Performance of InGaN/GaN Light Emitting Diodes with n-GaN Layer Embedded with SiO2 Nano-Particles

We demonstrate high-performance InGaN/GaN blue light emitting diodes (LEDs) embedded with an air-void layer produced by a dry-etch of nano-pillars in an n-GaN layer grown on patterned sapphire substrate (PSS), filling the space between nano-pillars with SiO2 nano-particles (NPs) and subsequent epitaxial overgrowth. The structure exhibits enhanced output power compared to similarly grown reference conventional LED without the air-void layer. This change in growth procedure contributes to the increase of internal quantum efficiency (IQE) and light extraction efficiency (LEE) resulting in a 13.5% increase of light output. LEE is 2 times more affected than IQE in the modified structure. Simulation demonstrates that the main effect causing the LEE changes is due to the emitted light being confined within the upper space above the air-void layer and thus enhancing the light scattering by the SiO2 NPs and preferential light via front surface.


Introduction
Light emitting diodes (LEDs) and laser diodes are widely used optoelectronic devices, but many important problems still require solving. One of them is the strong lattice-mismatch during GaN growth on alien substrates [1,2]. In the case of the growth on conventional sapphire substrate, the threading dislocation (TD) density is as high as 10 8 -10 10 cm −2 [3]. As an option to decrease the TD density and increase the internal quantum efficiency (IQE), epitaxial lateral overgrowth (ELO) has been studied [4]. Another inherent problem of GaN-based LEDs is the low light extraction efficiency (LEE) due to the relatively low angle of total internal reflection (TIR) caused by the large difference between the refractive indices of air and GaN. This limits the extraction of light generated from the multi quantum well (MQW) of LEDs so that only a small portion of the light escapes towards the outside [5]. To enhance LEE, air void structures embedded in GaN-based LEDs have been studied, which is also useful to increase IQE and thus the external quantum efficiency (EQE) as a result [6][7][8].
IQE in InGaN/GaN blue LEDs has been remarkably improved and has been steadily approaching 100%, so that efforts on further improvement of EQE studies have to be focused on enhancing the LEE [9]. As an approach applicable to mass production, epoxy or silicone encapsulating has been preferred because the process is easy and simple, and readily meets the yield and

Experiment
In experiments, our suggested SiO 2 NPs embedded PSS LEDs were compared with reference of a conventional PSS LED structure. First, a template of unintentionally doped u-GaN grown on PSS was prepared. A schematic illustration of the InGaN/GaN LED embedded with SiO 2 NPs and process thereof are shown in Figure 1. With metal organic chemical vapor deposition (MOCVD), 3-µm-thick undoped GaN (u-GaN) films were grown on c-plane PSS in conventional way. To make nano-pillars in GaN film, a 100-nm-thick SiO 2 layer was deposited as an interlayer on top of the u-GaN surface by plasma-enhanced chemical vapor deposition. With e-beam evaporation, a 10-nm-thick Ni layer was deposited on the SiO 2 interlayer. To form the self-assembled Ni metal clusters, the Ni/SiO 2 /GaN samples were treated with rapid thermal annealing (RTA) under N 2 flow at 850 • C for 1 min. Inductively coupled plasma (ICP) etching with the gases of O 2 and CF 4 was applied to pattern the SiO 2 layer using the Ni nano-dots as an etch mask and then, the u-GaN was further etched down to 1.5 µm with Cl 2 gas [22]. After that, the Ni nano-dots on SiO 2 , remaining on the tops of nano-pillars, were removed by buffered oxide etchant. As a result, a GaN template with vertically arranged nano-pillars was prepared. On the nano-pillar GaN template, the SiO 2 NPs were deposited by spin coating (5000 rpm, 30 s). We used commercial colloidal SiO 2 NPs with 100 nm diameter. This SiO 2 embedded nano-pillar template was used for ELO overgrowth. The u-GaN templates grown on PSS without the nano-pillars (reference) were loaded at the same time. After well-coalesced GaN seed layer was formed on top of the nano-pillars, a Si-doped 3-µm-thick n-GaN layer, a multiquantum-well (MQW) region, and a 200-nm-thick Mg-doped p-GaN top contact layer were grown in sequence. The MQW region consisted of five undoped InGaN (2 nm)/GaN (10 nm) quantum wells.  The cross-section images of the SiO 2 NP LED were obtained using a field emission scanning electron microscopy (FE-SEM). Room temperature photoluminescence (PL) mapping measurements were carried out with a 325 nm line of a 25 mW He-Cd laser as an excitation source. The current-voltage (I-V) and optical output (L-I) characteristics were measured by means of an on-wafer probing with indium contacts. The results were compared to those obtained from the reference sample-the growth conditions for both types of samples were the same, but for the fact of the presence of the nano-pillar region embedded with SiO 2 NPs in the modified structure.
The experimentally observed performance increase is compared with the simulation result. Because the structure of this experiment and PSS are intended to increase LEE with different geometries, the simulation is planned to understand how to further increase the efficiency, which means geometrical differences are compatible and complementary to each other even when the functions are overlapped. Detailed conditions for the simulation are described in Appendix A.

Experimental Results
As a structure to be placed away from PSS within the outer surface of LEDs, the GaN nano-pillars and the air-void surrounding the nano-pillars filled with SiO 2 NPs were fabricated as described above (Figure 1). To confirm the formation of nano-pillars and air-voids after regrowth, the cross-sectional images were obtained using FE-SEM. Figure 2a,b shows that the air-voids surrounding the nano-pillars were filled with the SiO 2 NPs. With this configuration, GaN overgrowth begins on the upper part of each nano-pillar. The overgrowth expands laterally crossing the air-void and merges with adjacent laterally overgrown regions starting from neighboring nano-pillars. Figure 2c,d shows that GaN layer is formed on the top of the air-void and nano-pillars. This picture means that while the upper space of the air-void of Figure 2a,b was covered with GaN overgrowth, SiO 2 NPs contributed to keep the shape and size of the air-void. As a result, the density of threading dislocations was diminished as shown in Appendix B. SiO 2 NP LED shows 4 times lower TD density than that of the reference, which is a considerable improvement of the crystalline quality.   Figure 3 shows the performances of SiO2 NP LED compared to the reference LED. When 20 mA current is injected into the SiO2 NP LED and the reference LED, forward voltage is 2.84 V and 2.97 V, respectively ( Figure 3a). The decrease of the forward voltage is considered as the result of the series resistance decrease caused by the TD decrease. This decrease in TD density comes in addition to the decrease of TD density produced by growth on the PSS which presents both in the reference and modified LED structures. From this perspective, the nano-pillar layer overcomes disadvantages of  Figure 3 shows the performances of SiO 2 NP LED compared to the reference LED. When 20 mA current is injected into the SiO 2 NP LED and the reference LED, forward voltage is 2.84 V and 2.97 V, respectively (Figure 3a). The decrease of the forward voltage is considered as the result of the series resistance decrease caused by the TD decrease. This decrease in TD density comes in addition to the decrease of TD density produced by growth on the PSS which presents both in the reference and modified LED structures. From this perspective, the nano-pillar layer overcomes disadvantages of dislocation density control in PSS, resulting in better performance of the forward voltage. In relation to LEE, Figure 3b shows that the light output of the SiO 2 NP LED is 13.5% higher than that of the reference LED. dislocation density control in PSS, resulting in better performance of the forward voltage. In relation to LEE, Figure 3b shows that the light output of the SiO2 NP LED is 13.5% higher than that of the reference LED.  Table 1 shows that the IQE of the SiO2 NP LED measured at 100 mA was 4.5% higher than that of the reference LED. The ABC model is well known to explain the rate of total recombination in LEDs. A, B, and C stands for Shockley-Read, radiative, and Auger recombination coefficient, respectively. The IQE was calculated with the ABC model under assumptions that the A and B coefficients were a function of current I, and C was much smaller than 10 −30 (cm 6 ·s −1 ) [23]. In the ABC model, the A coefficient is related to non-radiative recombination which describes the efficiency decrease due to non-radiative recombination on localized states. These defect levels can be due to localized states on dislocations and also to deep traps associated with point defects. However, in case of InGaN/GaN MQW LED, IQE increase was not proportional to TD decrease and localized. In composition fluctuation also affected the efficiency [24]. In addition, it has been observed that the density of deep Shockley-Hall-Read traps in modified structures was measurably lower than in reference structures [25]. Experiments with electron irradiation indicate that the increase in concentration of some of the detected deep traps correlated with the decrease of the EQE of irradiated LEDs [26].     Table 1 shows that the IQE of the SiO 2 NP LED measured at 100 mA was 4.5% higher than that of the reference LED. The ABC model is well known to explain the rate of total recombination in LEDs. A, B, and C stands for Shockley-Read, radiative, and Auger recombination coefficient, respectively. The IQE was calculated with the ABC model under assumptions that the A and B coefficients were a function of current I, and C was much smaller than 10 −30 (cm 6 ·s −1 ) [23]. In the ABC model, the A coefficient is related to non-radiative recombination which describes the efficiency decrease due to non-radiative recombination on localized states. These defect levels can be due to localized states on dislocations and also to deep traps associated with point defects. However, in case of InGaN/GaN MQW LED, IQE increase was not proportional to TD decrease and localized. In composition fluctuation also affected the efficiency [24]. In addition, it has been observed that the density of deep Shockley-Hall-Read traps in modified structures was measurably lower than in reference structures [25]. Experiments with electron irradiation indicate that the increase in concentration of some of the detected deep traps correlated with the decrease of the EQE of irradiated LEDs [26].

Simulation and Discussion
In the experiment, the air-void surrounding nano-pillars, the air-gap among SiO 2 NPs, and SiO 2 NPs themselves in the nano-pillar layer were designed to act as scattering centers together. To maximize light extraction performance, it is required to optimize conditions including the periodicity of the GaN pillars, the radius of the pillars, and the radius of SiO 2 spheres of the structure demonstrated in this paper. As a basic consideration, to increase LEE toward the top surface, air-voids between the nano-pillars can be advantageous in terms of improved scattering than air-voids filled with SiO 2 NPs because the refractive index gap between GaN and air is bigger than the one between GaN and SiO 2 , but only if the air-voids are as effective in ELO suppression of dislocation density as the voids filled with SiO 2 (Appendix C). However, this is not the only reason to adopt air to act as a scattering center. There was a case of jointly using air and SiO 2 at the same time that demonstrated effective light output enhancement with SiO 2 nano-pattern layer which was placed over the air-void layer [27].
To understand a mechanism of LEE increase in the experiment, we numerically investigated the four types of LED structures by full three-dimensional (3-D) finite-difference time-domain (FDTD) method. The schematic structures for FDTD simulation are shown in the left of each four groups in Figure 4b; Type0 (conventional LED on CSS); Type1 (conventional LED on PSS, reference LED in the experiment); Type2 (SiO 2 NP LED on CSS); Type3 (SiO 2 NP LED on PSS in the experiment).

Simulation and Discussion
In the experiment, the air-void surrounding nano-pillars, the air-gap among SiO2 NPs, and SiO2 NPs themselves in the nano-pillar layer were designed to act as scattering centers together. To maximize light extraction performance, it is required to optimize conditions including the periodicity of the GaN pillars, the radius of the pillars, and the radius of SiO2 spheres of the structure demonstrated in this paper. As a basic consideration, to increase LEE toward the top surface, air-voids between the nano-pillars can be advantageous in terms of improved scattering than air-voids filled with SiO2 NPs because the refractive index gap between GaN and air is bigger than the one between GaN and SiO2, but only if the air-voids are as effective in ELO suppression of dislocation density as the voids filled with SiO2 (Appendix C). However, this is not the only reason to adopt air to act as a scattering center. There was a case of jointly using air and SiO2 at the same time that demonstrated effective light output enhancement with SiO2 nano-pattern layer which was placed over the air-void layer [27].
To understand a mechanism of LEE increase in the experiment, we numerically investigated the four types of LED structures by full three-dimensional (3-D) finite-difference time-domain (FDTD) method. The schematic structures for FDTD simulation are shown in the left of each four groups in Figure 4b; Type0 (conventional LED on CSS); Type1 (conventional LED on PSS, reference LED in the experiment); Type2 (SiO2 NP LED on CSS); Type3 (SiO2 NP LED on PSS in the experiment).  Figure 4a shows the top and bottom direction LEE, respectively, as a function of time after source excitations. In the case of the top direction LEE, the SiO2 NP LED on PSS shows the highest LEE during most of the time. In contrast, in the case of the bottom direction LEE, at initial time, the LEE of the conventional LED on PSS is higher than that of the SiO2 NP LED on PSS. However, the LEE of SiO2 NP LED on PSS shows the highest LEE after 0.7 ps. Figure 4b-e show the vertical cut-views of intensity distribution of the electric field at different times after source excitations in four different LEDs to illustrate the LEE increase mechanism of the experiment. According to Figure  4a, the top emission of Type3 is 10% higher than that of Type1 at the beginning and then converges to a level similar to Type1 later. It is considered that the increase at the beginning of Type3 is due to the structure playing two roles of confining and scattering photons within the upper volume above the nano-pillars. Photons of Type3 exist densely within about half size volume of Type1, which  Figure 4a shows the top and bottom direction LEE, respectively, as a function of time after source excitations. In the case of the top direction LEE, the SiO 2 NP LED on PSS shows the highest LEE during most of the time. In contrast, in the case of the bottom direction LEE, at initial time, the LEE of the conventional LED on PSS is higher than that of the SiO 2 NP LED on PSS. However, the LEE of SiO 2 NP LED on PSS shows the highest LEE after 0.7 ps. Figure 4b-e show the vertical cut-views of intensity distribution of the electric field at different times after source excitations in four different LEDs to illustrate the LEE increase mechanism of the experiment. According to Figure 4a, the top emission of Type3 is 10% higher than that of Type1 at the beginning and then converges to a level similar to Type1 later. It is considered that the increase at the beginning of Type3 is due to the structure playing two roles of confining and scattering photons within the upper volume above the nano-pillars. Photons of Type3 exist densely within about half size volume of Type1, which raises probability of scattering at the top of the nano-pillar layer and increases top emission. This analysis is matched with the simulation results shown in Figure 4b,e. It is worth noting that absorption of the materials including MQW was not considered in the simulation, therefore, the LEE might be saturated earlier than the simulation results. According to the field intensity distribution of Type3 at 3 ps in Figure 4e, the amount of photons in the volume below the nano-pillar layer becomes smaller than that in the volume above the nano-pillar layer, which leads us to conclude that light extraction toward the backside would decrease because the layer works as a light barrier. In this case, PSS on the bottom helps to increase light extraction toward the backside because the patterns of PSS work as textured surface, and sapphire itself functions as encapsulating layer with the refractive index 1.8 between GaN (2.5) and Air (1).

Conclusions
This study was intended to build a LED structure to achieve high efficiency considering encapsulation. The LEDs in this experiment adopted nano-pillars and an air-void filled with SiO 2 NPs built in the GaN layer grown on the PSS within LEDs. The experimental results showed the increase of 13.5% light output with the increase of IQE. The simulation showed the nano-pillar layer working as a barrier to confine photons upwardly above the nano-pillar layer and also a reflector to scatter the crowded photons. The mechanism consisting of the two functions increased the light extraction efficiency to the front side.

Conflicts of Interest:
The authors declare no conflict of interest.

Appendix A. 3-D FDTD Simulation Conditions
In 3-D FDTD simulation, the radius of the half sphere of PSS and its periodicity was fixed at 2 µm and 4.5 µm, respectively. Here, we assumed that the nano-pillars arranged periodically with the hexagonal lattice. According to the FE-SEM images as shown in Figure 2, the radius of the nano-pillar was 100 nm and the periodicity and the height of the pillar was set as 300 nm and 1 µm, respectively. Also, we assumed that the SiO 2 spheres with the 50 nm radius were closely packed and filled in the air-void between the nano-pillars. The volume ratio of the materials in the nano-pillar layer is 57:31:68 (air:GaN:SiO 2 ). The total thickness of the GaN layer including the nano-pillar was fixed at 12.1 µm and the center of the 1 µm thick nano-pillar was located at 5.6 µm from the top surface. In order to consider the limited computational memory, the lateral size of the total calculation domain is limited by 4.5 µm × 4.5 µm, the sapphire thickness was set as 2.5 µm. In consideration of the size of the fabricated sample, the periodic boundary conditions were used in the horizontal direction, and the perfectly matched layer was used as an absorbing layer in the vertical direction. The refractive indices of the GaN, SiO 2 , and sapphire were set as 2.5, 1.5, and 1.8, respectively. In order to consider the c-plane sapphire substrate, the 100 E x and E y dipole sources (l = 460 nm ± 30 nm) were generated at 100 nm from the top surface with random phase and position. The light extraction efficiency was obtained by dividing the output power flux toward top or bottom with the total dipole radiation power.