Light interaction in sapphire/MgF2/Al triple-layer omnidirectional reflectors in AlGaN-based near ultraviolet light-emitting diodes

This study examined systematically the mechanism of light interaction in the sapphire/MgF2/Al triple-layer omnidirectional reflectors (ODR) and its effects on the light output power in near ultraviolet light emitting diodes (NUV-LEDs) with the ODR. The light output power of NUV-LEDs with the triple-layer ODR structure increased with decreasing surface roughness of the sapphire backside in the ODR. Theoretical modeling of the roughened surface suggests that the dependence of the reflectance of the triple-layer ODR structure on the surface roughness can be attributed mainly to light absorption by the Al nano-structures and the trapping of scattered light in the MgF2 layer. Furthermore, the ray tracing simulation based upon the theoretical modeling showed good agreement with the measured reflectance of the ODR structure in diffuse mode.


Results
The AlGaN/InGaN MQW NUV-LED chips were fabricated on c-plane sapphire substrates, and then the sapphire substrate was thinned to 110 mm by backside grinding and lapping using a range of slurries with different diamond sizes of 1, 3 and 5 mm, respectively, to control the surface roughness of the sapphire backside. In addition, chemical mechanical polishing (CMP) was used to make a mirror-like surface at the backside of the sapphire wafer. Subsequently, MgF 2 (130 nm) and Al (200 nm) layers were deposited conformally on the sapphire backside surface using an e-beam evaporator to form an ODR structure. Finally, the wafer was diced into separate chips by laser-scribing and breakage. Figure 1 shows a schematic diagram of the NUV-LED chip with MgF 2 /Al ODR.
The surface roughness of sapphire backsides prepared by lapping in the slurry with various diamond sizes (1, 3, and 5 mm) and by CMP (see Supplemental Information for the characteristics of interface roughness and MgF 2 ), was examined by AFM and confocal laser scanning. Figure 2 shows AFM images of the sapphire backsides with a scan area 2 3 2 mm 2 . The root mean square (RMS) roughness was 3.3 Å for CMP, and 53.8 Å (Slurry_1 mm), 99.9 Å (Slurry_3 mm), and 160.2 Å (Slurry_5 mm) for slurry sizes of 1, 3, and 5 mm, respectively. Similarly, the confocal laser scanning of sapphire backsides was performed with a scan area of 125 3 125 mm 2 as a function of the slurry sizes. The average roughness (R a ) was 60.0 Å (Slurry_1 mm), 80.0 Å (Slurry_3 mm), and 130.0 Å (Slurry_5 mm) for various slurry sizes. The RMS value is normally higher than that of R a , which is the arithmetic average of the absolute values in the roughness profile ordinate and R a is the effective surface roughness measure commonly adopted in general engineering practice. Therefore, this study employed the value R a from confocal laser scanning in the following work. Figure 3 shows the light output power-current (L-I) curves of GaN-based NUV-LEDs with and without MgF 2 /Al ODR. The light output power of the LEDs with ODR was higher than conventional NUV-LED without ODR. Fig. 3 also shows that the output power of the LEDs with ODR increased with decreasing surface roughness of sapphire with relative enhancements of 21.5% (Slurry_5 mm), 25.5% (Slurry_3 mm), 26.6% (Slurry_1 mm), and 30.9% (CMP), compared to conventional NUV-LED under a 60 mA forward current. It is worthy to note that NUV-LEDs with RMS roughness of 3.3 Å by CMP showed the highest output power (20.6 mW), meanwhile those with RMS roughness of 160.2 Å by slurry size of 5 mm yielded the lowest output power (18.1 mW) under 60 mA forward current among LEDs with ODR structure. These results suggest that the optical output power of GaN-based NUV-LEDs with an ODR structure is influenced significantly by the surface roughness of the sapphire backside.
The reflectance of the MgF 2 /Al ODR structure was measured using a Varian Cary 5000 UV-Vis-NIR through the opposite side of the double-polished sapphire. The integrating sphere system was designed to collect all the diffused photons from a solid surface. Figure 4 shows reflectance of 92.3% (CMP), 76.9% (Slurry_1 mm), 76.3% (Slurry_3 mm), and 73.4% (Slurry_5 mm) at 385 nm in diffuse mode, respectively. These observations agree well with the L-I data trend [Fig. 3] in that the output power of the LEDs and the reflectance of the ODR structure increase with decreasing surface roughness of the sapphire backside. Therefore, the surface roughness of the sapphire backside in the sapphire/MgF 2 /Al ODR structure plays an important role in determining the reflectance of the ODR structure and the light output power of the GaN-based NUV-LEDs.

Discussion
To understand the observed measurements, we conducted theoretical modeling of the roughened surface of sapphire backside to investigate the light interaction in the sapphire/MgF 2 /Al triple-layer ODR. Firstly, the absorption (Q ab ) and scattering efficiency (Q sc ) were calculated to determine the relationship between a single nanoparticle and photon. Secondly, Maxwell-Garnett theory was employed for quantitative analysis in layer-by-layer structures. Lastly, Monte Carlo ray tracing simulation, based upon the results of theoretical modeling, was performed to compare the calculated and measured reflectance of the ODR structure in diffuse mode. In this study, we assumed that the roughened surface of sapphire backside could be considered as a virtual homogeneous layer that is composed of collections of nanoparticles. Normally, the optical and electron energy loss properties of colloids can be modeled reliably by an ordered surface of metal spheres with a filling fraction appropriate to the surface roughness 14 . This would be suitable in an investigation of the optical interaction between a roughened surface and photon. The roughened interfaces of sapphire/MgF 2 and MgF 2 / Al could be configured as a MgF 2 particle layer and an Al particle layer, respectively. The Al metallic nanoparticle (MNP) is an intermediate reflector that enhances the near field and effective scattering cross section.
Before the level of nanoparticle array can be approached, the interaction relationship between a single nanoparticle and photon needs to be handled, since it is reasonable to analyze the nano-particle array based on the extension of the interpretation of single nanoparticle. In the single MNP model, Q ab and Q sc was calculated using Mie's theory, where Q ab and Q sc are the ratios of their respective total cross section to the physical cross section of the particle. Mie's theory is a general theory of light scattering by a spherical particle 15,16 . When the radius r of a particle is much smaller than the wavelength l of light (i.e. 2pr = l), the scattering cross-section of a particle varies with r 6 , while the absorption cross-section varies with r 3 . Therefore, for very small particles, absorption is more important than scattering. In addition, when the radius of MNP is much smaller than the incident wavelength, a localized surface plasmon resonance (LSPR) model should be considered further to interpret the interaction between the photon and MNP 17 . The LSPRs are the collective electron charge oscillations in metallic nanoparticles that are excited by light. They exhibit enhanced scattering and absorption at the resonance wavelength. The LSPR mode depends strongly on the extinction characteristics of the MNP structures, such as the dielectric functions of the metal and surrounding materials, size, shape, and density. Figure 5 shows the calculated Q ab and Q sc of MgF 2 and Al nanoparticles, respectively. The size of R a which generated a major absorption enhancement peak by LSPR mode was approximately 0.07 mm, but it is noteworthy to consider the efficiencies at the tail area with relatively small values. Fig. 5 also shows that absorption and scattering are rarely generated at the interface of sapphire-MgF 2 in the range of the calculated R a values. On the other hand, the absorption and scattering at the MgF 2 -Al interface increased with increasing particle diameter and the main interaction is the absorption induced by LSPR at the tail area. The scattering effect increased slightly over a 0.01 mm particle diameter. These results can be attributed to that absorption and scattering due to the LSPR do not occur www.nature.com/scientificreports SCIENTIFIC REPORTS | 5 : 9717 | DOI: 10.1038/srep09717 in a dielectric particle since plasma oscillation is rarely generated in the dielectric particle, which result in much smaller absorption and scattering for the MgF 2 dielectric particle at the sapphire-MgF 2 interface than the Al metallic particle at the MgF 2 -Al interface, as shown in Fig. 5. This suggests that the absorption and scattering effect at the MgF 2 -Al interface could be related to the light output power of the NUV-LEDs with MgF 2 /Al ODR structures.
Next, the effective refractive indices were calculated based on the effective medium theory (EMT) by Maxwell-Garnett, as extended by Polder and Van Santen to perform quantitative analysis of the optical characteristics [18][19][20][21][22] . The Maxwell Garnett approximation is a widely used method for calculating the bulk dielectric properties of inhomogeneous materials. In the effective medium theory, the inhomogeneous material is assumed to be composed of spherical inclusion particles embedded in a host material, both of which are assumed to be isotropic and to respond linearly to the incident light 22,23 . A 5-layer structure was implemented to obtain a correct interpretation of the absorption and scattering efficiencies. As shown in the inset in     Fig. 6, it was assumed that the sapphire-MgF 2 interface roughness consisted of a MgF 2 bulk layer and MgF 2 particle array, and the MgF 2 -Al interface roughness consisted of an Al bulk layer and Al particle array, which is a good approach for a more correct interpretation of the sapphire-MgF 2 and MgF 2 -Al interface roughness. The approach could be used to define the optical characteristics for virtual layers, such as the MgF 2 particle array and Al particle array. The Maxwell-Garnett formula was considered with a volume filling factor (FF), which is defined as the ratio of the volume of occupied particles to the volume with any thickness and the index of the effective medium layer (FF 5 V particle /V eff ). In addition, the complex optical constants of the virtual layer calculated through EMT were reflected in the Fresnel equations, which were used to define the optical characteristics for each real layer in the simulation. After obtaining the transmittance and reflectance from the Fresnel equation, the extinction coefficient was calculated, after which the extinction coefficient was divided into absorption and scattering. The ratio of scattering and absorption was applied to the ratio obtained from Mie's theory. Eventually, these procedures can reflect the real value in a ray tracing simulation. Figure 6 shows that the efficiency in the 5-layer system is increased tenfold, compared to that in the particle state. In addition, it is shown that as the particle size increases, the scattering and absorption efficiency levels increased with increasing particle size, which is consistent with the results obtained in the case of a single particle model. In Fig. 6, the absorption effect is shown to be the main factor, which generates an approximate nine-fold difference in efficiency, compared to the scattering at R a 5 13 nm and the absorption as a function of R a increased linearly to 20 nm, similar to the case of a single particle model. The scattering efficiency increased slightly near R a ,10 nm, even though the efficiency was much lower than that of absorption.
Finally, ray tracing simulation, based upon the results of theoretical modeling, was performed to compare the calculated and measured reflectance of the ODR. In this study, the Monte Carlo ray-tracing method, which is a representative way of simulating light propagation in LED chips was used to examine the light propagation behavior of sapphire/MgF 2 /Al triple-layer ODR structures. Figure 7 shows that a significant amount of photons can be confined between the sapphire and Al metal layer by a scattering process at the roughened interfaces and be guided in the MgF 2 layer, resulting in the increased absorption of trapped photons by the continuous internal reflection. Note that the amount of internal reflection is not negligible. The increased absorption by internal reflection in the ODR structure will reduce the light extraction efficiency of the LEDs with ODRs. Therefore, the backside surface roughness of sapphire critically influences the light extraction efficiency of LEDs with the ODRs through scattering at the rough interface. Figure 8 presents the calculated and measured reflectance for the sapphire/MgF 2 /Al ODR structure as a function of R a in diffuse mode. As shown in Figs. 5 and 6, the absorption efficiency increased almost linearly with increasing particle size in the single nanoparticle model as well as the 5-layer model, indicating a linear decrease in reflectance with increasing size. On the other hand, the measured reflectance did not decrease linearly with increasing R a . This discrepancy could be solved by considering the volume filling factor (FF) in the Maxwell-Garnett formula mentioned above. The calculated reflectance by ray tracing with the consideration of the FF showed good agreement with the measured reflectance in diffuse mode, as shown in Fig. 8. The calculated and measured reflectance decreased nonlinearly with increasing R a . The nonlinear decrease in reflectance with R a could be explained as follows. The nonlinearity can be divided into two sections; section A with a FF-dependent zone of R a ranging from 0 to 9 nm, which shows a rapid decrease in the reflectance with R a , and section B with a size-dependent zone in the range of R a over 9 nm. The FF value of section A was larger than that of section B, which is because the FF value increases with decreasing R a . Although the individual particle size is small in section A, the density (FF) is increased drastically, so the absorption effect is increased. The FF value of section B is relatively constant, but the individual particle size is increased, which means that the scattering effect plays an    important role in section B. As a result, absorption and scattering effects occur at the same time in section B. Therefore, the optical output power of NUV-LEDs with MgF 2 /Al ODR structures decrease gradually with increasing sapphire backside roughness, which was attributed to the absorption effect induced by LSPR and photon confinement in MgF 2 by the scattering effect.
In summary, we have investigated the mechanism of light interaction in the sapphire/MgF 2 /Al triple-layer ODR and its effects on the light output power in NUV-LEDs with the ODR structures deposited on the back-side surface of sapphire substrates with various surface roughness. The light output power of the NUV-LED with ODR deposited on the mirror-like surface of sapphire was improved by 30.9% compared to the conventional LED without ODR. The surface roughness of the sapphire backside in the MgF 2 /Al ODR structure played an important role in determining the reflectance of the ODR structure and the light output power of the LEDs. The dependence of the reflectance of the ODR structure on the surface roughness was attributed mainly to the absorption effect induced by LSPR and photon confinement in MgF 2 due to the scattering effect.

Methods
Fabrication. The NUV LED structures were grown on c-plane sapphire substrates by metal-organic chemical vapor deposition. Ammonia, trimethylgallium, trimethylaluminium, and trimethylindium were used as the precursors and biscyclopen-tadienilmagnesium and silane were used as the dopants. The epitaxial NUV-LED structure consisted of a low-temperature 30-nm-thick GaN buffer layer, 4-mm-thick n-type GaN layer, six pairs of 6-nm-thick Al 0.1 GaN/3-nm-thick In 0.03 GaN multiple quantum wells, a 25-nm-thick p-type Al 0.25 GaN electronblocking-layer to prevent carrier leakage from the active region, and a 0.2-mm-thick ptype GaN layer. The InGaN active layer was grown at 820uC under 200 Torr with a growth rate of 1 nm/min. The thicknesses and compositions in the AlGaN/InGaN MQWs were determined by x-ray diffraction (XRD) using a Cu K a x-ray source. An in-situ optical reflectometer was employed to monitor the morphological evolution and growth rates of epitaxial layers. After growth, thermal annealing was performed for 15 min at 725uC in a nitrogen atmosphere to obtain p-type conductivity of Mgdoped GaN. The AlGaN/InGaN MQW NUV-LED chips were then fabricated. All samples were immersed into H 2 SO 4 :H 2 O 2 solution for 10 min to remove metallic contaminants on the surface and then rinsed in running deionized water. The mesa structure for the 700 3 300 mm 2 chip was formed partially until the n-GaN contact layer was exposed using an inductively coupled plasma etching system in conjunction with Cl 2 and a standard photolithography process. The thin film of indium-tin-oxide for the p-ohmic metal was deposited as a transparent conducting layer by sputter deposition and alloyed in N 2 ambient for 60 s at 500uC to reduce the contact resistance. Wet etch of ITO was achieved by using HCl aqueous solution with photoresist as an etch mask. Subsequently, Ti/Al/Ni/Au films were deposited using an electron-beam evaporator for use as the p-and n-type contact metals, and a 0.12-mmthick SiO 2 layer was deposited by plasma enhanced chemical vapor deposition to passivate the mesa side wall. The sapphire substrate was thinned to 110 mm by backside grinding and lapping using a range of slurries with different diamond sizes of 1, 3 and 5 mm, respectively, to control the surface roughness of the sapphire backside.
In addition, chemical mechanical polishing (CMP) was used to make a mirror-like surface at the backside of the sapphire wafer after grinding and lapping to about 120 mm. MgF 2 (130 nm) and Al (200 nm) layers were subsequently deposited on the sapphire backside surface using an e-beam evaporator at room temperature to form an ODR structure. Finally, the wafer was diced into separate chips by laser-scribing and breakage.
Characterization. The reflectance on the sapphire/MgF 2 /Al triple-layer ODR structure was measured using a Varian Cary 5000 UV-Vis-NIR system. A Xenon lamp covering the entire wavelength range of 190-1100 nm was used as the incident light source. The current-voltage characteristics of the NUV-LEDs were analyzed at room temperature using a Keithley 2601A parameter analyzer, and the optical output power characteristics of the NUV-LEDs with FR4-PCB were analyzed using an integrated sphere with a calibrated power meter. The surface roughness of sapphire backsides prepared by lapping in the slurry with various diamond sizes (1, 3, and 5 mm) and by CMP, was examined by AFM and confocal laser scanning.