1. Introduction

Single-photon sources are indispensable components for the development of future quantum technologies, including quantum computation, quantum communication, and quantum cryptography [1–3]. Among the diverse single-photon sources including atoms [4], nitrogen vacancy centers [5,6], single molecules [7], and colloidal quantum dots (QDs) [8], epitaxially grown semiconductor QDs are promising candidates owing to their high quantum efficiency and short radiative recombination lifetime [1,9–11]. In addition, these QDs can be readily integrated with optical microcavities and electrodes, which enable the development of electrically driven devices [12,13]. However, typical semiconductor QDs are randomly distributed; therefore, there has been a growing interest in finding new methods to acquire site controlled QDs [14,15]. There has been noticeable advancement in site controlled QDs for the last decades. QDs at the apex of pyramid structures (apex-QDs) have attracted a considerable amount of attention because they provide a platform for large-array, site-controlled QDs [14–17]. By growing a thin, single quantum well layer on the top of a 3D pyramid structure, QDs are naturally formed at each vertex [18]. This method enables the fabrication of an array of site-controlled QDs. Apex-QDs have several advantages aside from their site controllability. The direction of linear polarization can be controlled by changing its elongation direction at the apex [19]. Additionally, deposition of a metallic layer on 3D pyramid structures automatically produces 3D tapered metallic cavities, which allow spontaneous coupling between QDs and plasmonic modes [20,21]. Recently, a detailed optical analysis of metal-coated nano-pyramid structures disclosed their unidirectional emission behavior in the downward direction [22].

In previous research using metallic cavities combined with apex-QDs, strong light emission (enhanced photoluminescence) was observed under continuous-wave (CW) excitation when compared to the case without a metallic cavity. Specifically, the dipole source power was greatly enhanced via Purcell effect that results in both higher quantum yield (and lifetime reduction) under CW excitation. These combined effects allow us to observe brighter PL by overcoming the metallic loss. However, when pulsed excitation is used for on-demand single-photon experiments, the reduction of the lifetime does not play a role to increase the repetition rate [23]. Therefore, it is relatively difficult to overcome the loss from a metallic cavity, and the alternative design with low metallic loss, preferably with guided directional radiation should be discussed [11,24–27].

Herein, we propose a system for efficient light collection from an apex-QD and suggest the optimal shape of the metallic mirror. The system comprises a metallic mirror, an apex-QD, and a dielectric layer inserted between a metallic layer and an emitter. A silver metallic layer plays the role as a mirror, enabling 94% of the light from the apex-QD to be guided downward. In addition, a tapered fiber is adopted to couple the QD emission to the fundamental mode of an optical fiber. A highly efficient coupling to the fundamental mode was numerically observed, which corresponds to 60% coupling efficiency with a tapered diameter of 800 nm. This study suggests a novel design for efficient light collection from a QD in pyramidal geometry.

2. Results and discussion

Figure 1(a) shows a schematic of the device comprising a pyramid structure, dielectric layer, and metallic layer. Such pyramid structure could be created by selective area epitaxy with patterned masks using metal-organic chemical vapor deposition. This bottom-up approach enables the simple creation of three-dimensional (3D) structures in a large area. A dielectric layer, in this case SiO₂, allows for the adjustment of the distance between the semiconductor pyramid and metallic layer. The insertion of a dielectric layer is a distinctive feature of previous studies in which a metallic layer was directly placed onto the pyramid structures. A wavelength-dependent refractive index is included as well as the imaginary part of the index which describes the absorption property of silver. Figure 1(b) illustrates the simulation setup used for the 3D finite-difference time-domain (FDTD, Lumerical Inc.) calculation. The power monitor has a cuboid volume of 7.0 × 7.0 × 1.3 µm³, enclosing the pyramid by 200 nm in both width and height. The monitor size is large enough so that any radiation with slight angle will be captures by the top or bottom side monitor. This means that the lateral side monitors mostly measure the surface plasmon polariton propagation and some portion of the free-space radiation which propagates along the surface. A dipole emitter polarized along the x-axis was embedded 10 nm below the apex and therefore represented an apex-QD. First, we conducted FDTD simulations to calculate the light extraction efficiency for the structure with the silver layer directly coated onto the pyramid as depicted in Fig. 1(c). Here, the extraction efficiency is the light captured by a hemisphere, which equal to the collection efficiency when the numerical aperture is 1. Such geometry was studied to enhance the photoluminescence from the quantum dot emission. More specifically, the thickness of the dielectric layer is 0 nm between the pyramid structure and metallic layer. The graph shows that only a small portion of light escaped the pyramid structure, while the majority was absorbed by the metal, as indicated by the blue triangular data points. Although the addition of the silver layer significantly reduced the extraction efficiency, this structure enables an increased dipole emitter intensity due to the reduced radiative lifetime or Purcell enhancement. This is because the pyramidal silver layer acts as a focused plasmonic nanocavity. However, under pulsed excitation of single-photon emitters, the extraction efficiency becomes an important figure of merit. Therefore, the proposal of a new design that maximizes the extraction efficiency of a semiconductor pyramidal quantum platform is crucial and will be key to achieving near-unity, on-demand single-photon sources.

 

Fig. 1. (a) Illustration of a system with pyramid structure, SiO₂ layer, and a silver mirror. (b) Simulation setup for the finite-difference time-domain analysis. A dipole emitter is located at the apex of the pyramid. (c) Plot of extraction efficiency showing normalized intensity as a function of wavelength.

Download Full Size | PDF

First, we investigated the effect of the dielectric layer between the pyramid (and hence an apex-QD) and metal layer. Prior to the simulation, feasible shapes of the metallic mirrors were experimentally investigated. Dielectric layers were deposited by sputtering, followed by silver layer deposition using an electron-beam evaporator. The cross-sectional transmission electron microscopy image in Fig. 2(a) shows that the silver layer maintains the original 3D pyramid shape when the thickness of the dielectric layer is relatively thin (50 nm). Whereas the 3D pyramid shape is flattened as the dielectric layer becomes thicker (240 nm) and forms an oval-shaped mirror, as shown in Fig. 2(b). Therefore, the possible mirror shapes that can be formed by standard deposition are either 3D pyramids or ovals. Planar mirrors are also feasible when the dielectric layer is much thicker than the size of the pyramid structure. Figures 2(c) and 2(d) show the extraction efficiencies for the pyramidal and oval mirrors for the SiO₂ layer thickness of 240 nm. Compared to the case without a dielectric layer (Fig. 1(c)), the metallic losses (blue line) are significantly reduced, while most of the light emitted is guided downward, indicating that the metallic layer acts as a mirror. Here, the downward radiation as the electric field power captured by the monitor below the dipole source divided by the power generated the dipole source at the apex of pyramid. However, owing to the 3D shape of the mirror, a resonant effect conveying metallic loss is observed for both the pyramidal (wavelength of 500 nm) and oval (wavelength of 550 nm) mirrors.

 

Fig. 2. Cross-sectional view of transmission electron microscopy (TEM) images showing (a) pyramidal- and (b) oval-shaped metallic layer. The dielectric (blue, falsely colored) and silver layers were deposited using sputtering and electron-beam evaporation, respectively. The extraction efficiency versus the wavelength is plotted for the (c) pyramidal and (d) oval mirrors for the SiO₂ layer thickness of 240 nm.

Download Full Size | PDF

To remove the metallic loss from the resonance effect, a planar metallic mirror is desirable; however, the standard deposition method requires a substantially thick dielectric layer for planarization. To circumvent this problem and to create planar mirrors on a structured substrate, as shown in Fig. 3(a), hydrogen silsesquioxane (HSQ) was introduced. HSQ was spin-coated onto the pyramid structure as a liquid form, followed by a high-temperature baking process to solidify the HSQ. Subsequently, we optimized the silver layer thickness while fixing the SiO₂ layer to 240 nm. Figure 3(b) shows that the thicker the silver layer, the better the reflection at the metal interface when SiO₂ remains at 200 nm. However, the effect of the thicker metal is saturated after 100 nm, so the silver layer thickness was fixed at 100 nm for the rest of the study. Subsequently, the SiO₂ thickness was gradually increased to determine the optimal thickness and achieve the maximum extraction efficiency. Figure 3(c) demonstrates that the extraction efficiency can reach 0.9 when the dielectric layer has a thickness of approximately 240 nm. This high extraction efficiency in one direction was preserved throughout the wide wavelength range.

 

Fig. 3. (a) TEM image showing a cross-sectional view of the pyramid with the planar SiO₂ layer. (b) Extraction efficiency in the downward direction with varying silver layer thickness. The SiO₂ layer thickness was fixed to 200 nm. (c) Extraction efficiency in the downward direction with varying SiO₂ layer thickness and fixed silver layer thickness of 100 nm.

Download Full Size | PDF

Next, a pyramid structure combined with an optical fiber was investigated. Emission from the dipole emitter embedded in the apex of the pyramid exhibited a Gaussian-shaped far-field emission, which is favorable for fiber coupling. Figure 4(a) shows a schematic of a QD-fiber hybrid system coupled with a tapered fiber having a diameter of 800 nm. Such structure can be created by combining two techniques, tapering fiber and transfer printing [28,29]. To calculate the coupling efficiency, the intensity of the coupled mode in a single-mode optical fiber is divided by the dipole emitter intensity. The power monitor in the simulation was located 10 µm below the end facet of the fiber, which only measures the power from the fiber-guided mode. Figure 4(b) shows the coupling efficiency for various types of mirrors. For comparison, two types of reference structures were included in the simulation. Ref. 1 is a pyramid structure without any metallic mirror and shows less than 1% coupling to a fundamental mode of the tapered fiber. Ref. 2 is a bare wafer coated with a metal layer without any 3D structures, also showing low coupling (< 4%). Meanwhile, the pyramid and oval shapes of the dielectric and metal layers exhibited coupling efficiencies of 0.2–0.4. The planar metallic mirror had a total coupling efficiency of 0.4–0.6 throughout the large spectral range. It is noteworthy that the coupling efficiency shown in Fig. 4(b) is for single-mode coupling, which can be further increased for multimode fiber collection. The propagating mode after the QD emission coupled to the fiber is shown in Fig. 4(c).

 

Fig. 4. (a) Schematic showing the semiconductor pyramid on an optical-fiber end facet. (b) Coupling efficiency from QD to optical fiber for various geometries. (c) Time evolution of electric field intensity showing emission from a dipole coupled to a fiber.

Download Full Size | PDF

3. Conclusion

Deterministic single-photon sources are important for the advancement of quantum technologies, such as quantum communication and computing. In particular, a high extraction efficiency of single-photon emitters is crucial for practical devices. A dielectric layer introduced between the pyramidal semiconductor and metallic layer reduces the metallic loss and enables near-unity light extraction. We experimentally tested feasible metallic mirror shapes and then implemented them in photonic simulations. We found that with a planar silver mirror geometry, a 0.94 portion of the light can be guided downward. This geometry also enables light emitted from a QD to be coupled to the optical fiber with a high efficiency of 0.6 at 600 nm. The optimization of the light extraction efficiencies for QDs embedded in the apex of pyramids paves a way for deterministic quantum emitters with near unity extraction efficiency.