especially when slow detectors are used. An example HBT measurement result from Ref. [44] is shown in Figure 1B. This result was obtained with pulsed excitation of a high-purity nanowire SPS.

Figure 1:

HBT and HOM measurements.

(A) HBT measurement scheme for characterizing single-photon purity. (B) Example HBT measurement result obtained with pulsed excitation of the nanowire SPS reported in Ref. [44] (the blue solid line is a fit to the measured data). (C) HOM measurement scheme for characterizing indistinguishability. (D) Example HOM measurement result obtained with pulsed resonant excitation of the micropillar SPS reported in Ref. [47] and inducing either parallel or perpendicular polarization between the two input modes of the beamsplitter. Figure reprinted with permission from: (B) Ref. [44], 2016 by the American Physical Society; (D) Springer Nature, Nature Photonics, Ref. [47], 2016.

The indistinguishability of two photons can be defined as [39]

where ρ^1 and ρ^2 are the density matrices of the photons, and ∥ρ^1−ρ^2​∥2 is their operational distance. Ideally, when the density matrices are equal, the two photons are fully indistinguishable with I(ρ^1,ρ^2)=1. Indistinguishability can be experimentally estimated via the so-called Hong–Ou–Mandel (HOM) interference measurement [45]. The HOM setup is schematically illustrated in Figure 1C and, like the HBT setup, consists of a beamsplitter, two single-photon detectors, and electronics for coincidence counting and readout. Here, photons emitted by an SPS are directed to both the beamsplitter inputs. Typically, the SPS is excited with pairs of trigger pulses, and the resulting train of single-photon pairs is split and directed to the two input modes of the beamsplitter in the HOM setup, with the pulse pair time separation accounted for by the added optical delay for the other input mode (see, e.g. Ref. [46] for more details). An example HOM measurement result from Ref. [47] is shown in Figure 1D. This result was obtained with a high-indistinguishability micropillar cavity SPS.

The idea in the HOM measurement is that, if two photons incident on the two input modes of an ideal 50:50 beamsplitter are in the same pure quantum state and overlap spatially and temporally in the beamsplitter, they will exhibit quantum interference (see, e.g. Ref. [48] for details) and will leave the beamsplitter together in the same output mode. Therefore, there will again be no coincidence counts. Clearly, this requires single-photon states at the inputs, and the HOM measurement is hence also sensitive to the single-photon purity. Purposefully making the photons fully distinguishable, e.g. by removing the overlap via a time delay or by having orthogonal polarizations, allows obtaining the HOM interference visibility as [39]

where C_I and C_D are the coincidence probabilities (or counts in the experiment) with and without the interference, respectively. If the photons are in pure states and the beamsplitter ratio is 50:50, the visibility V_HOM equals the indistinguishability as defined in Equation (2) [39]. Some measurement nonidealities, including the residual multiphoton emission probability, an unbalanced beamsplitter, the classical interferometer fringe visibility, and finite detector time response, have also been accounted for when extracting the HOM visibility from raw data [46], [47], [49].

The source efficiency η can usually be divided into the generation efficiency η_g and the extraction efficiency η_ext as η=η_gη_ext [39]. Generation efficiency states the probability of obtaining emission of a single photon per trigger and depends also on the used excitation (e.g. laser excitation power). Generation efficiency includes both the probability of preparing the emitter in the correct excited state with a trigger and the probability of single-photon emission via the correct radiative transition from that state. The excited state may also decay to the ground state through nonradiative pathways (if these are available), increasing the chance of obtaining zero photons per trigger and hence reducing the efficiency. The extraction efficiency, in turn, states the probability of collecting the emitted photon to an external element, and depends on the outcoupling efficiency from the source and the directionality of the emission from the source. Furthermore, the photon collection is also dependent on the external optical elements (e.g. the numerical aperture of the first lens in free-space collection optics). Unfortunately, there seems to be no clear consensus on the measurement conditions and procedures for SPS efficiency.

Note that, in measurements, single-photon purity and indistinguishability are typically treated as static, although these can actually be dynamically dependent on the excitation and the environment [50]. Single-photon emitters may also exhibit temporary (blinking) or permanent (bleaching) loss of emission under continuous optical excitation, although this is typically a larger concern for colloidal semiconductor QDs [51] than QDs embedded in bulk as discussed here. Furthermore, different measurement conditions can significantly affect the single-photon emission metrics. For example, resonant excitation of QD SPSs can improve both purity [52] and indistinguishability [47] compared to nonresonant excitation. Additionally, high-efficiency and low-dark-count-rate detectors (e.g. superconducting nanowire single-photon detectors) are required to measure high purity without applying corrections to the obtained result [52]. Therefore, comparing SPS measurement results may not be fair if the measurement conditions differ too much.

3 Single-photon emission from a semiconductor quantum dot

Single-photon emission from a semiconductor QD is based on radiative transitions between the discrete energy levels in the conduction and valence bands. These discrete levels are the result of three-dimensional quantum confinement of the carriers when the QD material has a bandgap smaller than that of the host semiconductor (with type I band alignment such that both electrons and holes are confined in the QD). A short discussion on the fundamental aspects of single-photon emission from semiconductor QDs is given in the following, while a more comprehensive review on the topic of excited states and single-photon emission in QDs can be found in Ref. [35].

Considering the lowest discrete energy levels forming in the conduction and valence bands of the QD (for electrons and holes, respectively), there are only a limited number of excited configurations. Each discrete energy level can support at most two electrons (or holes) with opposite spins due to the Pauli exclusion principle. Furthermore, the small spatial scale of the QD localizes the electrons and holes such that Coulomb interactions lead to the formation of excitons rather than independent electrons and holes. Note that the discrete energy levels in a QD are also referred to as s-shell, p-shell, and so on, following the notation of atomic energy levels. The different charge configurations of the s-shell are then biexciton |XX⟩, charged excitons |X±⟩, exciton |X⟩, charged ground states |g±⟩, and ground state |g⟩. These configurations are illustrated in Figure 2.

Figure 2:

QD states.

Schematic energy band diagram (conduction band E_C and valence band E_V) for a QD embedded in a bulk host semiconductor (left) with possible exciton configurations (exciton |X⟩, charged excitons |X±⟩, and biexciton |XX⟩) of the s-shell discrete energy levels (middle) and ground states (charged |g±⟩ and neutral |g⟩) corresponding to recombination of the excitons (right). Filled and empty circles represent electrons in conduction band and holes in valence band, respectively. Arrows represent the spin state (up or down).

Depending on the spin states, the exciton |X⟩ may or may not have an allowed optical recombination transition (bright and dark state, respectively) [35]. The biexciton |XX⟩, on the other hand, may only form in one way and recombine in two steps emitting two photons. However, the photons will have different energies corresponding to the biexciton binding energy [53]. Similarly, the added interaction in the charged exciton states |X⁺⟩ and |X⁻⟩ leads to different emission energies. Furthermore, a radiative transition from an exciton and the corresponding transition from a multiexciton configuration have different energies due to the effect of the interaction. Therefore, single-photon emission from a chosen transition can be extracted by filtering in energy [54]. The dipole-allowed transitions between these states and the ground state are strongly influenced by the orientation of the natural quantization axis of the QD (typically given by the small height in the vertical direction), leading to transition dipoles perpendicular to this axis [55].

Pure single-photon emission can thus be obtained by exciting the QD and spectrally filtering the emission such that only the photon from, e.g. the radiative recombination |X⟩→|g⟩, is extracted. Such narrow-band spectral filtering is also possible in integrated solutions [56]. With nonresonant excitation, electrons and holes are generated across the bandgap of the bulk host semiconductor embedding the QD and will diffuse to the QD and relax to the lower energy levels. In order to avoid re-excitation of the QD during a single excitation pulse (i.e. to avoid multiple single-photon extraction per pulse), decay of the generated carrier population in the host semiconductor should occur significantly faster than the radiative recombination in the QD [50].

On the other hand, resonant excitation may be used to directly excite the |X⟩ state, thus reducing the chance of re-excitation and improving the g⁽²⁾(0) value. However, it is then necessary to employ additional measures (e.g. a cross-polarization scheme) to reject the scattered excitation laser light [57], [58], [59]. Alternatively, the (quasi) resonant excitation may target the next lowest energy levels (p-shell) [60]. Even with resonant excitation, there is a finite chance for QD re-excitation within a single excitation pulse [61]. It is also possible to use resonant two-photon excitation of the |XX⟩ configuration and extract the emission from the |XX⟩→|X⟩ transition by spectral filtering [52], [61]. The benefit of the resonant two-photon excitation is that the QD re-excitation probability is strongly suppressed and that the laser energy is tuned to half of the |XX⟩ state energy and is hence sufficiently far away from the emission wavelength for efficient filtering.

Note that, with the biexciton, it is also possible to obtain a polarization-entangled photon pair [62] via the so-called biexciton–exciton radiative cascade [63]. Due to electron–hole exchange interactions, there is fine-structure splitting (FSS) between the energies of the two bright exciton states with opposing spins [64]. However, if the FSS is small enough, the cascade pair of photons can actually be emitted to a polarization-entangled state. For example, a small FSS can be a result of the QD structure [65] or of tuning with an electric field [66]. Therefore, semiconductor QDs can be used as sources of entangled photon pairs, e.g. with resonant two-photon excitation of the biexciton state [67], [68].

In practice, coupling of the QD emitter with its solid-state environment limits the single-photon purity and indistinguishability. For example, interactions of excitons with phonons causes broadening of the zero-phonon line and the appearance of phonon sidebands [69], [70]. This thermal broadening can lead to spectral contamination from transitions involving different exciton configurations and hence reduced single-photon purity [71]. Cryogenic operation temperatures are often employed to avoid the thermal broadening, although room-temperature SPSs would be preferred for practical reasons. In fact, selecting materials with large band-offsets and fabricating smaller size QDs can increase quantum confinement and Coulomb interaction, leading to larger energy separation between the different excited states. With such materials and small QDs, spectral contamination from other excited states could be significantly reduced to allow single-photon emission even at room temperature [31], [72].

Even with pure single-photon emission, indistinguishability may be limited because of dephasing. First, the emission line broadening due to inelastic exciton–phonon interactions also leads to loss of coherence, and elastic interactions are a source of pure dephasing [69], [73], [74], [75]. It was even proposed in Ref. [76] that coupling to phonons ultimately limits the simultaneously achievable indistinguishability and efficiency. In addition to phonons, the QD environment may contain charge traps with a fluctuating charge state generating a fluctuating electric field at the QD, and randomly oriented nuclear spins generating a fluctuating magnetic field, both of which can lead to dephasing [77]. At time scales longer than the exciton radiative lifetime, the electric and magnetic fields generated by the fluctuating charge and spin environment also lead to variation in the energy of the photons emitted (variation in the radiative transition energy) at different times and hence reduced indistinguishability with a large number of consecutive single photons [77], [78]. Note that charge fluctuations in the QD environment causing this spectral diffusion can be due to the effect of nonresonant optical excitation and temperature (phonons) [79], [80], [81], [82]. Employing resonant excitation of the QD can, therefore, lead to considerably reduced spectral diffusion [80]. Additionally, the QD emitter could couple to mechanical modes of the SPS structure via strain, also leading to spectral diffusion and reduced indistinguishability [83]. Indistinguishability can be improved by suppressing the effects of the environment, including employing cryogenic temperatures to reduce the phonon population and controlling the charge or spin environment with an applied electric field [47] or additional optical excitation [84]. Alternatively, indistinguishability may be improved by enhancing the spontaneous emission rate (reducing the radiative lifetime) using nanophotonic structures [85].

4 Nanophotonic structures for enhancement of emission and extraction

Semiconductor QDs inside a piece of bulk semiconductor are not good for high-performance SPSs, as the extraction efficiency is severely limited by the lack of directionality in the QD emission and by the total internal reflection occurring at the semiconductor–air interface (high refractive index contrast leads to a very narrow solid angle within which the emitted light can escape the bulk semiconductor and the extraction is in the order of a few percents for typical III–V semiconductors). The total internal reflection problem could be solved by using, e.g. solid or liquid immersion lenses [86]. However, a more elegant way is to employ nanophotonic structures, as these structures may not only improve the extraction efficiency but also enhance spontaneous emission to a desired optical mode inside the structure or inhibit emission to other modes. Furthermore, nanophotonic structures offer, in principle, the possibility for on-chip integration.

For both extraction efficiency and single-photon indistinguishability, it is highly desirable that an SPS emits to a single, well-defined optical mode. The preference in emission coupling to a desired optical mode within a photonic structure can be expressed by the β-factor [87]

where Γ is the spontaneous emission rate to the desired mode supported by the structure, and γ is the spontaneous emission rate into all other modes. The extraction efficiency then further depends on the outcoupling efficiency of photons in the desired mode and the directionality of the outcoupled light field (which in turn affects how well the emitted photons in the mode can be collected).

Various photonic structure designs have been employed for semiconductor QD SPSs, including planar cavities [58], [66], micropillar cavities [47], [84], [88], [89], [90], [91], [92], microdisk cavities [93], [94], photonic crystal cavities [95], [96], [97] or waveguides [59], [98], [99], and novel photonic structures such as nanotrumpets [100], optical horns [101], and nanowires [33], [44]. An important early demonstration of QD single-photon emission was achieved using a microdisk cavity [93]. So far, cavity structures (especially micropillar cavity structures) have provided the best performance in top-down-fabricated SPSs [47], [52], [92], [102], while bottom-up-grown nanowire SPSs tend to employ the nanoantenna scheme introduced in Ref. [33]. These two types of photonic structures are briefly discussed here, while a more general review on interfacing QD single-photon emission with photonic nanostructures can be found in Ref. [35].

4.2 Nanowire nanoantenna

Nanowires can embed QDs along their axis and act as waveguides with highly efficient, directional outcoupling after proper design. The idea of using QDs obtained via axial nanowire growth as SPSs was mentioned, e.g. in Ref. [110] in 2002, and likely even before that, while some of the early experimental realizations of this idea include Ref. [111] in 2005 and Ref. [112] in 2010. The nanowires in Ref. [111] exhibited g⁽²⁾(0)<0.5, demonstrating operation as SPSs. In Ref. [112], improved single-photon emission (g⁽²⁾(0)=0.12) as well as biexciton–exciton radiative cascade was obtained. Common to these two examples is that the nanowires were still used as such without further engineering effort to improve the emission or light extraction.

In 2009, a nanowire structure working as a nanoantenna, which greatly improves the source efficiency, was proposed in Ref. [33]. The nanoantenna design constitutes three different factors as illustrated in Figure 3. First, the ratio of the nanowire diameter to the emission wavelength is optimized such that there is only one guided mode (i.e. the fundamental HE₁₁ mode) available along the nanowire axis into which the emission can couple. Furthermore, the diameter-to-wavelength ratio is chosen to maximize the funneling of emission into that mode by suppression of coupling to the continuum of radiation modes. Second, the HE₁₁ mode may travel toward the substrate (away from the light collection direction) but can be directed back by using a properly designed bottom mirror (e.g. a dielectric/metal mirror [113]). This design also requires tuning the QD-to-mirror distance in order to obtain an antinode in the electric field at the QD, so that the reflection enhances maximally the emission into the HE₁₁ mode (i.e. enhances the Purcell factor of the mode). Third, if the nanowire tip is fabricated to have a conical taper toward the top, the HE₁₁ mode will be adiabatically expanded outside the nanowire. Then, the mode couples out into a low-numerical-aperture emission lobe. Therefore, the extraction efficiency becomes enhanced as a result of the minimized reflection of the HE₁₁ mode back to the nanowire. In addition, the low-numerical-aperture emission lobe from the tapered tip makes the collimation easier (compared to the case of a flat nanowire tip), facilitating photon collection with external optics of limited numerical aperture. To some extent, these features had already been discussed earlier, e.g. emission to guided modes in Ref. [32], bottom mirror designs and performance in Ref. [114], and the tapered tip in Ref. [115].

Figure 3:

Schematic nanowire nanoantenna SPS design.

The nanoantenna design includes (I) optimized nanowire diameter for funneling the QD emission into the guided HE₁₁ mode, (II) bottom mirror to reflect the downward emitted photons (modal reflection coefficient r_b), and (III) tapered nanowire tip to adiabatically expand the guided mode outside the nanowire for minimized backreflection (transmission T(θ) into an upward cone with angle θ).

High β-factor values above 0.9 are achievable with the nanowire nanoantenna design [33], [104]. The high β-factor values are additionally obtained over a relatively broad wavelength band (Δλ/λ=0.26 [33], [116]) compared to the narrow resonances in cavities [33], which gives more tolerance to fabrication imperfections. Such a broadband response also facilitates an easier use of quasi-resonant excitation or resonant two-photon excitation and generation of entangled photon pairs with different wavelengths, both of which are more difficult to match with cavity modes. On the other hand, this broadband operation may also limit the ultimate trade-off between single-photon indistinguishability and efficiency (see the discussion in Ref. [76]). If constructive interference is assumed for the field reflected by the bottom mirror at the emitter, and multiple reflections inside the nanoantenna are not taken into account (i.e. if we assume that the reflection of the HE₁₁ mode at the nanowire tip is negligible), the extraction efficiency for the nanowire antenna may be written as [33]

(5)ηext=T(θ)β(1+|rb|)221+β|rb|),

where T(θ) is the tip transmission into an upward cone with angle θ and r_b is the reflection coefficient for the guided mode at the bottom mirror. At the optimized condition of T(θ)≈1 and |r_b|≈1, Eq. (5) further simplifies to η=2β/(1+β). Theoretically, the extraction efficiency could then go as high as around 95% [33]. This, however, does not take into account any loss mechanisms such as scattering due to sidewall roughness. A more detailed inspection of the nanowire nanoantenna design can be found in the review in Ref. [116].

5 Single-photon source fabrication

Both top-down-fabricated and bottom-up-grown SPSs most often employ vapor-phase epitaxial crystal growth methods including metal-organic vapor phase epitaxy (MOVPE), molecular beam epitaxy (MBE), and chemical beam epitaxy (CBE). The main difference, however, is in how the device structures are obtained: in top-down fabrication, patterning and etching are used to selectively remove grown material, while in bottom-up nanowire fabrication, patterning can be used to achieve selective growth of material. Nanoscale patterning is typically achieved via electron beam lithography (see, e.g. Ref. [117]) or nanoimprint lithography (see, e.g. Ref. [118]), although optical lithography may certainly be used for patterning micrometer-scale pillars and aperture openings. Both top-down and bottom-up nanowire approaches have benefits and shortcomings, which are briefly discussed in the following.

5.2 Bottom-up-grown nanowire sources

Bottom-up growth of semiconductor nanowires offers a way to fabricate high-aspect-ratio structures with smooth sidewall surfaces and both axial and radial heterostructures or doping profiles. Due to the nanowire geometry, stress resulting from lattice mismatch is more efficiently accommodated via strain relaxation in the radial direction without the formation of dislocations [135], [136], [137]. Therefore, heterostructures in nanowires can employ a wider variety of materials and compositions than in planar configurations where epitaxial thin-film growth requires lattice matching and the aforementioned Stranski–Krastanov QD growth requires suitable lattice mismatch.

There are two distinct growth modes by which nanowires can be realized: vapor–liquid–solid (VLS) and selective-area epitaxy (SAE). In general, III–V nanowires can grow either epitaxially or non-epitaxially and tend to prefer the [111] crystalline orientation [138] with polytypism in the crystal structure between the zincblende and wurtzite structures (unlike bulk III–V materials which tend to only exhibit the zincblende structure, except for the nitrides) [139]. Note that the difference in the two growth modes is mainly in the axial nanowire growth, whereas the radial vapor–solid growth is similar for both modes. Both growth modes allow forming heterostructure QDs.

The VLS nanowire growth, in short, is mediated by a metallic droplet that is assumed to be in liquid phase and collects the growth species (at least group III) introduced in vapor phase, leading to nucleation and solid crystal growth below the droplet. The growing nanowire then lifts up the droplet that sits at the tip of the nanowire. The VLS growth is schematically illustrated in Figure 4A. The metallic droplet material can either be one of the group III growth species (which is often called self-catalyzed or self-assisted growth) [140] or a foreign material, among which Au is the most common and well known [141]. Nanoscale patterning of openings in a mask layer for self-assisted growth, or Au disks for Au-assisted growth (with or without a mask), may be used to define the nanowire growth sites [30], [117], [142].

Figure 4:

Schematic illustration of the nanowire growth modes.

(A) VLS growth mode where axial growth is mediated by a metallic droplet (typically Au). (B) SAE growth mode where growth takes place at an opening in a mask layer. Radial growth takes place via direct vapor—solid growth in both modes. The growth direction (axial or radial) is indicated with blue arrows, and heterostructure insertions (QDs) are indicated with red color. The ideal case is depicted here, where axial and radial growth can be independently controlled to obtain the desired nanowire geometry.

The VLS growth mode was originally introduced by Wagner and Ellis [143], who considered the growth of Si "whiskers" with the aid of Au droplets. Since then, more research was conducted on Si [144], after which the focus shifted to mainly III–V materials such as GaAs, GaP, InP, InAs, and their ternaries [145], [146], [147], [148]. In the past couple of decades, considerable research effort has been made to understand the effect of various growth conditions and substrate preparations for VLS nanowire growth [149], [150], [151], [152]. It has become possible to obtain nanowires of high crystal quality [139], to control the crystal phase [139], [153], to switch between axial VLS growth and radial vapor–solid growth [154], to dope the nanowires during growth [155], and to obtain axial and radial heterostructures [28], [30], [110], [156]. Despite the significant progress that has been made, the detailed growth mechanism is still not fully understood and research in this area is going on [27], [151].

SAE growth, on the other hand, is direct vapor–solid growth and is based on growth mask layers and differences in the nucleation and crystal growth on different crystal facets due to differences in surface energies [157]. Openings in the growth mask exposing the underlying substrate define the locations where nanowires start to grow, and for axial growth when the substrate surface is a {111} plane, the growth conditions are selected such that the {1¯10} facets have significantly lower growth rate than the {111} facets. Then, {1¯10} sidewall facets emerge and the growing crystal assumes a vertical nanowire shape with hexagonal cross-section. Ideally, the radial growth can be fully suppressed during axial growth, and the nanowire diameter is set by the size of the mask opening. The SAE growth is schematically illustrated in Figure 4B. Note that, unlike in the figure, the mask opening does not need to be a hexagon and the nanowire may grow laterally wider than the opening to assume the hexagonal shape (even in the case of negligible radial growth rate afterward).

Typical III–V materials for SAE nanowire growth include GaAs [157], [158], InP [159], InAs [160], and some ternary compounds [158]. Since patterning is already a part of the process, regular arrays with a square or hexagonal lattice are typical. As with VLS growth, it is possible to obtain high crystal quality [159], to control the crystal phase [161], to switch between axial and radial growth [29], to dope the nanowires during growth [29], and to obtain axial and radial heterostructures [29], [162]. In principle, SAE growth is simpler than VLS growth, as only two phases, vapor and solid, are involved and no foreign material, such as Au, is present. Still, the growth dynamics are complicated by, e.g. dependence on size and spacing of the mask openings, on the evolving nanowire geometry during the growth, and on the relative supply of group III (or V) constituents in the growth of ternaries [163], [164], [165]. Consequently, understanding the subtleties and obtaining a high degree of control in nanowire SAE growth is a challenge.

Conceptually, obtaining QDs in nanowires with either growth mode is simple: new materials are briefly introduced during the axial nanowire growth such that a section of the lower bandgap material will be inserted in the growing nanowire. Patterning of the metallic droplets in VLS or the mask openings in SAE defines the lateral position of the nanowire, diameter of the droplets or openings defines the QD diameter, and axial growth times define the QD vertical position and height. Therefore, patterning combined with bottom-up growth offers full control over the positioning and size of the QD. Radial growth may then be used to fully embed the QD inside the nanowire. Alternatively, it is possible to clad the nanowire with an atomic layer deposition (ALD) oxide shell in order to obtain a waveguide structure [166]. However, nanowire heterostructure growth is not trivial in practice. For example, obtaining abrupt interfaces in axial growth (especially with VLS) is difficult due to various memory effects leading to composition gradients [27], [167], [168], [169]. In Au-assisted VLS, the solubilities of group V species in the Au droplet are low compared to those of group III [148]. It is therefore generally easier to form axial QDs by switching of the group V material during the growth than by switching group III, which is however still possible [168]. Regardless, a rather impressive level of control in growing QDs in nanowires has been achieved. This control allows, e.g. fabricating pairs of QDs with small enough spacing such that the electronic states become coupled. This coupling was recently demonstrated in Ref. [170], where a coupled QD pair in a nanowire emitted entangled photon triplets via a triexciton triple cascade.

Compared to top-down fabrication, there are some major advantages with the bottom-up nanowire growth for SPS fabrication: wide material compatibility, deterministic fabrication yielding a single QD per nanowire, and natural alignment of the QD to the nanowire waveguide axis. The most researched material system is InAsP QDs in InP nanowires, with which the emission can span the wavelength range starting from around 880 nm and including the telecom C-band [171], [172] (at cryogenic temperatures). For example, an SPS operating at the wavelength 1310 nm (in the telecom O-band) has been demonstrated with this material system [172]. Single-photon emission has also been demonstrated, e.g. around 725 or 765 nm with GaAs QDs in AlGaAs [173], [174], 286 nm with GaN QDs embedded in AlGaN [31], and 468 nm with InGaN QDs (or nanodisks) embedded in GaN [175]. Various III–nitride QDs should overall be able to cover emission from ultraviolet to telecom wavelengths [175]. Furthermore, it is also possible to grow nanowires with basically all these materials on top of Si [174], [176], [177], [178], with the prospect of III–V SPS integration with Si photonics. Assuming symmetric radial shell growth, the axial QD becomes embedded exactly on the axis of the nanowire waveguide in one monolithic growth step, quite unlike in the previously discussed top-down fabrication with alignment procedures. Still, the nanowire SPSs may also need to be individually characterized, as the QD emission wavelength may vary from wire to wire due to growth variations.

On the other hand, there is no feasible way to grow nanowires with both axial QDs and DBR stack cavity structures for improved indistinguishability. These two features cannot be simultaneously achieved because thick nanowires are needed for efficient DBR stacks [114], which is incompatible with axial QD growth. Furthermore, nanowire growth processes are in general not quite as well optimized as traditional planar growth (e.g. thin-film growth). In addition to the challenge of obtaining well-defined QDs with certain size and abrupt interfaces, avoiding imperfections in the growth of the nanowire itself, such as changes in crystal structure or orientation [149], [179], [180], is also not trivial. Defects in crystal structure can create charge traps, affecting the local electrostatic environment of the QD and adversely affecting the single-photon emission properties [44]. In addition to states related to crystal structure defects, states related to the nanowire surface may also act as charge traps [181]. Therefore, surface passivation techniques (e.g. additional shell growth [182], [183] or ALD coating [184]), which prevent the formation of surface states within the bandgap range, could also be employed. Regardless of the difficulties in growth optimization, high-quality nanowires with QDs have been demonstrated with various material systems and techniques [156], [162], [171], [185].

One example of the state-of-the-art nanowire nanoantenna SPS fabrication can be found in Ref. [44]. The fabrication process can be roughly divided into the following steps: (i) deposition of SiO₂ growth mask layer on an InP substrate and patterning of openings filled with Au droplets (presumably by electron beam lithography, wet etching, Au evaporation, and lift-off as in Ref. [171]); (ii) InP nanowire axial growth with the InAsP QD insertion, and (iii) mixed InP axial and radial growth to cap the nanowire to the correct diameter for waveguiding and to obtain a tapered tip for efficient light extraction. Fabrication of the bottom mirror was omitted in this case but could be achieved by peeling off the nanowires in a polydimethylsiloxane (PDMS) film and depositing the mirror on the bottom side [186], or possibly by using an embedded Au mirror under the SiO₂ mask as proposed in Ref. [116]. It is of note that the fabrication process here is considerably simpler than that for the micropillar cavity discussed in Section 5.1. On the other hand, this nanowire design does not include the possibility for emission tuning with an electric field.

It can further be noted here that, due to the high spatial symmetry, group III–V QDs in the [111] nanowire growth direction should exhibit vanishing FSS [65] and, therefore, also perform well as sources of entangled photon pairs via the biexciton–exciton radiative cascade. However, a nonvanishing FSS has actually been seen in experiments [187], which was attributed to compositional inhomogeneity in the ternary InAsP QD. Regardless, entangled photon pair emission has been demonstrated from InAsP QDs in bottom-up-grown InP nanowires in several papers [187], [188], [189]. The nanoantenna design is highly suitable for entangled photon pair sources as well, because of the relatively broadband effect of emission funneling into the guided mode [188].

6 State of the art

Nanowire SPSs following the nanoantenna design were experimentally demonstrated in 2010, first with top-down fabrication methods [113] and later with bottom-up growth [173], after which the approach has become quite ubiquitous for experimental bottom-up nanowire sources (see, e.g. Refs [44], [154], [171], [172], [186], [190], [191]). Experimental state-of-the-art results are discussed in the following, and Table 1 provides an overview of the obtained performance values. State-of-the-art results with top-down QD SPSs are also given for comparison. Brightness values are not included here because of the lack of comparable measurement conditions.

7 Current challenges and outlook

It is apparent from the state-of-the-art comparison that bottom-up nanowire sources tend to be outmatched, performance wise, by the other QD-based designs. Especially, micropillar cavity sources have exhibited simultaneously high purities and indistinguishabilities with moderately high extraction efficiencies [47], [92], [102]. Furthermore, a top-down-fabricated cavity-based source with electrical operation and 1550 nm telecom emission has been demonstrated [205]. Other designs with electric contacts allow for tuning of the emission by an applied electric field [47], [91], [206], even combined with integrated lasers for on-chip excitation [207]. However, the bottom-up nanowire sources offer, in principle, more straightforward, deterministic fabrication and more freedom with the material choices and compositions. It could be argued that, taking these fabrication benefits into account, bottom-up nanowire SPSs are already a superior option for applications that require just efficient and pure single-photon generation regardless of indistinguishability.

Since the designs employing planar growth and top-down fabrication currently tend to have the edge in demonstrating both individually and simultaneously high values of purity and indistinguishability, one of the challenges for bottom-up nanowire sources is to improve their performance in order to provide a truly viable alternative. First, the fabrication and growth processes should be developed to simultaneously obtain optimized bottom mirrors and nanowires of high structural quality with optimized tapered tips in order to realize the theoretical extraction efficiencies exceeding 90%. Second, higher indistinguishability is needed. Unfortunately, in the presented nanoantenna scheme, it is not possible to obtain cavity structures with DBRs like in planar or top-down-etched micropillar designs. This is because the nanowire core diameter needs to be initially small to define the QD, and DBR stacks only in such a small diameter nanowire core are insufficient [114] (and forming a DBR stack in the axial direction during the radial growth is not feasible). Nanowire SPSs might still benefit from techniques already adopted elsewhere to improve performance. Especially, employing resonant s-shell excitation or the resonant two-photon excitation technique could considerably improve the purity and indistinguishability as seen in top-down fabricated SPSs. Some other techniques to investigate might include temporal filtering with amplitude modulation [94] and resonant excitation using adiabatic rapid passage with frequency-chirped pulses [196]. Additionally, QD emitter coupling to mechanical modes of the nanowire SPS structure might be worth investigating. Furthermore, the single nanowire nanoantenna design is not the only option. For example, in Ref. [208], a design with an annular-grating-patterned hyperbolic metamaterial in conjunction with nanowire QDs was proposed to provide both spontaneous emission enhancement and directional light output.

Another important area for improvement is the available emission wavelength range and tuning. For example, single-photon emission at the telecom 1550 nm wavelength using the InAsP material system is still challenging with bottom-up nanowires [172], whereas with top-down-fabricated SPSs emission at this wavelength was first demonstrated in 2005 [212]. The earlier demonstration with top-down-fabricated SPSs is largely due to the fact that planar growth and self-assembled Stranski–Krastanov QD growth processes are older and more well developed than nanowire QD growth. However, since the nanowire geometry allows much less stringent requirements for lattice matching, nanowire growth will have the edge in this regard if the growth processes can be optimized to a sufficiently high degree.

Perhaps a more important development direction then is to employ techniques for emission wavelength tuning, as it is still difficult to obtain several nanowires with QDs on the same chip with small enough inhomogeneous spectral broadening for applications requiring SPSs with certain wavelengths. QD emission tuning has been demonstrated in top-down designs with electric fields [47] and strain [213], [214]. Strain-tuning has been demonstrated with bottom-up nanowire SPSs as well [193]. Additionally, emission wavelength tuning with an external magnetic field [174] or by laser-induced material intermixing [215] has recently been reported for nanowire QDs. Although nanowire QD emission wavelength tuning with electric fields has been reported [216], [217], to the best of our knowledge, this has not been employed in nanowire SPSs.

Achieving electrical excitation with bottom-up nanowire nanoantenna SPSs also still remains a challenge. Since some of the potential applications would prefer electrical operation, this is an important problem to solve. Some designs for electrical operation have been proposed. For example, in Ref. [209], it was proposed that indium tin oxide (ITO) could be used as a transparent top contact, while ITO and gold could be used as both the bottom mirror and contact. A schematic illustration of this design is shown in Figure 5A. However, it is not trivial to combine an axial p–n or p–i–n junction with an embedded QD and the shell growth required for the proper diameter and the tapered tip.

Figure 5:

Illustrations of some proposed designs for future nanowire SPSs.

(A) Electrically operated nanowire SPS with ITO used as a transparent top contact. (B) Scheme for on-chip integration of a nanowire SPS with planar waveguide designs. Selected nanowire SPS is first transferred to the substrate with a nanomanipulator, after which the SiN waveguide is fabricated. (C) Photonic crystal waveguide structure (left) realized with nanowires (with the prospect of including one with an embedded QD) and simulated mode profile (right) showing additional vertical light confinement due to the nanowire heterostructure. Figure reprinted with permission from: (A) Ref. [209], 2010 by the Optical Society of America; (B) Ref. [210], 2016 by the American Chemical Society; (C) (left and right) Ref. [211], 2014 by the American Physical Society.

Lastly, the integration of nanowire sources with other components is not straightforward. Since one of the most tangible benefits of the nanowire approach is the deterministic positioning of the QD, it would seem well suited for pursuing the realization of applications that require large-scale integration, such as integrated optical quantum information processing. Unfortunately, the vertical geometry of the nanowires, while naturally suited for vertical emission, is not a good match to the mostly planar components developed for integrated photonics.

One solution to this issue was proposed and demonstrated in Ref. [210], where nanowire nanoantenna sources were first fabricated on a separate substrate and then individually characterized, selected, and transferred to the device substrate with nanomanipulators. The nanowires could be laid on the substrate with defined locations and orientations, and the waveguides and other components could then be fabricated on top of the nanowires. The result of this scheme is illustrated in Figure 5B. While it was reported that the scheme worked well, one could argue that it is not very suitable for true large-scale integration as the pick-and-place step with nanomanipulators is a delicate and slow serial process. A similar scheme was very recently reported [218], where the nanowire nanoantenna SPS was placed on top of a SiN waveguide such that on-chip optical pumping could couple from the waveguide to the nanowire and the SPS emission could couple from the nanowire to the waveguide. On the other hand, it would be possible to use nanowire sources in their natural vertical geometry if their emission could couple to a planar waveguide below or above the nanowires. There also exists a fabrication method for 3D waveguides in glass with femtosecond laser direct-writing [219], which could possibly be compatible with vertical nanowire sources. Furthermore, it is also possible to realize photonic crystal waveguides with nanowires [211], in which case both the waveguides and sources would be realized with nanowires. The nanowire photonic crystal waveguide and light confinement considered in Ref. [211] are illustrated in Figure 5C. Indeed, exploring novel schemes for integrating nanowires in their vertical geometry with other components, planar or otherwise, offers one interesting avenue for future research.

8 Conclusions

Bottom-up-grown nanowire SPSs benefit from deterministic positioning of both the embedded QD and the devices with respect to each other and have mostly followed the nanoantenna design, achieving rather impressive performance. Although it has not yet been experimentally demonstrated, the nanowire nanoantenna should be able to achieve extraction efficiency above 90%. It is also well suited for coupling the emission into an optical fiber because of the engineered Gaussian far-field emission pattern. Near-unity single-photon purity has been achieved, as well as relatively high indistinguishability and brightness. Furthermore, room-temperature operation has been achieved with III–nitride QDs.

However, despite this promising progress, presently the bottom-up-grown nanowire SPS approach has not demonstrated a clear advantage over top-down fabrication approaches. First, higher performance has been obtained with top-down designs, especially with regard to indistinguishability. Second, nanowires naturally assume a vertical shape and vertical emission direction, while most of the components designed for integrated photonics are planar. Third, a single bottom-up-grown nanowire nanoantenna cannot presently incorporate a photonic cavity that arguably offers better ultimate indistinguishability–efficiency trade-off than a waveguide. However, the deterministic positioning is, at least currently, much more feasible in nanowires, and the nanowire growth process supports a wider variety of materials and compositions. It seems possible that both the bottom-up nanowire growth and top-down fabrication could be used in the future, with each approach being better suited for some specific applications.

Further research on nanowire-based SPSs is thus merited. In addition to improving the performance, tuning the emission wavelength with various strategies (e.g. strain and electric field) could be investigated further. For on-chip integrated applications, electrical excitation or on-chip optical excitation would be desirable, of which the former has not yet been achieved with the nanowire nanoantenna structure. Truly scalable fabrication process for integrated designs is also an important open issue that has not been tackled with top-down approaches either.