1. Introduction

III-nitride based light-emitting diodes (LEDs) have become a widely adopted technology for lighting and displays due to their ever-increasing luminosity and efficiency. Current R&D is focused on micro-LED devices for near-eye and mobile operation [1,2], and on improving the quality of longer wavelength (green, amber, red) emission [3,4]. Towards these goals, homoepitaxy on free-standing GaN substrates has emerged as a promising technique with potential to radically accelerate progress in the field [5]. Moving away from foreign substrates (sapphire, silicon carbide, silicon) eliminates large lattice mismatch at the substrate growth interface, improving crystal quality, and expands the design space of LEDs by enabling novel device designs and packaging schemes [6,7]. Moreover, growth on nonpolar or semipolar substrates can reduce the quantum-confined Stark effect [8] and efficiency droop [9,10], as well as enable direct polarized light emission [11–13]. Adopting this technology, however, requires reconsideration of light extraction strategies currently employed in today’s LEDs.

Light extraction, largely controlled by Fresnel losses [14], is a major determinant of the overall efficiency of an LED. Large index contrast between the GaN device (n ~2.5) and its surroundings (air or silicone encapsulant) results in a narrow escape cone, with critical angles from 24° (air) to 38° (silicone) from normal, above which, the majority of light is trapped by total internal reflection (TIR). Conventional sapphire-based InGaN/GaN LEDs solve the extraction problem by using patterned sapphire substrates. Thin-film devices, where the substrate has been removed, typically outcouple through the nitrogen face (backside) of the device, which can be patterned using the well-known photoelectrochemical (PEC) wet etch technique [15], or by other lithographic means. An alternative approach is to pattern the gallium face (topside) of the device with graded-index (GRIN) nanopillar-, moth-eye-, or photonic band gap (PBG)-like structures using optical, nanosphere, or nanoimprint lithography and subsequent etching [16–22]. For example, Choi et al. reported a two-fold enhancement in photoluminescence (PL) compared to a flat surface by exploiting GRIN effects and strong coupling of guided modes generated by thin-film TIR (Fig. 1(a)) with the nanostructured interface [18], and Matioli et al. reported an extraction efficiency of 94% by outcoupling through an embedded air-gap photonic crystal [21]. Although effective for photoexcited devices, topside patterning is not technologically feasible for electrically pumped LEDs because (i) a topside contact cannot easily be applied to a nano- or micro-scale patterned surface; (ii) applying a remote p-contact far away from the patterned area leads to current spreading problems [16]; (iii) etching patterns into, or close to, the active InGaN/GaN multiple-quantum-well (MQW) layer induces non-radiative defects that decrease light output [23]; and (iv) the pattern must be very shallow (i.e., the p-GaN layer above the MQWs is usually < 300 nm), limiting the aspect ratio of GRIN features—and the types of light-matter interactions—that can be manipulated without etching into the active layer.

 

Fig. 1 Schematic views of light rays propagating through (a) a thin-film sapphire/GaN LED and (b) a backside micro-structured free-standing GaN/GaN LED. In (a), thin-film TIR creates guided modes strongly coupled to the device topside. In (b), TIR modes are delocalized throughout the bulk chip, and backside outcoupling causes forward and reverse specular and diffuse (dashed) scattering. (c) SEM image of silica colloidal crystal mask and process flow to create moth-eye-like features on the backside outcoupling surface of the LED chip.

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For homoepitaxially grown volumetric devices (i.e., when the native substrate is retained), the utility of topside patterning is further diminished by weak coupling of guided modes—now delocalized across hundreds of microns into the substrate—with the structured interface (Fig. 1(b)). These devices must therefore rely on surface roughening and chip shaping to randomize light trajectories and break the TIR condition [7]. While PEC etching is a candidate for structuring these devices, it suffers from reproducibility issues [24], pattern geometry cannot be freely optimized, and it is known to attack essential fabrication components such as metal contacts, backside reflector layers, and mounting wax. Furthermore, PEC roughening is highly selective to the nitrogen-polar c-plane and does not work with semipolar and nonpolar device orientations [25,26]. Other backside surface roughening techniques, involving contact lithography plus dry etching [27], have been proposed for semipolar LEDs, but these methods introduce significant additional process complexity and cost, as well as reproducibility and scaling issues.

In this work, we demonstrate high efficiency light extraction (4.8-fold total enhancement and up to 9-fold at normal incidence, relative to a flat surface) from InGaN/GaN MQW structures grown on semipolar GaN substrates with moth-eye-like backside surface structuring produced by a facile and scalable Langmuir-Blodgett colloidal lithography process. The resulting PL enhancement is comparable to that obtained in polar GaN devices roughened by state-of-the-art PEC etching. We optimize this enhancement through systematic performance analysis of structuring across multiple length scales, including the graded-index, near-field, and refraction-limited regimes, made possible by modifying the backside outcoupling interface of the device. Because of its simplicity, range of optical control, and wide substrate compatibility, the colloidal lithography technique is a viable alternative to existing commercial processes and a future pathway for enhanced extraction engineering in free-standing polar, nonpolar, and semipolar III-nitride LEDs.

2. Experiment

InGaN/GaN samples were homoepitaxially grown by atmospheric pressure metal organic chemical vapor deposition (MOCVD) on free-standing semipolar $(20\overline{2}1)$ and c-plane GaN substrates provided by Mitsubishi Chemical Company (MCC) and Sciocs Company Limited, respectively. Epitaxial structures consisted of a 1 μm n-type GaN:Si layer, an unintentionally doped (UID) five-period MQW active region, and a 30 nm UID GaN capping layer. The back surface of each sample was polished using 3 μm polycrystalline diamond slurry to an optically smooth finish.

Silica colloids (d = 170, 310, 960, 2530 nm; Bangs Laboratories, synthesized using a modified, semi-batch Stöber process) were functionalized with allyltrimethoxysilane (ATMS, Sigma-Aldrich, >98%) in acidic ethanol, cured overnight in a vacuum oven (343 K, 8 h), and redispersed in 1:3 ethanol:chloroform. The colloidal mask was then deposited on the polished back surface of the sample by a Langmuir-Blodgett dip-coating process described elsewhere [28], leaving behind a hexagonally close-packed monolayer of silica spheres (Fig. 1(c)). The masked samples were then dry etched in an inductively coupled plasma reactive ion etcher (Panasonic E640 ICP-RIE) using Cl₂/N₂ (22.5/7.5 sccm) with 500 W ICP power and 300 W bias at 0.2 Pa, with the colloidal layer acting as a hard mask. The duration of the dry etch was scaled with the diameter of the silica colloids and etching proceeded until the masks were fully removed; vertical GaN structures with angled sidewalls resulted due to shrinking of the mask during Cl₂/N₂ etching (Fig. 1(c)). For comparison, c-plane samples were also grown and polished to the same specification as previously described, then roughened using a PEC wet etch. Samples were immersed in 2.2 M KOH and illuminated using a mercury arc lamp (750 W) for 15 minutes.

Angle-resolved, far-field PL spectra were collected at room temperature two times for each sample: first, with an optically smooth backside, and second, with a roughened backside. A 266 nm Q-switched Nd:YAG pulsed laser (1 mm spot size) was used to optically excite the quantum wells (through the GaN capping layer) at 8° incidence from the sample normal as the sample was rotated (azimuthally) about its normal at 3 Hz. Since the excitation source energy was well above the bandgap of GaN, pump light was fully absorbed in the first pass through the sample, eliminating any pump light recycling effects due to reflection. PL emission was collected at various angles (θ) from 0° to 90° in 2° increments with a 1 mm core optical fiber mounted to an optical goniometer system; light from the fiber was then directed to a UV-Vis spectrometer (Ocean Optics USB2000+) to record a full PL spectrum at each angle. The spectral intensity (I) of each angular (θ) scan was integrated from λ = 375–550 nm for each of the structured and unstructured (or polished) cases. An angle-resolved enhancement factor $EF(\theta )$ was calculated for each sample by comparing the structured $I_s(\theta )$ and polished $I_p(\theta )$ integrated intensities: $EF(\theta )=I_s(\theta )/ I_p(\theta )$.

3. Results and discussion

SEM images of the plasma-etched surface structures in GaN are presented in Figs. 2(a)–(c). The sidewall angle of conical features was controlled primarily by the etch selectivity of GaN to SiO₂. As the hard mask was etched, more of the underlying GaN substrate was exposed and subjected to the dry etch, creating a semi-periodic, two-dimensional array of hexagonally close-packed conical structures with aspect ratios of ~3:1. The chosen etch chemistry gave an etch selectivity of 6:1 GaN:SiO₂ and a sidewall angle of approximately 75°. To emphasize the topography that was obtained, the images in Figs. 2(a)–(c) were recorded from areas of limited structured surface coverage near the edge of each sample. Surface coverage and pattern uniformity for the overwhelming majority of each sample were nearly 100%. Defects in the pattern were predominantly grain boundaries between rotated colloidal crystal mosaics, which are in fact beneficial for light extraction, as they act as additional scattering sites to aid in breaking the TIR condition.

 

Fig. 2 (a-c) SEM images of moth-eye-like surface structures in GaN realized using colloidal lithography via Langmuir-Blodgett dip-coating and plasma dry etching; initial silica mask sizes were (a) 170 nm, (b) 960 nm, and (c) 2530 nm. (d) SEM image of photoelectrochemically (PEC) etched c-plane GaN nitrogen face using KOH.

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Figure 2(d) shows PEC wet etching results on the nitrogen face of a c-plane GaN sample. The crystallographic pyramids formed were bounded by stable $\left\{10\overline{1}\overline{1}\right\}$ facets of the GaN crystal, having a sidewall angle of ~45° and a base diameter from 2 to 5 μm [29]. In general, the reproducibility of this etch technique could not be well controlled. Various surface pre-treatments were attempted before an acceptable amount of surface coverage and feature uniformity could be achieved, but subsequent trials using identical conditions often yielded a range of pyramid sizes and coverage. Furthermore, while the surface coverage of pyramids using PEC was acceptable, it could not match the 100% coverage achieved with colloidal lithography.

Representative angle-resolved, integrated PL data (d = 170 nm, 2530 nm) for the polished and structured InGaN/GaN samples are given in Fig. 3(a), with the extraction enhancement factor for each surface structure given in Fig. 3(b). The extraction enhancement for samples patterned by colloidal lithography improved as the feature pitch increased from 170 nm to 2530 nm. This trend is explained by considering the prevailing scattering optics for each case. For an unstructured interface, the majority of light incident beyond the escape cone (θ > θ_crit) is specularly reflected back into the chip. This creates guided modes that are eventually absorbed by high-index material. For a structured interface, scattering mechanisms emerge that disrupt these guided modes, break TIR, and therefore improve the extraction efficiency of the device.

 

Fig. 3 (a) Polar plot of integrated (λ = 375-550 nm) total PL emission from five-period InGaN/GaN multiple-quantum well (MQW) structures on GaN substrates roughened using 170 nm and 2530 nm silica colloids. Integrated PL emission for a polished reference surface and for an ideal Lambertian diffuser are also shown for comparison. (b) Polar plot of enhancement in PL extraction from MQW devices with roughened GaN-air interfaces, normalized by the emission from a flat GaN device surface. MQWs were excited using 266 nm light at 8° incidence from normal, and curve annotations represent the initial silica colloid size (e.g., d = 170, 310, etc. nm) used as the etch mask.

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Comparison of the structured far-field PL for d = 170 and 2530 nm masks with an ideal Lambertian diffuser (Fig. 3(a)) indicates that the scattering strength of the interface depends strongly on the interface geometry. For structures where d / λ >> 1, specular and diffuse scattering occur, significantly improving extraction of light outside the escape cone. Diffractive effects from the two-dimensional, semi-periodic surface grating also emerge at this length scale, although this enhancement is secondary. For d / λ ~1, the scattering strength of the interface decreases and diffractive effects are eliminated, thereby decreasing the transmission of incident light beyond the escape cone. For d / λ << 1, the scattering strength approaches that of a planar interface, and Fresnel optics dominate. While specular reflections for TIR are largely conserved, diffuse scattering processes enhance extraction relative to the unstructured case. Additionally, in this long-wavelength limit, the surface structuring creates a graded index (GRIN) of refraction (i.e., the moth eye effect [30]), which greatly reduces Fresnel loss at the interface. Because TIR is preserved by the absence of scattering phenomenon, the GRIN interface is only effective at increasing transmission of guided modes incident within the escape cone. Surface structuring at this length scale, in general, has limited utility for isotropic emitters such as nitride LEDs.

The PEC etched sample had the highest overall extraction enhancement of all structures explored, although the largest colloidal structuring (d = 2530 nm) exhibited near-comparable performance. The effectiveness of these largest features relative to smaller ones underscores the advantage of backside over topside roughening for electrically pumped devices. Patterns in the refractive limit (d >> λ) are possible only on the backside of the device, where there is freedom to form microscale features without compromising electrical and optical performance. In contrast, the topside outcoupling surface is limited laterally by the requirement to form a large-area p-contact and vertically by epitaxial proximity of the active layers to the chip surface. Additionally, the trend in how size affects performance further demonstrates the ineffectiveness of evanescent coupling techniques—such as those commonly implemented on the topside of thin-film LEDs—for non-thin-film LEDs, since guided modes overlap weakly with the outcoupling interface. These observations call for continued exploration of the design space of colloidal structuring, including optimization of sidewall angle through modification of etch parameters and extension to larger silica masks. Further investigation is expected to yield structures that match or exceed the performance of state-of-the-art PEC roughening, the latter being ineffective on semipolar GaN-based devices.

4. Summary

We have demonstrated improved light extraction in III-nitride light-emitting structures using a facile approach for creating nano- and micro-structured backside surfaces that enhance outcoupling by breaking the TIR condition via increased diffuse scattering and diffractive effects. This colloidal lithography technique, involving Langmuir-Blodgett deposition and plasma etching, is highly tunable across multiple length scales and exhibits high reproducibility and surface coverage. Utilization of the device backside as the primary outcoupling interface presents a technologically feasible approach for fabricating electrically activated devices, by avoiding the complications presented by topside patterning. An overall PL extraction enhancement of 4.8-fold (angular average), with peak extraction enhancement of 9-fold at normal incidence, was shown using a 2530 nm surface structure pitch. This improvement was comparable to the enhancement observed using state-of-the-art PEC etching on c-plane GaN, a technique that is incompatible with most GaN crystal orientations. Colloidal lithography, therefore, is a simple, tunable alternative to current PEC etching on c-plane devices and an enabling backside surface structuring technology for future nonpolar and semipolar free-standing GaN devices.