Polarized single-photon sources ,  are essential for applications in quantum information sciences, such as quantum key distribution , ,  and optical quantum computing . To develop these non-classical light sources, the nanophotonics of semiconductor quantum dots (QDs) , ,  has been a field under intense scientific investigation. Although ultrapure and highly indistinguishable single-photon generation has been achieved in various arsenide-based QD systems , , , , , the large band offsets and strong exciton binding energies of III-nitride materials are needed for the realization of polarized photon emission , ,  and room temperature operation , . These polarized single-photon sources can then fulfill the need for on-chip polarization encoding in quantum cryptography, such as the BB84 protocol . However, previous studies of polar c-plane (0001) InGaN QDs reveal that only selected QDs with large-shape anisotropies can exhibit high degrees of optical linear polarization (DOLP) , , which are also in agreement with our own investigations . Furthermore, in most conventional c-plane nitride QD systems, different anisotropies could result in random polarization axes, which are highly undesirable in the implementation of polarization-based protocols in potential applications. Consequently, much effort is needed to define the anisotropy, in order to obtain consistently high DOLPs with deterministic polarization directions. Such experimental reports in the nitrides are limited to the manipulation of pyramidal geometries , elliptical QDs , or the use of nanowires , , where the geometries of the structures make electrical contacting challenging. As such, a simpler and more practical method is needed to achieve polarization control, for the realization of on-chip polarized single-photon generation and related applications.
In this work, we report a combined theoretical and experimental investigation of a planar epitaxial self-assembled semiconductor QD system – non-polar a-plane (11–20) InGaN/GaN QDs – that provides not only a statistically high DOLP but also a fixed polarization direction determined by the underlying material crystallography. Furthermore, while the DOLPs of a-plane quantum wells (QWs) are limited to ~0.60 , we report a much higher average DOLP of ~0.90 in a-plane InGaN QDs. Previous investigations have reported polarization properties of some a-plane InGaN QDs along  , orthogonal to those reported in a-plane QWs (along [1–100]) , , . We find that this is a special case to the general behavior of a-plane QDs. Here, more rigorous measurements of the DOLP have been made upon a large number of QDs using high extraction efficiency QD-nanopillar structures. Theoretical simulations have also been undertaken to elucidate the origin of the linearly polarized emission, producing results in agreement with our experimental findings.
Furthermore, it is well known that for InGaAs/GaAs QD, shape anisotropies have a significant effect upon the optical polarization properties of the QDs . The experimental observation of high DOLPs raises the question of how strongly shape anisotropies affect the optical properties of self-assembled a-plane InGaN/GaN QDs and, thus, how reliable these QDs might be in generating highly polarized photons. Hence, we also provide the first investigation of the effect of dot anisotropy on the DOLP of a-plane InGaN QDs, and couple our findings to insights from statistically significant experimental studies.
2 Materials and methods
2.1 MOCVD growth of the QD sample and fabrication of nanopillars
The a-plane InGaN QD sample was grown by metal-organic vapor phase epitaxy in a 6×2-in Thomas Swan close-coupled showerhead reactor on an r-plane sapphire substrate using trimethylgallium, trimethylindium, and ammonia as precursors. The a-plane GaN template was prepared using a silicon nitride (SiNx) interlayer method to control the defect density . After the deposition of a low temperature GaN nucleation layer at 500°C, a 1-μm-thick seed GaN layer was grown at 1050°C and a V/III ratio of 60. A single SiNx interlayer was grown at 900°C using a silane (SiH4) flow rate at 0.2 μmol min−1. A three-dimensional growth step was carried out at a pressure of 300 Torr using a V/III ratio of 1900, which was followed by a two-dimensional coalescence step using a V/III ratio of 60 at 100 Torr. The as-grown a-plane GaN template, utilizing the SiNx interlayer, has a dislocation density of 4×109 cm−2 and a basal plane stacking fault density of 2.6×105 cm−1 , .
The InGaN QDs were grown using a modified droplet epitaxy method . A 2.5 nm thick InGaN epilayer was grown at 695°C and 300 Torr, which was immediately annealed in N2 atmosphere for 30 s at the growth temperature. This annealing process results in the formation of In/Ga metallic droplets, which will re-react with ammonia during the GaN capping to form InGaN QDs (an initial ~10 nm GaN cap was grown at the InGaN growth conditions, and another ~15 nm GaN was grown at 1050°C using H2 as the carrier gas). The QDs were positioned in the center of a 50-nm-thick intrinsic GaN layer (unintentionally doped GaN – uid GaN), which was clad by ~600 nm of Si-doped GaN (dopant concentration ~3×1018 cm−3) at the bottom and ~200 nm of Mg doped GaN (dopant concentration ~3×1019 cm−3) on the top. An atomic force microscopy (AFM) image of an uncapped sample following the growth and anneal of the InGaN layer and a schematic of the full sample structure are shown in Figure 1A and B, respectively.
Silica nanospheres (d≈180 nm, fabricated in our laboratory ) were dispersed in ethanol and deposited onto the sample by drop casting. The nanospheres act as the etch mask for the nanopillars. The sample was subsequently dry-etched in an Oxford Instruments PlasmaPro 100 inductively coupled plasma etch system to a depth of ~350 nm using a gas mixture of Cl2 and Ar. The residual silica nanospheres were removed by ultra-sonication in acetone, followed by a buffered oxide etch. SEM images of the nanopillars before and after the removal of the residual silica nanospheres are shown in Figure 1C and D, respectively, where the diameter at the top of the nanopillar is ~180 nm. The tapered shape is formed naturally during the dry-etching process.
2.2 Optical characterization
The sample was mounted in an AttoDRY800 closed-cycle cryogenic system that maintains a stable sample temperature of 5 K. As shown in Figure 1E, an 80-MHz Ti:Sapphire laser system generates 1-ps pulses at 800 nm, providing two-photon excitation for the sample. It has been previously established that under multiphoton excitation, structures with higher degrees of quantum confinement have greater relative absorption cross-section . As such, a two-photon excitation produces better signal-to-background ratios for our sample, which contains both QDs and a fragmented QW.
A single-mode fiber with a 4-μm core spatially filters and transmits the excitation laser pulses onto a collimating lens, which then passes the beam to a 100× NIR objective with a numerical aperture of 0.5, producing an ~1-μm laser spot for sample excitation. A power density of 2 MW cm−2 is chosen so that the QDs have the strongest emission before saturation takes place. Because of the use of two-photon excitation, this power is higher than the typical ~kW cm−2 intensity used in one-photon excitation. The PL from the sample is then collected by the same objective and directed to an Andor Shamrock 500i half-meter spectrograph with variable slit size and a grating of 1200 lines mm–1. An AndoriDus 420 Si-based charge-coupled device (CCD) is thermoelectrically cooled to –50°C for low-noise detection, enabling μ-PL measurements with a spectral resolution of ~38 pm. The PL can also be spectrally filtered and passed on to a pair of photomultiplier tubes for standard Hanbury Brown and Twiss measurements.
For polarization-resolved μ-PL, a rotatable polarizer cube and a half-wave plate are introduced in the optical collection path. The transmission axis of the polarizer is set to 0° on the rotation mount and aligned parallel to the c-axis component of the sample PL. Hence, a polarizer rotation of θ would correspond to the angle away from the c-axis in the growth plane, as shown in Figure 1E.
Ensuring high accuracy in polarization-resolved μ-PL spectroscopy is experimentally challenging in a number of ways, including random sample drift, PL intensity fluctuations, and difficulty in measurement when approaching the weaker polarized component. In order to ensure the precision of measurement as far as possible, three precautions have been taken during the course of measurement: (1) The half-wave plate was rotated by –θ/2 for a polarizer angle of θ, thus, maintaining a constant axis of PL polarization and correcting an ~10% difference in polarization-sensitive detection of the system. (2) The slit of the spectrometer was opened wide enough to account for slight optical alignment changes caused by the rotation of the polarizer cube, so that PL intensity remained constant at angles 180° apart. (3) To counteract any sample position drift, a reference measurement of the maximum intensity was immediately made after the data at each θ was taken, and μ-PL results were normalized accordingly during analysis.
2.3 Theoretical simulations
To address the electronic and optical properties of a-polar InGaN/GaN QDs from a theoretical perspective, we applied a flexible k·p model, accounting for strain and built-in fields, as described in detail elsewhere , , , . To study the DOLP, band mixing effects in the valence band are of central importance. As such, a six-band Hamiltonian to describe the hole states and a single-band effective mass approximation for electrons are used. In the following study, the x-axis of our coordinate system is parallel to the crystal c-axis. A schematic illustration of the coordinate system is given in the inset of Figure 2A.
3 Results and discussion
3.1 Theoretical calculations of DOLP
Information regarding the QD geometry and indium content, which is difficult to obtain experimentally, is required for calculation inputs. Previous studies on InGaN QD systems assumed lens-shaped geometries , . We followed this assumption, and based on earlier AFM results , chose a base diameter of 30 nm and a height of 2.5 nm as our starting point, with indium content varied between 15% and 25%. All calculations were performed on a 50×50×30-nm3 supercell with periodic boundary conditions. With these assumptions, the calculated ground state transition energies were in the range of 2.7 to 2.9 eV, close to typical experimental values , , , , , ,  and those discussed below. Therefore, the chosen geometries and indium contents should give a reasonable description of the structures considered here. A detailed analysis of built-in fields, electronic structure, excitonic and biexcitonic properties of the systems under consideration is given in Ref. .
The outcome of our k·p calculations for a dot with a circular base predicted a hole ground state with 97%
However, it is important to note that self-assembled QDs are unlikely to be perfectly symmetrical. Results on both InGaAs QDs  and c-plane InGaN QDs ,  reveal that dot shape anisotropy plays an important role and affects their properties quite significantly due to band mixing effects. Anisotropy affects the degree of quantum confinement, which causes energetic shifts in the
A smaller dimension, and thus stronger confinement effects, along the x-direction will further increase the DOLP as it approaches unity. This is attributed to the lower effective mass of the
To strengthen the argument that the DOLP is extremely robust against shape anisotropies, we have also varied the geometry and size of the dot. First, to study the impact of the QD size on the DOLP, we have kept the geometry to be lens-shaped but reduced the in-plane dimensions of the system. Here, for the symmetric dot, dx=dy=24 nm. To consider the same range of in-plane aspect ratios α, dy has been varied between 24 and 4 nm. The results of this study are shown in Figure 2B (red circles), revealing that the change in the QD in-plane dimensions affects the DOLP only very slightly.
To further extend this analysis, we have also investigated the influence of the QD geometry on the DOLP. To this end, we have drastically changed the QD geometry from a lens-shaped dot to a cuboid. The length and width of the cuboid is assumed to be of 24 nm with a height of 2.5 nm. Figure 2B shows the data (black squares) of the DOLP as a function of α for the cuboidal dot. As one can infer from this study, in comparison with the lens-shaped systems, the reduction of the DOLP only happens at higher α values (α =5). Consequently, the DOLP in cuboid-shaped dots would even be more robust against shape anisotropies.
As such, our theoretical studies predict high experimental DOLP values, with very small variations caused by QD shape anisotropies, indium content variations, size, and geometry differences. To validate the simulation results and gain further insights from the experiments, we perform optical characterization of non-polar a-plane InGaN/GaN QDs.
3.2 Experimental and statistical investigations of QD emission
The PL spectra of the two cross-polarized components of a single QD are shown in Figure 3, with its emission intensities at 10° intervals displayed in the right inset. The data were fitted with
According to the illustration in Figure 1E and the definition of θ, the polarization axis can, hence, be determined to be along the m-axis, the same as the simulation predicts. To further quantify how polarized the emission is, we invoked the DOLP formula described previously and calculated a ρ of 0.92 for this QD, again showing good agreement with the theoretical results for α values between 1 and 2.
Additionally, the intensity variation plot is shown on top of an optical microscope image of the sample. The a-plane sample surface exhibits striated features along the c-axis , further demonstrating the orthogonality between the polarization axis and the crystal c-direction. As such, the PL polarized parallel to the c-axis should correspond to the weaker polarized component of QD emission, instead of the stronger one as previously reported .
In order to achieve statistical significance for this finding, we investigated the absolute values of DOLP of 180 QDs individually. In this investigation, only QDs with a peak intensity of >50 counts s−1 were included in this investigation, in order to ensure measurement accuracy. The distribution of
The spread of the values in Figure 4A is attributed to variations of QD size, shape, and indium content. There are 23 QDs for which the weaker polarized component cannot be detected at all, giving a DOLP of unity. As explained in the theoretical simulation, this could be caused by a compression of the QD geometry along the c-direction. Those with DOLP values lower than average could be attributed to a compression along the m-axis (cf. Figure 2A and B). Furthermore, the calculated standard deviation is only 0.08, which signifies very small fluctuations around the high average DOLP. As such, the robustness of DOLP against changes in size, shape anisotropy, and indium content have been demonstrated both theoretically and experimentally. The data in Figure 4A and B indicate that there are no discernible correlations between QD energy and DOLP (of their respective QW), thus, a-plane InGaN QDs emit highly polarized photons across all attainable wavelengths.
The alignment of the polarization axis was also studied during the polarization measurement. In order to avoid selection bias, the polarizer was initially set to 45°. For each QD emission observed in the PL spectrum, the polarizer was then rotated from 0° to 90°, to determine the angle at which the maximum and minimum intensities occurred. Of the QDs, 91% exhibit polarization aligned along the m-axis (within a 10° error), which agrees with the simulation results. However, there are 9% of the studied QDs polarized along the c-axis. In our theoretical framework, this would mean that the hole ground state is predominantly
An example of an a-plane QD polarized along the c-direction, as one of the 9% cases, is shown in Figure 5. The QD at ~505 nm has its maximum intensity at θ=0°, corresponding to a polarization axis along the crystal c-direction. However, the underlying a-plane fQW still behaves as expected, and has its maximum intensity at θ=90°. The QD has a DOLP of unity, and the QW has a DOLP of 0.27, both of which are in agreement with the statistics in Figure 4A and B, respectively. As such, we show evidence of cross-polarized QD and QW emissions from our a-plane InGaN QD sample. Because of the suppression of the QW background in these 9% cases, we are able to achieve higher dot-to-background ratios for the QDs with a polarization axis along the c-axis, which are beneficial for the development of purer single-photon sources than that shown in Figure 3, with g(2)(0) values closer to 0. Overall, our experimental and theoretical data show that compared to QDs fabricated with c-plane nitrides, arsenides, or other semiconductor materials, a-plane InGaN/GaN QDs are able to achieve efficient linearly polarized single-photon emission with consistently high DOLPs and a deterministic polarization axis.
In conclusion, this work provides a statistically significant investigation of the polarization properties of a-plane InGaN QDs with high experimental precision. Cross- polarized photon emissions from 180 QDs produce an average DOLP as high as 0.90, with a small standard deviation of only 0.08. Theoretical k·p simulations have also demonstrated similarly high DOLP for these QDs, which is almost insensitive to small size differences, shape anisotropies, and indium content changes. The polarization axis has been theoretically and experimentally determined to be mostly along the crystallographic m-axis direction, with a small (9%) minority along the c-axis. It is also important to note that the studied a-plane InGaN QD systems outperform a-plane QW systems in terms of the DOLP. The statistically high DOLP, fixed polarization axis, and insensitivity to size, shape, and indium contents offer a-plane InGaN QDs unique advantages in polarization control compared to their c-plane InGaN and GaN counterparts, and to QDs based on other materials, such as InAs or CdSe. In summary, polarized single-photon sources based on the non-polar a-plane InGaN QD system are good candidates for the development of quantum information applications.
This research was supported by the UK Engineering and Physical Sciences Research Council (EPSRC) Grants EP/M012379/1 and EP/M011682/1, and the Science Foundation Ireland (Project No. 13/SIRG/2210). T.W. is also grateful for the award of the National Science Scholarship (NSS) as PhD funding by the Singapore Agency for Science, Technology and Research (A*STAR).
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