Direct generation of linearly polarized single photons with a deterministic axis in quantum dots

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 (SiN_x) interlayer method to control the defect density [31]. 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 SiN_x 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 SiN_x interlayer, has a dislocation density of 4×10⁹ cm⁻² and a basal plane stacking fault density of 2.6×10⁵ cm⁻¹ [31], [32].

The InGaN QDs were grown using a modified droplet epitaxy method [33]. 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.

Figure 1:

Sample structure, processing, and setup of optical experiment.

(A) AFM image of an uncapped QD sample grown on a-plane GaN template, with z-scale=5 nm. (B) Schematic material structure for the nanopillar p-i-n sample with InGaN QDs. Also shown are SEM images (30° tilted view) of nanopillars (C) before and (D) after the removal of the residual silica nanospheres. (E) Schematic of polarization-resolved micro-photoluminescence (μ-PL) setup, illustrating the sample orientation and consequent PL composition before passing through the polarizer in the plane of view.

Silica nanospheres (d≈180 nm, fabricated in our laboratory [34]) 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 [35]. 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 [17], [36], [37], [38]. 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.

Figure 2:

(A) DOLP ρ as a function of the in-plane aspect ratio α and indium content of a lens-shaped a-plane InGaN/GaN QD. The inset shows the coordinate system, the definition of θ as the in-plane angle away from the crystal c-axis (same as that defined in the experimental setup), and the definitions of d_y and d_x as the in-plane dimensions of a QD used in the theoretical investigation. α is defined as α=d_x/d_y. (B) ρ as a function of α, size, and geometry of a QD.

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 [39], [40]. We followed this assumption, and based on earlier AFM results [33], 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 [27], [32], [33], [41], [42], [43], [44] 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. [36].

The outcome of our k·p calculations for a dot with a circular base predicted a hole ground state with 97% | Y〉-like and only 2% |​X〉-like character, indicating that the emitted light should be polarized perpendicular to the c-axis (along the m-axis). The intensities measured perpendicular and parallel to the wurtzite c-axis, I⊥ and I∥, should reflect largely the | Y〉- and |X〉-like orbital contributions to the hole ground state, respectively. According to the DOLP formula, ρ=(I⊥−I∥)/(I⊥+I∥), an a-plane InGaN QD with a circular base is, hence, predicted to have a ρ of 0.96. This result is in stark contrast with theoretical studies of c-plane InGaN QDs, where ρ, due to the c-plane symmetry, is 0 for dots with no in-plane anisotropies [15], [16].

However, it is important to note that self-assembled QDs are unlikely to be perfectly symmetrical. Results on both InGaAs QDs [30] and c-plane InGaN QDs [15], [16] 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 |​X〉-,| Y〉-and | Z〉-like state and, thus, their contribution to the band mixing effects for the hole ground state. It is, therefore, important to study how significant this effect is in our QDs by modifying the dot geometry in the simulation. We define the in-plane aspect ratio α as α=d_x/d_y, where d_x and d_y are the in-plane dimensions of the dot base along the x- and y-directions, respectively. Here, for a circular base, d_x=d_y=30 nm, and α =1. A schematic illustration of the convention is given in the inset of Figure 2A.

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 | X〉-like states along this direction and an increase in the energetic separation of | Y〉-and | X〉-like states. Correspondingly, the more interesting situation is what happens if the dot geometry is modified along the y-direction. Such an anisotropy should affect states with a high | Y〉-like orbital contribution more strongly, again due to the fact that | Y〉-like (| X〉-like) states exhibit a low (high) effective mass along the y-direction [45]. Please note that the coordinate system used in this work is different from that used in Ref. [45]. More details on the coordinate system used here can be found in Ref. [38]. Hence, calculations were performed at d_y=30, 15, 7, 6, and 5 nm, as the QD base becomes more elliptical. The results for ρ as a function of α and indium content are shown in Figure 2A. We see that ρ is almost constant for α values between 1 and 2, and decreases only slightly for α =3, independent of indium content. It is important to note that α =3 already presents a significant “deformation” of the dot (d_x=30, d_y=10). Consequently, the calculations show that in a-plane InGaN QDs, the DOLP ρ is very insensitive against shape anisotropies and indium composition changes. It should be noted that, in principle, Coulomb effects can mix contributions from excited (single-particle) states into the excitonic ground state [46]. However, our calculations reveal that the first few excited hole states are all almost entirely | Y〉-like in character. Thus, mixing of different hole states via Coulomb effects will not affect the orbital character discussed here. A detailed discussion of excited states and how this affects the DOLP at elevated temperatures is beyond the scope of the present study and will be reported elsewhere.

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, d_x=d_y=24 nm. To consider the same range of in-plane aspect ratios α, d_y 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 I(θ)=I⊥cos2(θ−φ)+I∥sin2(θ−φ), where I⊥,I∥,and θ follow the same definitions explained previously, and φ is the angle at which the maximum of function occurs. As both cross-polarized components should exhibit Malus’ law type intensity variation, two sinusoidal fits with a phase difference of 90° are used in the equation. The sinusoidal intensity change, thus, demonstrates that the QD emission is polarized. Furthermore, the φ is found to be 92°±1°, indicating that the maximum intensity occurs at θ=92° and 272°, indeed corresponding to the direction perpendicular to the c-axis. The small difference of ~2° is attributed to the error of sample placement in the cryostat.

Figure 3:

The μ-PL of the two cross-polarized components for a QD at 503 nm (~2.46 eV). Top inset demonstrates the emission of single photons with a raw g⁽²⁾(0) of 0.47, which becomes 0.06 after a standard background correction (~75% QD intensity). Right inset shows sinusoidal intensity variation of the QD emission and axis of polarization with respect to striations on the sample surface.

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 [31], 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 [27].

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 | ρ | for these QDs is shown in Figure 4A. The high mean | ρ | of 0.90 provides direct evidence that non-polar a-plane InGaN QDs are strongly polarized photon emitters. Furthermore, due to the modified droplet epitaxy growth routine [33], the a-plane QDs studied in this work were formed on top of fragmented QWs (fQWs). In the μ-PL experiments, we observe sharp emission features from the QDs together with the underlying fQW emission over the same spectral range, such as that in Figure 3. As such, we are able to not only measure the DOLP for the QDs but also for the underlying a-plane fQWs. For each of the 180 a-plane QDs we investigated, the | ρ | of their respective fQWs are shown in Figure 4B.

Figure 4:

The 180 a-plane InGaN/GaN (A) QD and (B) underlying QW DOLP variation with emission energy.

The statistical distributions have been fitted with Gaussian profiles. The means and standard deviations of the Gaussian distributions are (A) 0.90±0.08 and (B) 0.46±0.14, respectively.

All | ρ | data of QDs fall in the range between 0.60 to 1.00, in contrast to those of QWs between 0 and 0.80. The average | ρ | of 0.46 for the QWs, which is in agreement with the latest literature findings [26], is also much less than the average of 0.90 for the QDs. From a fundamental perspective, this is interesting because out of a-plane nanostructures, only a-plane QDs possess such high DOLPs. From a technology viewpoint, coupled with the ability to achieve single-photon emission, a-plane QDs are well suited for the generation of single photons with polarization control and useful for the development of quantum information applications. A typical g⁽²⁾(0) measurement from one of our dots is shown in the top inset in Figure 3, where we measure emission of single photons with a raw g⁽²⁾(0) of 0.47, which becomes 0.06 after a standard background correction (~75% QD intensity).

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 |​X〉-like in orbital character. From Figure 2A, one can infer that ρ drops significantly for α >3, and more so with higher indium content, as the confinement effects due to increased band offsets become stronger, making asymmetries in the QD geometry more prominent. Producing a predominant |​X〉- like hole ground state would, hence, require an extreme deformation of the QD (d_x=30 nm, d_y=6 nm) and very high indium content. In addition to strong shape anisotropies, alloy fluctuation effects might also contribute to the observed behavior [47]. As such, the previous report [27] is an investigation of these 9% QDs, which is a special case to the general behavior of a-plane InGaN QDs. It is also worth noting that the DOLPs of such QDs are similarly high and follow the same distribution as that shown in Figure 4A.

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.

Figure 5:

The μ-PL of a QD (~505 nm) and its underlying fQW.

The QD is polarized along the c-direction, while the fQW is polarized along the m-direction, corresponding to one of the 9% special cases in which a-plane QDs are polarized parallel to the crystal c-axis.