1. Introduction

The high output power GaN-based light-emitting diodes (LEDs) have attracted astonishing attention for various illumination applications such as back light units for liquid crystal displays and solid state lightings [1]. However, the commercial LEDs require further improvements in optical output power. In this context, many techniques have been developed for improving the light output power, such as surface texturing [2,3], use of patterned sapphire substrate [4], photonic crystal structure [5], embedded SiO₂ pattern [6], and insertion of distributed Bragg reflector [7], etc. Recently, our group has reported the use of embedded silica nanospheres (SNs) to enhance the performance of GaN-based blue LEDs [8]. The embedded SNs were found to boost the optical output power as a result of light scattering. In addition, the light emission was observed to increase with increasing amount of SNs embedded in the LED. However, the amount of SNs that can be embedded in a device is limited due to the availability of small space offered by the hexagonal etch pits. In this letter, we demonstrate the advantages of inverted hexagonal pyramid structure (hereafter referred to as honeycomb cone) in which a large amount of SNs can be stacked as multiple layers to enhance the light output power. The improvement of light output power is discussed on the basis of Mie scattering theory [9,10] and light refraction at the interface between GaN and embedded honeycomb cone. The multiple scattering invoked at the silica nanosphere stacking layers (SNSL) promised a significant enhancement in the optical performance of LEDs.

2. Experiments

Figure 1 shows the schematic illustration of key steps for fabricating SNSL embedded LED. Firstly, a SiO₂ layer of 100 nm thickness was deposited onto sapphire substrate by plasma-enhanced chemical vapor deposition. The SiO₂ film was then patterned for hexagonal dot patterns of 4 μm in diameter with a periodicity of 2 μm along the <11-20>_sapphire direction by using photolithography and wet etching by buffer oxide etch solution, as shown in Fig. 1(a).

 

Fig. 1 (Color online) Schematic illustration of key steps for fabricating SNSL embedded LED: (a) SiO₂ dot patterns on sapphire substrate. (b) formation of honeycomb-cone-shaped GaN by selective area growth. (c) self-assembled silica nanospheres on honeycomb cones. (d) the epilayer structure after the re-growth step.

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The SiO₂ mask-patterned sapphire substrate (SMPSS) was set into the metal organic chemical vapor deposition (MOCVD) chamber for the growth of GaN honeycomb cone structures. GaN nucleation layer was first deposited at 560°C, followed by un-doped GaN layer at 1020°C for 90 min. During this growth stage, well-aligned honeycomb cones with {10-1-1} facets were formed on the SMPSS, as shown in Fig. 1(b). Then, SNs of 500 nm in diameter were spin coated onto the honeycomb cones under optimized conditions [Fig. 1(c)]. A re-growth of un-doped GaN layer was conducted at 1120°C for 120 min, which results in the formation of embedded structures, as shown in Fig. 1(d). Subsequently, a Si-doped n-type GaN was grown at 1120°C for 60 min. After completing the growth of n-type GaN, five period multi-quantum wells (MQWs) of InGaN/GaN pairs for a 460 nm emission were grown at 780°C, and finally a 110 nm thick Mg-doped p-type GaN was grown at 1000°C. After the growth of the LED epitaxial layers, general fabrication and package processes were performed. For comparison, similar device structures without SNSL were also fabricated on planar and SiO₂ mask-patterned sapphire substrates (referred to as conventional flat and SMPSS LEDs, respectively).

3. Results and discussion

Figure 2(a) shows top view scanning electron microscopy (SEM) image of well-aligned periodic honeycomb cones. The honeycomb cones have an opening of about 6 μm in diameter and a depth of 5.5 μm. In addition, the honeycomb cone contains six {10-1-1} facets. We were able to control the size and depth of the honeycomb cones by varying the growth conditions or the size and distribution of SiO₂ dot patterns. These honeycomb cones acted as a basket to confine the SNs. Figure 2(b) shows the cross-section of honeycomb cones that are filled with SNs. It is worth to note that the SNs are stacked as multiple layers in honeycomb cones by employing a simple spin coating method. Figure 2(c) shows top-view SEM image of the re-grown GaN. The re-growth is originated from the top regions of {10-1-1} facets that do not contain any SNs. Moreover, the growth is restricted at the inclined facets of {10-1-1} that are shrouded by the SNs, resulting in the embedded SNSL in honeycomb cones. It can be understood from the inset of Fig. 2(c) that SNs are filled only in the honeycomb cones and the surface of the re-grown GaN layer is highly smooth, signifying the complete coalescence of the layers.

 

Fig. 2 (Color online) SEM images at different stages of SNSL embedded LED growth (a-c): (a) Top view image of the honeycomb cones. (b) cross-sectional view image of SNs stacked in honeycomb cone. (c) top view image of the surface of re-grown GaN. Inset is the cross-sectional view image. (d) I-V characteristics of three different LEDs studied.

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The current-voltage (I-V) characteristics of the LEDs were measured in order to understand the effect of embedded SNs on the device electrical properties. Figure 2(d) shows the typical I-V curves obtained from three different LEDs studied. All the devices had a similar forward voltage (defined at an injection current of 20 mA) of ~3.4 V. This indicates that the introduction of honeycomb cones with SNSL did not adversely affect the electrical performance of the device. It has been reported that the leakage current in the reverse voltage region could increase due to introduction of threading dislocations (TDs) during the epilayer growth [11]. The leakage currents measured at −10 V for conventional, SMPSS, and SNSL embedded LEDs are 5200, 390, and 42 nA, respectively. The low leakage current of SMPSS LED compared with the conventional one could be attributed to the bending of TDs by lateral growth during re-growth stage. However, some TDs can still propagate to the top surface. On the other hand, the leakage current of SNSL embedded LED is nearly 10 times and two orders smaller than the values observed for SMPSS and conventional LEDs, respectively. This result signifies substantial blocking of TDs by the SNSL.

Using a confocal scanning electroluminescence microscopy (CSEM) the microscopic electroluminescence characteristics and the light propagation at SNSL have been investigated. CSEM is an effective experimental tool for analyzing the optical characteristics such as light propagation and local light output. We employed CSEM with a spatial resolution of 200 nm at an injection current of 1 mA to obtain the images. One of the most significant findings of our study is the distribution of light emission from the SNSL. Figure 3(a) shows the three-dimensional CSEM image obtained from the SNSL embedded LED. The spatial distribution of the light emission can be clearly visualized from the variations in color contrast. The image also signifies strong light emission at regions where the SNSL is embedded. A cross-sectional view (x-z axis) of the CSEM image in Fig. 3(b) demonstrates the effect of light scattering and refraction from the SNSL. We observe intense light emission towards the upward direction and a relatively weak light emission in the regions between adjacent honeycomb cones along the x-direction.

 

Fig. 3 (Color online) (a) CSEM image showing spatial three-dimensional EL light emission from embedded SNSL. (b) cross-sectional view (x-z axis scan) of the CSEM image. (c) Poynting vector distribution at the half-wavelength surface away from the GaN/air interface. (d) diffuse reflectance spectra of the LEDs.

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To verify measurement data, simulation model using Opti-finite difference time domain method (FDTD) software package is provided. Three structures with period of 5.52 μm are simulated. The first structure is the conventional flat LED, the second one is formed by uniform SiO₂ dot pattern on sapphire substrate and in the third one, SNSL is embedded in LED structure. The inset of Fig. 3(c) shows the simulation structure of SNSL embedded LED. To deal with finite-size effect and the reduced size of our simulation, we considered two different types of boundary conditions for the simulations. The top and bottom sides of the LEDs are directly attached to a numerically absorbing boundary known as the perfect matched layer. This absorbing boundary is not physical and is introduced only for suppressing the reflection at the unphysical boundary of a computational space. Physically, this corresponds more or less to the case of a LED with a light source confined in this region. Outside of this LED, once again, we introduce a perfect matched layer to block numerical reflections. We can also apply a periodic boundary condition to the left and right sides of LED. This corresponds to an infinite size LED, but with the light sources also periodically identified. This periodic case, however, neglects completely the finite-size effect. Thus, our simulations with two different boundary conditions should reveal complementary features in the study of LED. The calculation of the extracted light is done by computing the normal component of the Poynting vector at the half-wavelength surface away from the GaN/air surface and presented in Fig. 3(c). The Poynting vector of the SMPSS LED is slightly higher than that of the conventional LED due to the embedded SiO₂. On the other hand, the Poynting vector of the SNSL embedded LED is much higher than those of the other LEDs. The relaxation of SNSL also creates relatively lower peaks closer to center and higher at the edge of honeycomb cone as a result of relaxation from neighboring honeycomb cones. As a result, the optical power calculation on the output shows 24% enhancement for the embedded SNSL LED.

Diffuse reflectance spectra were recorded using a UV-VIS-NIR spectrophotometer (JASCO V-570), where the samples were illuminated from the front side and the reflected light was detected under diffuse reflection geometry in order to understand the light scattering effect of embedded SNs. Figure 3(d) shows the reflectance spectra of all the three samples. The spectra reveal an abrupt cutoff at the wavelength of 460 nm, i.e. around the absorption edge of the MQWs in the GaN. In case of SMPSS LED, the reflectance is slightly improved compared with that of conventional LED, whereas for the SNSL embedded LED, a 14% higher reflectance is observed at 460 nm. Also, the reflectance spectra and the simulation results both showed a similar tendency, demonstrating that the embedded SNSL resulted in the enhancement of reflection by changing the direction of the light path. These results envisage that the embedded SNSL might improve the light output power by scattering the emitted photons at SNs.

From the microscopic point of view, Mie scattering theory was applied to explain the scattering mechanism at SNs, because the average size of SNs employed in this study was ~500 nm, which is close to the emission wavelength of the LED. The emitted light can be efficiently scattered from 500 nm silica particles embedded in GaN. The Rayleigh regime is applied at a size parameter of x = 2πr_pn₁/λ <<1, and the Mie regime is applied at x = 2πr_pn₁/λ ≥ 1. It has been reported that Mie scattering at silica particles embedded in a device might play a role in increasing the optical path length [10]. If one considers that the light from active layer propagates to bottom side perpendicularly, then more light will be scattered omnidirectionally in accordance with Mie scattering theory. Once the incident light hits the top surface of SNSL, part of the scattered light would propagate towards the upper direction and the other part would propagate in the horizontal direction to adjacent SNs, where they may undergo a chain of scattering events. The light intensity at the top layer was found to be larger than that at the bottom side, because the intensity of first scattered light is relatively stronger than the intensity of multiply scattered light. This could be in part attributed to the fact that the top layer has a maximum number of SNs compared to any other layers due to the geometric shape of the honeycomb cone. Moreover, part of the multiply scattered light that meets {10-1-1} facet with 62° is refracted to the bottom side due to the difference in refractive indices (n) between the SNs (n ≈ 1.45) and the GaN (n ≈ 2.5). However, the intensity of refracted light is relatively weak as shown in Fig. 3(b). As a result, the light emission towards upward direction is stronger than that at side direction due to multiple Mie scattering at the SNSL and geometric shape of honeycomb cone.

To further validate these results, the far-field radiation patterns from packaged LED chips were measured at 20 mA. The beam profile of the LED was characterized by an OL 770 multichannel spectroradiometer. In Fig. 4(a) we compared the results obtained from the conventional and the SNSL embedded LEDs. It is evident from the figure that the tendency of light propagation is significantly altered in the later case as a result of multiple Mie scattering at the SNSL. The divergent angles (angle of half-maximum emission intensity) measured on the front sides of the conventional and SNSL embedded LEDs are 150° and 128°, respectively. The smaller divergent angle obtained for the SNSL embedded LED indicates that more light is extracted towards the upward direction as compared with conventional LED. This observation corroborates the results discussed earlier.

 

Fig. 4 (Color online) (a) beam profile. (b) the light intensity ratio (I_R) at each angle (I_θ). (c) light output power-current characteristics of the LEDs.

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To analyze the ratio of light intensity at vertical to side direction, the intensity ratio, I_R, was calculated at various angles from −90° to 0°. Here, the I_R, defined as the intensity at each angle (I_θ) per minimum intensity at side direction (I_min) is given as: I_R = I_θ / I_min. We assume that the light intensity at −90° is minimum (I_min). The angle at which light escape to side direction is calculated to be 30°, as shown in the inset of Fig. 4(b). It is observed that the I_R of both devices at side direction has similar tendency. However, in the upward direction (−60° < x < 0°) I_R has rather a very different tendency. For instance, in the case of conventional LED, maximum I_R is observed around −55°. In addition, the intensity at this angle is about 4 times higher than I_min and attains saturation for lower I_θ values in the negative direction. Alternatively, for SNSL embedded LED, I_R increases exponentially with increasing I_θ and the intensity at 0° (vertical direction) is about 10 times higher than I_min. This implies that the light emission along the vertical direction is much stronger in the SNSL embedded LED.

The light output-current (L-I) measurements were carried out using optical detector and detection program (Star Client). Figure 4(c) shows the variations in light output power measured from the top of the LEDs as a function of injection current. As shown in Fig. 4(c), the light output power of the SNSL embedded LED is 2.7 times higher than that of conventional LED at an injection current of 20 mA. This significant enhancement in the light output power could be primarily attributed to the multiple Mie scattering at SNSL. In addition, improvements in crystalline quality of the re-grown GaN may also have contributed to this improved emission efficiency.

4. Summary

In summary, the introduction of embedded honeycomb cones with SNSL led to the increase of optical output power in GaN-based LEDs. The emitted light from the active layer is multiply scattered at SNs and refracted at the interface between SNs and GaN due to the difference in refractive indices. This has been explained on the basis of Mie Scattering theory. Moreover, the ratio of light intensity at vertical to side direction was 2.5 times higher and the divergent angle was 33% smaller for the SNSL embedded LED, compared to that of conventional LED. The light output power of the SNSL embedded LED was enhanced by 2.7 times, as compared with conventional flat LED, at an injection current of 20 mA. These results signify that both the embedded silica nanospheres and the geometric shape of the honeycomb cones are effective in redirecting the light and enhancing the light escaping probability.