Non-polar nitride single-photon sources

Non-polar nitride single-photon sources are developed in order to minimise the undesired side effects caused by the internal fields of polar nitrides, while retaining the benefits of high-temperature single-photon generation from a semiconductor quantum dot platform. As a relatively newer single-photon source, several reports have already been made highlighting their interesting optical and photophysical properties. These include an average ultrafast radiative exciton recombination lifetime of <200 ps, an average slow-timescale spectral diffusion of <40 μeV, polarisation-controlled single-photon generation up to 220 K, and temperature-dependent fine-structure splitting. In this review, the photophysics, improvement of optical properties, and future of non-polar nitride single-photon sources will be closely examined based on current reports in the literature.


Single-photon sources
Quantum technologies have begun to manifest their importance in an age where demands for private communications and greater computational prowess have never been stronger. The promise of fundamentally secure communication motivates the development of a plethora of quantum optic and optoelectronic systems. At the heart of these systems are single-photon sources [1][2][3], driven optically or electrically, and candidate devices have been fabricated with multifarious nanomaterials and nanostructures in search for the most optimal emission characteristics under realistic operation conditions.
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An ideal single-photon source for these applications should strictly provide on-demand generation of only one photon at ultrashort temporal intervals, with predefined and deterministic optical linear polarisation, at temperatures relevant to onchip environments. For the purpose of quantum computation [4][5][6][7], these single photons should also be indistinguishable in their optical properties [8,9]. While current single-photon platforms are situated at the lower end of the technology readiness levels (TRLs), existing proof-of-concept systems should allow clear pathways for future reproducibility and scalability.
Since the first experimental demonstrations of antibunching in single atoms [10,11] in the 1970s, there has been tremendous progress in the development of single photon emitting platforms. In particular, the emission properties of semiconductor quantum dots (QDs) [12][13][14] are akin to atom-like two-level systems owing to their confinement in all three spatial dimensions, while being more than three orders of magnitude larger than single atoms. Their physical dimension and electrical contacts can also be controlled much more easily in the solid state than other single-photon emitters. For this reason, arsenide-based QDs have lead the research in this field of photonics by producing highly pure and indistinguishable photons [15][16][17][18][19][20][21].
With these mature systems, free-space quantum key distribution over a distance of >50 km [22] and quantum computation with complexity rivalling that of early classical computers [23] have both been demonstrated. For quantum computing developments in particular, unlike qubits in superconducting Sycamore chips [24] or electrostatically defined QDs [5,7], the demonstration of quantum supremacy is achieved via an all-optical boson sampling model [23,25]. The advantage of such an optical quantum computational scheme is that it does not suffer from the need for superconductivity to mitigate quantum decoherence, nor does it require <1 K operation temperatures that are usually only achievable in dilution refrigerators [7]. Instead, the challenge lies in the development of highly efficient single-photon sources, detectors, more useful operation temperatures, and their integration into photonic platforms. However, while current arsenide developments on resonantly excited, precisely (thermally or electrically) tuned, quantum electrodynamically enhanced cavity-based nanostructures have circumvented the complications and undesired effects of their mesoscopic solid-state environment, their operating temperatures are still limited to the cryogenic regime by their semiconductor band offsets and exciton binding energies.
The reliance on cryogenic temperatures of these devices has motivated a search for high-temperature single-photon sources, particularly in defect-based systems. Nitrogen and silicon vacancy (NV and SiV) centres in diamonds [26][27][28][29], colour centres in ZnO [30][31][32] and SiC [33,34] have all been demonstrated to operate as single photon emitting fluorescent point defects at room temperature. More recently, carbon nanotubes containing oxygen-related defects are shown to emit single photons at ambient conditions [35,36], with wavelengths tuneable to the telecommunication standard of 1.55 µm [35]. Interestingly, defects found in GaN wafers without the need for further fabrication can also operate as single-photon emitting sources at 300 K [37][38][39]. With the advent of 2D materials, deeply localised defect states not only generate single photons [40,41], but retain these properties even at 800 K [41]. However, the true challenge with all defect-based platforms lies in achieving electrical injection and scalable device fabrication. Without the ease of solidstate manipulation, integration into semiconductor platforms and established processing technologies, the path forward for higher TRL development of these novel systems into realistic on-chip devices is less clear.
However, compared to the more established arsenide platform, progress in the development of nitride semiconductors has been hindered by their poor material quality, e.g. high threading dislocation densities [51]. The complex mesoscopic environment contains numerous potential minima that could act as carrier trapping sites, thereby introducing a greater number of non-radiative exciton recombination pathways and negating the potential benefits of high-temperature operation. The problem not only delayed the first breakthrough in InGaN light-emitting diodes (LEDs) to 1994 [58], but also pushed the realisation of high-temperature nitride single-photon sources [59] to more than a decade later in 2006. Stranski-Krastanov GaN/AlN QDs grown by metal-organic vapour-phase epitaxy (MOVPE) and enhanced by etched mesa structures produce a raw g (2) (0) of 0.53 at 200 K, which is a temperature accessible by commercial Peltier coolers. By embedding single QDs with heights of 2-5 nm and diameter of ∼20 nm into the apex of nanowires, room temperature single-photon generation from GaN/AlN QDs has been achieved in 2014 [60] (figure 1(a)). The limit of high-temperature operation was then updated to 350 K [61]-the highest of all semiconductor QD platforms so far-two years later with the same sitecontrolled system ( figure 1(b)). As well as high-temperature operation, interface-fluctuation GaN QDs have achieved a homogeneously broadened exciton linewidth of only 27 µeV and g (2) (0) of 0.02 in an ultraclean environment [62] (figures 1(c) and (d)).
In order to extend the range of emission wavelengths beyond UV, indium can be added to GaN to tune the exciton transition energies towards the blue-green section of the visible spectrum. These emitters are thus better suited for more efficient free-space data transmission and detection over a short range [63]. After the first observation of resolution-limited sharp peaks from InGaN QD-like samples [64] in 2000, singlephoton generation from distributed Bragg reflector (DBR)based cavity-enhanced InGaN QDs [65] was demonstrated 7 years later, with g (2) (0) values less than 0.3. Since then, several other methods for the fabrication of InGaN single-photon sources have been reported [66][67][68][69][70][71][72][73][74][75][76][77][78]. Nonetheless, owing to the greater challenge in developing an InGaN platform, none of these systems have yet been developed into ones with optical properties comparable to the aforementioned site-controlled dot-in-nanowire or ultraclean interface-fluctuation GaN QDs.
The most commonly used crystal plane for nitride QDs is the polar c-plane (figure 2(a)). However, the lack of inversion symmetry of the space group leads to piezoelectric fields in the nitride system. For instance, in a polar InGaN/GaN system, the lattice mismatch between the two materials results in a piezoelectric field along the crystal c-direction. Additionally, the asymmetric distribution of cationic and anionic charges and the resultant spontaneous polarisation further increases the built-in field along this axis. The built-in fields in polar nitride  [60]. Copyright (2014) American Chemical Society. (b) Evidence of single-photon generation from the polar nitride system in (a) at 350 K, the highest of current semiconductor QD-based single-photon sources. Reprinted with permission from [61]. Copyright (2016) American Chemical Society. (c) Smallest extent of fast-timescale spectral diffusion recorded in a nitride platform, using polar interface-fluctuation QDs. Reprinted with permission from [62]. Copyright (2017) American Chemical Society. (d) Purest single-photon generation recorded in a nitride platform, using the same system as (c). Reprinted with permission from [62]. Copyright (2017) American Chemical Society.
heterostructures tend to spatially separate the electron and hole and hence reduce their wavefunction overlap (see comparison in figures 2(b) and (c)). The reduced exciton oscillator strength limits the radiative transition rate of the carriers, resulting in not only slower repetition rate, but decreased probability of radiative transition at higher operation temperatures as well. The built-in fields also result in a redshift of the emission, commonly termed the quantum confined Stark effect (QCSE).

Non-polar nitride quantum dots
In order to minimise the undesired effects caused by internal electric fields in polar nitrides, non-polar solutions can be employed. One of the approaches is to develop cubic, instead of hexagonal wurtzite, nitride QDs. While this method circumvents the complication of wurtzite built-in fields, the zincblende phase of nitrides is thermodynamically unstable and more challenging to fabricate. Nonetheless, one of the developments has made use of plasma-assisted molecular beam epitaxy (PA-MBE) to fabricate non-polar cubic GaN QDs on SiC/Si(100), and reported both reduced QCSE and singlephoton generation at 100 K [79] (figures 3(a) and (b)). The signature of increased oscillator strength is also manifested in the short sub-400 ps radiative lifetime, as shown in figure 3(c).
Another approach involves QD growth along one of two non-polar planes of wurtzite nitrides, as shown in figure 2(a). For a lens-shaped QD, the effects of the internal field would thus be limited to the side facets with components parallel to the crystal c-direction. Non-polar QD-like GaN structures grown along both the m- [80] and a-directions [80][81][82] by MBE have been reported, demonstrating sharp emission features characteristic of QDs up to 180 K. Unfortunately, Hanbury Brown and Twiss (HBT) experiments were not performed on these nanostructures to assess their single-photon performance. In the case of non-polar InGaN QDs, while MOVPE routines have been attempted on high-quality GaN substrates, such as Ammonothermal ones, no QD-like emitting nanostructures have been reported with these methods. It was not until recently had the challenging task of non-polar InGaN QD growth been achieved on both the a- [83,84] and the m-plane [85,86], using several unique fabrication routines. Epitaxial growth using MOVPE is possible for a-plane InGaN QDs on GaN grown on an r-plane sapphire substrate. The first such successful process was adapted from a process previously used for c-plane QD grown and is termed modified  Time-resolved measurement of a QD emitter from the same cubic nitride system at 4 K, demonstrating the absence of internal fields. Reprinted from [79], with the permission of AIP Publishing. droplet epitaxy (MDE) [83]. This involves an annealing step that induces the decomposition of a typically 10-monolayer thick InGaN epilayer resulting in the formation of nanoscale metallic droplets which are converted into nitride QDs in the presence of NH 3 during GaN capping. Radiative recombination rate, optical polarisation and fine-structure splitting (FSS) measurements [87] have been made at cryogenic temperatures using these samples. For single-photon studies and higher temperature operation, nanopillars have been fabricated from the initial planar structures [88] (figure 4). The resultant structures effectively enhance the photon extraction efficiency and isolate a few single QDs in each pillar, thereby facilitating optical investigations. Single-photon emission with polarisation control up to a temperature of 220 K has been reported with these structures [89]. Recently, an alternative MOVPEbased approach to MDE has been developed for non-polar materials, in which InGaN QDs are formed via a process somewhat reminiscent of the Stranski−Krastanov growth mechanism which is widely exploited in other III-V semiconductors for QD formation. Although some details of the resulting QD size distributions are inconsistent with the usual models of SK growth, the process nonetheless involves the self-assembly of InGaN three-dimensional islands on an underlying twodimensional layer which acts as a quantum well. As is also common in SK growth, optimisation of the capping strategy to grow the final barrier layer above the QD structure is vital to achieve good optical properties. A capping process referred to as quasi-two-temperature (Q2T) growth has been successfully employed, in which the InGaN QDs are capped by an initial 2 nm GaN layer at the InGaN growth temperature, after which the temperature is ramped at 860 • C in 90 s before the final capping with an additional GaN layer. In this review, we refer to QDs grown employing a Stranski-Krastanov-like process and capped using this approach as Q2T QDs. After a few stages of development [90][91][92], this Q2T method has improved the morphology of the InGaN epilayer (see comparison in figures 5(a) and (b)) and several of the a-plane QDs' optical properties, and allows the fabrication of electrically driven single-photon emitting devices (figure 5(c)).
In the m-plane case, there have not yet been any reports of InGaN dot formation based on a planar epitaxial routine. As workarounds, two methods based on nanowires have been proposed. The first method introduces a silane flux as interruption before the growth of the core-shell structure, which induces non-uniformity and formation of QD-like nanostructures (figure 6(a)) on the middle and lower portions of the nanowire sidewalls [85] (figures 6(b)-(d)). Polarised single-photon generation has been reported up to 100 K from these m-plane InGaN QDs. Subsequently, the formation of polar c-plane, semi-polar (10)(11), and non-polar m-plane InGaN QDs have been demonstrated at the top of MBE-grown pencil-like nanowire structures (figures 6(e) and (f)). Singlephoton emission has been also reported in all three types of QDs at cryogenic temperatures. More detailed discussion of their specific single-photon characteristics will be given in later sections. In this work, we examine the current state of single-photon sources based on InGaN QDs grown without using the conventional wurtzite polar c-plane, focusing on specifically on their optical properties.

Review layout
In the following sections, a review of important optical characteristics of non-polar nitride single-photon sources and the experimental efforts in their optimisation will be presented. Section 2.1 clarifies the range of emission energies and current brightness for these QDs, evaluates their variations at higher temperatures, and discusses how they compare to other semiconductor QD platforms. In section 2.2, the rationale behind the increased exciton oscillator strength in non-polar systems is explained. Theoretical work elucidating the origin of fast radiative lifetimes and experimental efforts clarifying the current performance are also highlighted. The degrees of both fast-and slow-timescale spectral diffusion in non-polar InGaN QDs are explained in section 2.3. Unique optical polarisation properties of these non-polar nitride materials are discussed in detail in section 2.4 and its subsections, covering the QDs' performance at both cryogenic and high temperatures, as well as temperature-dependent fine-structure splitting (FSS) and its possible relationship to phonon scattering processes. In section 2.5, an overview of the progress of single-photon generation with non-polar nitride QDs is presented, along with a comparison to other polar nitride and arsenide platforms. The current progress and challenge of non-polar nitride singlephoton sources are discussed in the conclusion in section 3.

Emission energy and intensity
As explained in the introduction, the inclusion of indium allows the creation of the InGaN alloy, and shifts the exciton energies to the blue region of the visible spectrum. At the moment, non-polar systems reported in the literature mostly rely on stochastic dot formation processes that do not result in a single deterministic emission energy. The range of wavelengths that non-polar InGaN QDs can emit is mostly from around 420 to 550 nm (or approximately 2.25 to 2.95 eV) at cryogenic temperatures. Several example single QD spectra from typical non-polar a-plane InGaN QDs are shown in figures 7(a) and (b). For both cases, a laser spot of approximately 1 µm diameter with saturating two-photon power was used to excite the QD sample. The nanostructure excited in figure 7(a) exhibits sharp emission features characteristic of a QD. The variations in the number of QDs, their emission intensity, and their emissive mesoscopic environment in each spectrum are indications of the stochastic nature of the current self-assembled QDs. While there are ongoing research efforts to fabricate non-polar nitride QDs more deterministically, in terms of both spatial formation control (e.g. site-controlled QDs) and optical properties, it is at this stage important to investigate the QDs' optical properties with statistical significance to understand their underlying photophysics with more useful insights, as several reports [85,[92][93][94] have done. Unlike typical arsenide systems [16], the temperature sensitivity of non-polar nitrides is relatively lower owing to their larger bandgap and stronger exciton binding energies. Starting from cryogenic conditions, the amount of redshift over a temperature increase of ∼200 K is ∼30 meV. The behaviour of this energy shift has also been reported to follow established semiconductor models well [85], which has also been used as an important study to ascertain that the origin of the emission is not from defects.
The typical peak emission intensity for non-polar nitride QDs could also vary between a few hundred to several tens of thousands cts/s. The detected photon count rate, or integrated intensity, could reach the order of ∼10 kcts s −1 , as figure 7(a) shows. These are possible thanks to the use of nanopillars, which provides enhancement in extraction efficiencies. While these intensities are still low compared to arsenide platforms, the performance of non-polar InGaN QDs is similar to their polar counterparts. It is important to note that the efficiency of the optical instruments used, and different excitation conditions, could result in drastically different maximum count rates of these emitters. For instance, research in polar nitrides have shown that with lower excitation powers, single-photon purities are improved [78]. In this case, a decrease in the mount in excitation power will result in a reduced maximum count rate. As the absolute external quantum efficiency is <0.1%, and still much lower than more established single-photon platforms, more developments are required to improve both the efficiency and the emission intensity, before a more meaningful comparison to other non-nitride platforms can be made. However, at elevated temperatures, nitride single-photon sources demonstrate their advantage in brightness compared to other semiconductor QD systems. This is especially so in non-polar InGaN, where the enhanced exciton oscillator strength results in a greater probability of radiative, instead of non-radiative, recombination. The integrated intensity of several reports from a-plane systems [89,91] at ∼200 K still remain at >10% of that at 5 K, in stark contrast to typical arsenide ones where the intensity would drop below 1% before 100 K is reached. The reported temperature dependence of integrated intensity for non-polar InGaN QDs also follow conventional semiconductor behaviour closely, where a single-channel Arrheniustype quenching model is usually sufficient to describe the brightness reduction.

Radiative recombination lifetime
There are several factors that could contribute to the oscillator strength of non-polar nitride QDs. The most direct impact of using a non-polar system is in the reduction of QCSE. With stronger electron and hole wavefunction overlap, radiative transition rate of the exciton is significantly enhanced. However, unlike ideal non-polar quantum wells, in non-polar quantum dots, interfaces still exist which are not aligned along the non-polar axis, and hence there is still a component of the built-in potential that is caused by the firstorder piezoelectricity and spontaneous polarisation [95]. However, the second-order piezoelectricity has been found to cancel out a significant portion of this built-in potential. Coupled with the Coulomb effects between the electron and holes [95,96], oscillator strengths much greater than those observed in polar nitrides can be achieved from non-polar nitride QDs (figure 8). The cancellation effect has been found to be only significant in the non-polar case, and much less impactful in both polar and semi-polar scenarios. Experimentally, typical lifetime measurements of carriers in polar nitride QDs can be in the range of 1-10 ns [97]. With a reduction of QCSE in semi-polar emitters, the experimentally reported timescale become 600 to 900 ps [86]. The MDE development of nonpolar a-plane QDs results in lifetimes between 400 and 600 ps [83,89], confirming the theoretical finding that the secondorder piezoelectricity acts to increase the oscillator strength of non-polar QDs more significantly than semi-polar ones. Out of the non-polar a-and m-plane nanostructures, it has been demonstrated that m-plane QDs have even faster radiative recombination rate, with a statistical average of 260 ps, suggesting they have even lower residual built-in fields than their a-plane counterparts [85].
However, it is important to note that the mesoscopic environment of the emitting QD does have a non-negligible impact on the radiative recombination lifetime. In particular, carriers could be trapped in nearby sites of a QD for a period of time much longer than the exciton recombination process. The electric fields generated, albeit much weaker than the situation in polar nitrides, would add to the total residual QCSE of non-polar QD emitters. In more recent studies of a-plane InGaN QDs with significantly improved epilayer morphology and reduced number of carrier trapping sites, an average radiative lifetime of 173 ps has been achieved [92]. An example of these ultrafast radiative recombination lifetimes is shown in figure 9(a). A similar lifetime of 157 ps has also been reported from electrically pump single-photon device based on comparable a-plane samples [101], demonstrating its reproducibility. These recombination rates are now truly an order of magnitude faster than single-photon sources based on conventional c-plane InGaN QDs, increasing their potential repetition rate from near-GHz to ultrafast multi-GHz. The effects of mesoscopic environment also provide a possible explanation to the slightly longer (400 to 600 ps) lifetimes reported for the m-plane platform based on pencillike nanowires [86], and slower radiative recombination rate (300 ps) of cubic InGaN where QD side facet residual fields should not be present [79]. Therefore, as an InGaN QD's lifetime approaches 600 ps or faster, it is not only dependent on symmetry, crystal planes, composition and size, but is also limited by the local environment. Unfortunately, it is not currently possible to quantify the environment of each individual QD, especially for self-assembled systems. In general, a single-photon platform should aim for the cleanest environment possible, for benefits in not only radiative recombination rate, but several other factors to be discussed later.
One example of fast lifetimes in polar nitrides is the development of site-controlled dot-in-nanowire systems [60]. The ultrasmall GaN QD in an ultraclean environment has an exciton radiative lifetime of only 300 ps, despite being polar in nature. However, while a clean mesoscopic local environment is desirable, size reduction is unlikely to have an equally large effect in non-polar InGaN QDs. In polar nitrides the separation of electron and hole increases as the dot size increases [49]. In the case of non-polar cubic QDs, size should theoretically only affect the emission energy, which has a relatively smaller impact on lifetime unless the energy change is significant, due to the well-known inversely proportionality between the two. Theoretical studies have been conducted for non-polar a-plane InGaN QDs [96], and concluded that their radiative recombination rates are highly insensitive to different sizes. For example, while the lifetime of a lens-shaped c-plane dot scales almost linearly with its in-plane dimensions, that of an a-plane one would only increase by 7% with a 4-fold larger base diameter. The investigation also finds that this insensitivity is caused by the Coulomb interaction between the electron and holes, which mostly offsets any increase in residual fields present at larger sizes. This implies that potential future developments of smaller dot sizes similar to state-of-the-art GaN QDs, are unlikely to lead to further significant reductions in the recombination lifetime of non-polar InGaN QDs.

Spectral diffusion
Carriers in the vicinity of a QD create an instantaneous electric field, causing a Stark shift of its emission energy. This phenomenon is called spectral diffusion and is prevalent in nitridebased single-photon platforms due to their higher intrinsic threading dislocations, defect densities, and thus greater capacity to create carrier traps. It is important to note that although the physical principle of spectral diffusion remains the same, the sources of these local fluctuating electric fields can be put into two categories. In most of the current InGaN systems, the QDs themselves are surrounded by InGaN QWs. Upon optical or electrical carrier injection, these QWs will also be excited, thereby creating transient electric fields at nanosecond timescales as carriers pass by the QDs. These spectral jumps cannot be observed directly due to the much longer acquisition time resolution of current spectroscopic technologies. On the other hand, defect-related carrier trapping sites retain charges for much longer timeframes (ms to s), and these slower timedependent energy shifts can be captured experimentally.
Although several investigations have been made on the slow-timescale spectral diffusion (STSD) of different polar platforms [62,73,98], the magnitude of STSD has only been reported on a-plane InGaN QDs [92] out of the current nonpolar systems. As shown in figures 9(b) and (c), the most recent Q2T development of a-plane InGaN QDs sees significant reduction in STSD compared to previous MDE ones. One possible explanation of this is that the QW underlying the QDs is more homogenous in this growth methodology, compared to MDE growth which requires partial decomposition of the QW. This may result in fewer carrier trapping sites. Further statistical studies also reveal an average STSD of 33.8 µeV, which is nearly an order of magnitude lower than similarly grown polar systems [98], and on par with state-of-the-art GaN platforms [62]. The result further demonstrates the ability of non-polar InGaN to operate as single-photon sources with less emission energy uncertainty. However, to truly progress towards the generation of indistinguishable photons, both slow-and fasttimescale spectral diffusion need to be minimised, and the latter is more challenging to quantify or alleviate.
Since fast-timescale spectral diffusion (FTSD) cannot be directly measured via micro-photoluminescence (µPL), the stochastic spread of Fourier-limited Lorentzian profiles results in a near-Gaussian distribution. In µPL data analysis, it is also advisable that a Voigt profile [99] combining both Gaussian and Lorentzian contributions should be used for the greatest accuracy. In most cases where the lifetime-bound lower limit of exciton transition energy uncertainty (∼1 µeV) is several orders of magnitude lower than the measured one (∼1 meV), a Gaussian fit alone also provides a reasonable approximation. Thus, the linewidths of QDs measured in µPL are direct indications of the degree of fast-timescale spectral diffusion. However, since the mesoscopic environment of each QD can be highly complex, the strength of the fluctuating electric field caused by itinerant carriers in the QDs can also vary tremendously. In the available non-polar m-plane systems, linewidths of and 3.7 [85] and 0.5 meV [86] have been reported. The much larger linewidth of the former can be explained by its unique QD fabrication method, whereby a silane-induced growth interruption is employed which could have created significantly greater number of carrier trapping sites than the latter platform. The relatively large linewidth of cubic InGaN QDs (2.1 meV) also coincide with arguments made in the previous section, with both their slower than expected radiative lifetime and the large linewidth being attributable to the impact of charge trapping at defects. (Cubic GaN in particular suffers from a high density of stacking faults, which could be a candidate carrier trap). For non-polar a-plane InGaN QDs, the linewidth of QDs in most reports are in the range of 0.3 to 3 meV, with 1 meV being both the mean and median [87,89,[91][92][93][94][100][101][102][103]. Although no reports of linewidth <300 µeV have been made yet, the statistics in figure 9(d) suggest that the best current data are limited by the spectral resolution of the relevant experiment, not the fundamental properties of the QDs themselves. An extension of the Gaussian profile could indicate several QDs with linewidths close to the values of <100 µeV reported from polar GaN interface fluctuation dots [62].
Nonetheless, these linewidths are still much greater than their Fourier-limited values, and the fluctuating emission energies pose a significant challenge in realising photon indistinguishability. The pathway for the reduction of itinerant charges in the surroundings of a QD is not immediately obvious. For applications in quantum computing, reducing the exciton transition linewidths of non-polar InGaN (and indeed other nitride) QDs is as important as achieving purer singlephoton emission. A first step in tackling this challenge is to understand the mechanism and details of fast-timescale spectral diffusion. Autocorrelation measurements can used to probe the extent of spectral diffusion of this kind [104,105], and have been recently performed in a polar GaN system [106]. A characteristic diffusion time of 20 ns is measured, indicating a window of 20 ns for the potential generation of truly indistinguishable photons before a Stark shift occurs. Similar measurements were later performed in polar InGaN QDs, yielding a characteristic diffusion time of 260 ns [107]. The order-of-magnitude larger diffusion time makes it relatively easier to achieve the emission of indistinguishable photons. Such measurements should be performed on the non-polar platforms in order to understand the nature of their fast-timescale spectral diffusion under a QCSE-minimised environment better. From that point onwards, it would be more possible to devise potential methods to reduce the extent of diffusion or prolong the characteristic diffusion time.
It is important to note that for several other quantum information applications except quantum computing, such as quantum key distribution [108][109][110] using the BB84 protocol [111], there are no strict requirements for photon indistinguishability. However, in these cases, the generation of linearly polarised light (either intrinsically or externally via a polariser) and the reliable emission of single photons are indeed necessary.

Optical polarisation 2.4.1. Material instead of nanostructure.
Optical linear polarisation control from a single-photon source can be achieved either intrinsically in the material and nanostructure, or externally using polarisers and a half-wave plate. However, with an unpolarised source, the use of a polariser will reduce the upper limit of its external quantum efficiency by 50%. Although this upper limit per se in nitride-based single-photon platforms is currently bottlenecked by numerous other factors, a gain in polarisation efficiency of up to 50% should not be ignored. It is well known that the first two valence bands of polar nitride are degenerate at the Γ-point. Both theoretical and experimental studies have confirmed that a symmetrical polar nitride QD should have a polarisation degree of 0 [112][113][114], as the hole ground state would have a near-equal contribution of |m⟩-and |a⟩-like sp3 orbital characteristics.
Using this property, a symmetry-breaking element can be introduced, lifting the degeneracy and altering the degree of valence band mixing. Therefore, polar nitrides are generally sensitive to shape anisotropies, and have the potential to generate highly polarised photon output, as shown by several reports in the literature [74,86,115]. However, the challenge then lies in the control of polarisation, as stochastically formed QDs with random variations of dimension, geometry and material contents could result in a wide range of polarisation degrees and directions. Statistical analyses have indeed demonstrated such distributions in a polar system [112]. It would therefore be necessary to perform prior measurements to identify individual QDs with high polarisation degrees, and make use of external half-wave plates to control their polarisation directions.
In order to achieve greater reliability in polarisation output, the symmetry-breaking element needs to be controlled. In polar nitrides, there are currently several solutions leveraging on the engineering of anisotropies in the emitting nanostructures. Horizontally lying nanowires are the most straightforward solution [52,66,72,116]. The different dimensions between a nanowire's length and width naturally creates a large anisotropy. The dipole oscillates preferentially along the long axis of the wire, achieving near-unity polarisation degrees with deterministic polarisation angles. However, the electrical contacts for horizontally lying nanostructures are very challenging to make, especially on a wafer level (currently reports are limited to contacts on individual nanowires [66]).
A different method is to modify the in-plane geometry of standing nanostructures. Elongated pyramids [117] and elliptical nanocolumns [118,119] are among the most successful developments, demonstrating high polarisation degrees along fixed directions. In particular, the statistical average polarisation degree of elliptical structures is ∼0.7, due to the limited anisotropy attainable by ellipses. Nonetheless, it does make electrical contacting potentially less difficult due to the larger diameters compared to nanowires. The greater anisotropies allowed by asymmetrical pyramids could output an average polarisation degree of 0.9, along several directions of the wurtzite hexagon.
For the relatively recent, non-polar nitride QDs, no engineered nanostructures for polarisation control have yet been reported. However, the growth along a semi-polar or nonpolar plane already breaks the valence band degeneracy. For instance, in the case of non-polar a-plane, the contribution of |a⟩-like orbital characteristics could theoretically drop from ∼50% to ∼1% [93]. With a mixing of 97% |m⟩-like and 2% |c⟩-like contribution, the in-plane optical polarisation degree can easily exceed 0.9 for a lens-shaped base-symmetric QD, in stark contrast to polar nitrides. Statistically significant experimental investigations demonstrate an average polarisation degree of 0.9 over a range of 0.6 to 1, where the majority (>80%) of values lie between 0.75 and 1 [93]. These findings are also reconfirmed by subsequent optical investigations on different samples [92] and electrically driven devices [101]. Degree of polarisation results from non-polar m-plane QDs [85,86] also fall into a similarly high range of 0.5 to 1. When combined with theoretical insights, it is shown that the effects of random anisotropies, size and geometry differences under realistic settings are mostly overcome by the use of the nonpolar material alone at cryogenic temperatures. Therefore, even without anisotropy control or nanostructure engineering, non-polar InGaN QDs are reliable sources of single photons with deterministic polarisation control, that can be driven both optically and electrically.
Interestingly, the investigation on a-plane InGaN QDs shows that 10% of the emitters have their polarisation directions aligned to the crystal c-axis [87,93], orthogonal to the 90% majority which are parallel to the m-direction as expected. Although there is no method to control the formation of these c-aligned QDs yet, and their structural nature is not well understood, they provide a significant advantage in realising high dot-to-background ratios. Due to the orthogonality of polarisation axes between the QD and its underlying QW, the intensity of the QWs are polarisation-suppressed when the QD's emission along the c-direction is maximised by an external polariser. It is likely that this particular species of QDs is the key in reducing undesired background QW emission and achieving much higher single-photon purity in non-polar InGaN QDs.

Insensitivity of optical polarisation to high temperatures.
Despite the potential of nitrides to operate at temperatures much higher than cryogenic conditions, fewer than 10 single photon emitting systems have shown operation >100 K [52,60,61,67,69,79,85,89,103], and four are above the Peltier cooling threshold of 200 K [61,67,69,89]. Out of these reports, only a few detailed investigations of the QDs' behaviour at higher temperatures have been performed. Due to the scarcity of these reports, thermally assisted processes are not yet fully understood, and temperature-dependent optical properties and material parameters have not been evaluated and confirmed with significant experimental data. In nonpolar InGaN QDs, the order-of-magnitude increase of exciton oscillator strength makes the likelihood of radiative emission greater. At higher temperatures where the competition between radiative and non-radiative processes determine the probability of single-photon emission, a non-polar QD is more likely to operate at much higher temperatures, all other things being equal. This could be the reason why the first m-plane and a-plane single-photon sources are already able to operate at 100 and 220 K respectively. Furthermore, since a-plane InGaN QDs are the only known semiconductor QD platform to generate polarised photons up to >200 K, detailed investigations could reveal new insights or previously unknown behaviours of optical properties.
The unique polarisation properties of non-polar a-plane InGaN QDs brought more research teams together for collaborative efforts in elucidating its underlying physics [94]. Theoretical investigations combining k · p theory and Fermi-Dirac statistics, with realistic consideration of QDs' shape anisotropies have been conducted. These results have also been compared to a complete set of statistically significant experimental polarisation degree measurements up to 200 K. The reported results in figure 10(a) not only have a very close agreement, but also shed light onto the gradually larger spread of polarisation degrees at higher temperatures. Based on the combination of theoretical and experimental results, the estimate that most self-assembled QDs should have an in-plane anisotropy of less than two has also been confirmed.
This set of results also demonstrated that non-polar InGaN QDs should have very temperature-insensitive polarisation properties up to 100 K, a result that can also be confirmed with previous statistics obtained with m-plane InGaN QDs [85]. The orbital contributions for the first few excited hole states are also predominantly |m⟩-like in character, similar to the situation at cryogenic temperatures. A more significant drop in polarisation degree only occurs when the temperature is increased further beyond 100 K. At these temperatures, the mixing of |m⟩-like and |c⟩-like orbital characteristics becomes more significant, and the effect of shape anisotropy becomes stronger. In a way, the non-polar InGaN QDs becomes more 'polar-like'.
Due to the extremely good agreement between the theoretical and experimental results, it is also reasonable to assume that the simulation findings for temperatures between 200 and 300 K are a close prediction for the QDs' actual behaviour. Unfortunately, experimental measurements in this temperature regime are not yet possible with current non-polar InGaN QDs. Nonetheless, the theoretical results can be used as a guideline for the fabrication of future devices. Combining the use of the non-polar material with basic forms of nanostructure engineering could result in highly robust polarised singlephoton emitters operating even at room temperature.

2.4.3.
Temperature-dependent fine-structure splitting. The development of non-polar InGaN QDs not only demonstrated the possibility of ultrafast, polarisation-controlled singlephoton generation, but also opened up the underexplored area of high-temperature semiconductor QD photophysics. In particular, FSS energy is the difference between the exciton transition energies of the two orthogonally polarised photon states. In the case of non-polar a-plane InGaN QDs, for instance, this energy can be measured between PL components that arise from the |m⟩-like and |c⟩-like states respectively. However, previous measurements of FSS in a nitride system are highly challenging due to the relatively large spectral diffusion between 100 and 300 µeV [98]. As mentioned in section 2.3, with the latest development of a-plane QDs, the degree of STSD has been reduced by an order of magnitude. These nonpolar QDs are hence much better candidates for the precise and efficient measurement of FSS. Combined with their ability to operate at temperatures up to ∼200 K, the temperature dependence of FSS can also be investigated.
At low temperatures, several reports [87, 100, 120, 121] from both polar and non-polar nitrides have indicated that the magnitude of the FSS is around 0.5 meV, which is an order of magnitude higher than in arsenide systems [122][123][124][125][126]. However, the most recent investigation from a-plane InGaN QDs found a previously unexpected temperature-dependence for the FSS. As the temperature is increased to 200 K, the FSS increases by more than 20 times, as shown in figure 10(b). Closer scrutiny of the process of FSS increase revealed a constancy at T <100 K, and a quasi-linear increase at T >100 K. The result is further confirmed by five other QDs ( figure  10(c)). The result is a very perplexing one, as no current theories suggest such an FSS change only after a certain temperature.
The report went on to conduct statistics of linewidth and FSS at the same temperatures up to 200 K (figure 10(d)), on the grounds that investigations on other materials have suggested a linkage between exchange and phonon interactions [127,128]. As linewidth broadening is a measure of the extent of thermally assisted phonon scattering, such an investigation with linewidth reveals a possible correlation between the degree of Coulomb exchange and phonon coupling. However, in order to better understand the underlying mechanism, theoretical studies need to be conducted as well. Furthermore, it is even more curious to realise that several of the QDs' optical properties undergo a drastic change at the temperature is increased beyond 100 K, such as quenching of emission intensity (a potential reason why some systems [79,85] can only operate up to 100 K), accelerated broadening of linewidth, larger reduction of optical polarisation degree, and quasilinear increases of FSS. It is not unlikely that an unknown thermally assisted process that becomes activated at 100 K is causing these changes, and this can only be determined by further ongoing research and collaborations. HBT autocorrelation studies are the mandatory tests to determine whether a light source is indeed emitting single photons. This is achieved by examining the well-known second order autocorrelation of the photon statistics, While g (2) (0) < 1 demonstrates the phenomenon of antibunching and emission of non-classical light that follows sub-Poissonian photon statistics, g (2) (0) < 0.5 has been widely accepted by the community as the minimum requirement for the presence of a true single-photon emitter. This likely originates from the fact that g (2) (0) = 0.5 is the quantum mechanical threshold between a one-photon and two-photon Fock state [12]. However, in realistic single-photon systems, this argument represents the upper limit of the true g (2) (0) for that emitter itself. Other sources of undesired photons, e.g. background QW emission in nitride QDs, are not in the same basis as the quantum emitter, and therefore not considered by the said quantum mechanical treatment. From an experimental perspective, a series of N time stamps would result in N events recorded away from time 0. If at most N/2 of these times involve the incidence of more than 1 photon onto the beam splitter, whether it is caused by the presence of a nonsingle-photon Fock state or the contamination from a separate photon source, there would be a higher probability of single-, instead of multi-photon generation. Therefore, the condition of g (2) (0) < 0.5 still stands, but the true g (2) (0) value likely needs to be much lower than 0.5 in order to compensate for the presence of background signals.
This situation is especially relevant in the case of non-polar InGaN (and indeed most polar nitride) QDs, because of the aforementioned broad QW emission due to alloy disorder. A background correction method originally proposed for diamond-based single-photon sources [29] have been widely used in the nitride community [60,61,85,86,89].
The rationale behind equation (2) is a phenomenological one. The size of the HBT dip with background signals (1 − g (2) raw (0)) and that without these unwanted signals (1 − g (2) cor (0)) should scale proportionally with the square of the dot intensity ratio (ρ 2 ), due to the presence of two detectors in an HBT setup. For instance, the raw and corrected values should be the same if all signals originate from the quantum emitter itself. Therefore, the value of g (2) cor (0) should be an estimate of the true purity of the solid-state single-photon Fock state generator. However, these g (2) cor (0) values should only be used as a guideline or an attempt to understand the qualitative situation of the emitter, instead of a quantitative performance benchmark, for three reasons: (1) the correction formula  does not have a rigorous theoretical background, and occasionally produces unphysical and unreasonable results at small dot intensity ratios. (2) There are often intrinsic difficulties in the estimation of accurate dot intensity ratios, especially in self-assembled systems. (3) The corrected values, even if accurate, are not a true measurement of the performance of a single photon emitting platform, unless actual background signal reduction can indeed be achieved in the system. With these considerations, we will only look at the raw g (2) (0) values reported in the non-polar literature.

2.5.2.
Non-polar single-quantum emitters. The first nitridebased single-photon sources reporting g (2) (0) < 0.5, without the use of the wurtzite polar c-plane, are the PA-MBE-grown cubic InGaN QDs [79]. A raw g (2) (0) of 0.25 was achieved at 4 K, which increased to 0.47 at 100 K. In wurtzite symmetry, non-polar m-plane QDs grown on nanowire sidewalls are reported to emit single photons with a g (2) (0) of 0.28 at 4 K, and 0.49 at 100 K [85]. As the temperature increases beyond 100 K, the g (2) (0) value breaks the threshold of 0.5. Notably, the same system also reports simultaneous linear polarisation orthogonal to the long axis of the nanowire, which persists up to 100 K without signs of reduction. Both of these two systems have hence reached the regime of liquid nitrogen cooling, providing advantages over conventional single-photon platforms that require more complex liquid helium cooling.
Unfortunately, the restricted nanowire geometry of the mplane QDs does not have adequate local heat dissipation for operation at even higher temperatures. The second m-plane InGaN QD system reported with pencil-like nanowire structures has a g (2) (0) of 0.40 with highly polarised single-photon emission at 10 K. However, the performance of these nonpolar QDs at higher temperatures has not been mentioned. The first successful HBT results for non-polar a-plane InGaN QDs were reported with a g (2) (0) of 0.37 [91]. The single-photon nature of the emission persists up to a temperature of 220 K with a slightly increased g (2) (0) of 0.47. This is currently the highest temperature at which a non-polar nitride system has been reported to demonstrate single-photon generation. More interestingly, the optical polarisation properties also remain up 220 K. This is an important milestone for non-polar nitride single-photon development, as it is at the moment the only semiconductor QD single-photon source of any material that can generate ultrafast single photons with predefined and deterministic optical polarisation properties at temperatures reachable by on-chip cooling (>200 K). To achieve 100% linearly polarised emission at 220 K, the system only needs to sacrifice 10% (with a polarisation degree of 0.8), rather than 50%, of its external quantum efficiency. The PL emission of the QD remains up to 250 K, when the g (2) (0) increases to 0.71. HBT experiments performed on subsequent a-plane samples yielded g (2) (0) of 0.39 [92] and 0.47 [93] at 4 K. It is unfortunate that although the latest Q2T development have in some ways significantly improved the quality of aplane InGaN samples, these materials exhibit even stronger overlap of the QW and QD emission wavelength than their MDE counterparts. As a result, it became more difficult to identify QDs with good dot-to-background ratios. Nonetheless, in electrically driven a-plane devices based on the Q2T development, a g (2) (0) of 0.18 has been reported [101], with detection limitations considered but without background correction (thus the true performance of the device). The system has the lowest g (2) (0) of all non-polar single-photon sources reported so far, and is the only one that has been demonstrated to operate under electrical carrier injection. Optical linearly polarisation with a deterministic axis along the crystal mdirection has also been reported. The PL of these devices has currently been shown to persist up to a temperature of 130 K. A comparison of the single-photon characteristics of these nonpolar nitride platforms discussed is presented in table 1, along with comparison to similar semiconductor QDs systems and other important optical properties of single-photon sources.

Concluding remarks
The progress of non-polar single-photon development has been fast. Within half a decade, several systems have demonstrated single-photon emission, achieved polarisationcontrolled operation at on-chip temperatures, and completed the building of an electrically driven device. There is, of course, scope for improvement in the nitride QD system, leading to meaningful applications in quantum information sciences. Although the minimum requirement for single-photon generation has been reached by the non-polar systems discussed in this work, they only do so without a high singlephoton purity (e.g. figures 11(a) and (b)). Looking at table 1, the lowest polar nitride g (2) (0) reported is 0.08 with ultraclean interface fluctuation QDs, while the typical g (2) (0) for mature arsenide-based systems is consistently at least an order of magnitude lower [15,16]. Studies have indicated that g (2) (0) < 0.1 is the requirement for the implementation of quantum key distribution protocols [1]. However, this does not necessarily imply that current non-polar nitride single-photon sources do not have the potential for these applications. The progress towards higher technology readiness levels, or TRLs, happens in several stages. Arsenide single-photon sources have been established for a longer time than nitrides, and are at a stage whereby advanced resonant excitation and highly efficient collection are possible with precisely tuned and Purcellenhanced photon emission. Polar nitrides achieved singlephoton emission at 200 K from planar epitaxial structures in 2006 [59]. After a decade, site-controlled systems with a much purer g (2) (0) and an unprecedented QD operation temperature of 350 K were realised [61]. At the same time, development has also shifted towards the improvement of emission properties [62].
For the newer non-polar InGaN QDs, we have reached well beyond the stage of the 2006 GaN developments [59], and there is still much potential for further improvement. For instance, in the current investigations high excitation powers were generally used in order to achieve the highest possible single-photon emission temperatures. Studies have shown that in nitride QDs, a combination of both lower excitation power and photon energies closer to resonant conditions could result in a significant reduction of the g (2) (0) values [78]. As non-polar InGaN single-photon sources are in the initial proofof-concept stage, similar investigations that could unveil better single-photon purity have not yet been performed. As improved growth routines are developed, the overall dot density and emission brightness could be further increased. In fact, we have already seen a sizeable improvement in lifetimes and slow-timescale spectral diffusion, comparable to more established GaN platforms, as highlighted in previous sections. We have recently made significant progress in the measurement of fast-timescale spectral diffusion using an autocorrelation approach for non-polar a-plane InGaN QDs, and hope to publish these results soon. Together with ultrafast radiative recombination rates and statistically high degrees of polarisation with deterministic polarisation axes, these optical properties demonstrate the unique advantages of non-polar InGaN QDs. Furthermore, these advantages are enhanced by the ability to achieve operation temperatures (i.e. temperatures at which the generation of ultrafast polarisation-controlled single photons is possible) that can be reached by on-chip cooling solutions. When compared to current GaN/AlN systems, the ability of current non-polar systems to achieve electroluminescence and electrically driven single-photon generation is also a key step forward towards higher TRLs. Therefore non-polar nitride QDs are progressing at an accelerating pace towards the onchip generation of purer single photons that could enable the implementation of quantum key distribution protocols, following a comparable route taken by nitride and earlier arsenide single-photon sources, but with a more established starting point.
Therefore, a clear pathway towards further development and conversion into higher TRLs is available. The hightemperature operation of non-polar QDs also allowed new observations, investigations and insights to be made. We are in the initial stages of unveiling unknown physical processes and phenomena for QD-based single-photon sources in the nitride system. The behaviour of the high-temperature polarisation and FSS could be just a tip of an iceberg, and more hightemperature photophysics might be uncovered with the continued collaborative development of non-polar nitride singlephoton sources.