High-efficiency vertical GaN slab light-emitting diodes using self-coherent directional emitters

We demonstrate a highly-efficient, large-area (1x1 mm 2 ) GaN slab light-emitting diode using a vertically directional emitter produced from constructive interference. The vertical radiation can be coupled effectively into leaky modes from the beginning and thus a high-extraction efficiency can be expected with reduced material absorption. The far-field measurements show that the desired vertical emission profiles are obtained by varying the thickness of the dielectric layer between the emitter and bottom silver mirror. With the combination of a light extractor of a randomly textured surface, the output power was increased ~1.4 fold compared to a non-patterned device at a standard current of 350 mA without electrical degradation. ©2010 Optical Society of America OCIS codes: (230.3670) Light-emitting diodes; (270.1670) Coherent optical effects; (260.3160) Interference. References and links 1. M. R. Krames, O. B. Shchekin, R. Mueller-Mach, G. O. Mueller, L. Zhou, G. Harbers, and M. G. 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Introduction
Light-emitting diodes (LEDs) have made rapid inroads into the classical lightning market owing to energy efficiency and reliable lifetime [1][2][3].Vertical GaN LEDs with high extraction efficiency are particularly attractive on account of excellent thermal properties [4][5][6][7].However, extraction of the lower-order guided modes with a large energy portion without electrical degradation is still a challenge [8][9][10][11][12][13][14].Metal-supported vertical GaN blue LEDs are strong candidates for large-sized back-light units in liquid crystal displays and general lighting because the conducting substrate in vertical LEDs provides a superior thermal path to that of the insulating sapphire substrate used in conventional lateral LEDs [4][5][6][7].By introducing a light extractor, such as a photonic crystal pattern on the top surface of the vertical LEDs, the photons can be coupled efficiently into a leaky medium before they are absorbed by the material [15][16][17][18][19][20].However, such a light extractor cannot render all existing guided modes with different wavevectors to satisfy the phase matching conditions for diffraction [8][9][10].Moreover, the lower-order guided modes occupying larger fractions of the photons generated are barely diffracted due to the inferior spatial overlap between their modal distribution and the light extractor [8,9].Several structures have been proposed to solve these problems.For example, a thin GaN slab vertical LEDs supporting a small number of guided modes showed large extraction and external quantum efficiency, however, current spreading and mechanical stability are still challenging issues [11][12][13][14].This letter proposes an approach to increase the extraction efficiency without degrading the thermal and electrical properties.A significant change in the emission profiles was achieved by appropriately positioning a highreflectivity mirror below the active medium, which resulted in a large extraction efficiency without increasing the operating voltage.

Fabrication
Our LED structure consisted of an n-i-p GaN slab including three pairs of InGaN multiplequantum wells (MQWs), a bottom Ag mirror, and an ITO layer between the slab and mirror [Fig.1(a)].The ITO layer acts as an excellent diffusion barrier to an unwanted leakage current and provides the desired optical path length for a fixed p-GaN thickness [bottom, Fig. 1(b)] [20,21].The electroluminescence (EL) with a centre wavelength of 450 nm and full-width at half-maximum (FWHM) of 25 nm was emitted from the MQWs and reflected by the Ag mirror with a high reflectivity >90% [21,22].A specific emission profile can thus be obtained through either constructive or destructive interferences [23].For example, the vertical radiation becomes predominant if the distance between the MQWs and mirror satisfies the constructive interference condition along the normal direction, as shown in the calculated electric-field profile [top, Fig. 1(c)].On the other hand, if the distance meets the destructive interference condition, the vertical radiation vanishes and most of light is emitted outside of the critical angle for total internal reflection [bottom, Fig. 1(c)].Note that d is the distance from the first quantum well close to p-GaN to the bottom mirror.The desired angular distribution of emission can be produced by simply varying the ITO thickness in this LED structure.The thickness of the MQWs was designed to be <λ/2n: if the active material is too thick, the interference effect will average out and disappear.Also, a slab thickness of ~4 µm is sufficiently large to exhibit good electrical characteristics [17,20].In order to extract more photons, dense and random arrays of pyramidal structures with an average distance of ~1 µm were introduced to the top surface of the n-GaN layer [top, Fig. 1(b)] [19].
The large-area (1x1 mm 2 ) vertical GaN slab LED was fabricated using the following procedures.Heterostructures of (GaN buffer layer)/(2 µm-thick undoped GaN layer)/(3 µmthick Si-doped n-GaN layer)/(37 nm-thick three pairs of InGaN/GaN MQWs)/(80 nm-thick Mg-doped p-GaN layer) were deposited subsequently on a sapphire substrate by MOCVD.ITO and Ag layers were then deposited by sputtering, which was followed by the electroplating of a 100 µm-thick Cu support layer [17].The initial sapphire substrate was detached by a laser lift-off process using a pulsed KrF laser with a wavelength of 266 nm .On the inverted n-side-up samples, ICP-RIE was performed using Ar 2 and BCl 3 /Cl 2 gases until the highly doped n-GaN surface was exposed.The following photolithography and ICP-RIE processes defined isolated mesa structures with an area of 1x1 mm 2 .A chemical etching process using KOH formed a randomly textured surface on the top n-GaN surface and finally an n-type electrode consisting of Cr/Ni/Au was deposited by electron-beam evaporation.

Results
The far-field profiles were measured to determine how the angular distribution of light emission is changed by the distance between the emitter and mirror.In the far-field measurements, the sample was unencapsulated to remove the effect of the shape of the mold.The sample and photodetector were rotated in the φand θ-directions, respectively, and the emission intensity was measured over the entire hemisphere with a resolution of 3° for both directions.The p-GaN thickness was fixed to 97 nm and the ITO thickness, d ITO , was varied from 20 nm to 80 nm to determine an optimal resonant condition for vertical radiation.The ellipsometry measurement showed that the refractive index and extinction coefficient of ITO is 2.0 and 0.1, respectively.The absorption of ITO was neglected because the reflectivity of ITO/Ag mirror did not depend on the ITO thickness when the thickness was smaller than 80 nm. Figure 2(a) shows a schematic diagram of the far-field measurement setup that records the emission intensities over the entire hemisphere with a resolution of 3° for the azimuthal (φ) and polar (θ) angles [25].A randomly textured surface renders the far-field distribution Lambertian regardless of the initial radiation pattern.However, photons within or nearby a light cone are coupled out more efficiently than those far outside the light cone [9,10] so that the control of the radiation pattern can improve the extraction efficiency even after the introduction of a light extractor.Therefore, the measurements in Fig. 2 Interference does not occur when d is an integer number of quarter wavelengths due to a phase shift by the Ag reflector [23].The increased optical power at d ITO = 20 nm also agrees well with the simulation showing increased enhancement by constructive interference [Fig.2(c)].The little discrepancy of d between the simulation and experiment stems from the difference of a phase shift from the Ag reflector.Also, the amplitude of the modulation in the experiment was relatively smaller than that in the simulation because a single point dipole source was used in the simulation instead of the MQWs.The successful demonstration of vertical radiation of an emitter offers a new approach to reducing the travel distance of light as well as the coupled light into leaky modes without significant material absorption.The optical and electrical properties of the LED devices with the randomly textured surface were examined quantitatively.In Fig. 3(a), using the two LED devices with the different p-GaN thicknesses of 97 nm and 80 nm, the optical output power was measured at a standard current of 350 mA as a function of the ITO thicknesses.The difference of these p-GaN thicknesses was not chosen as the half cycle of the oscillation period.The separately normalized output power was plotted as a function of the effective distance between the MWQs and Ag mirror, d, which includes the p-GaN and ITO thicknesses.The oscillation pattern with a maximum at d ~2.4•(λ/4n) and a period of ~(λ/2n) showed good agreement with the FDTD simulation in Fig. 2(c).The optical power in the constructive interference was increased to ~20% compared to the power in the destructive interference.Indeed, the output powers were changed significantly by d and the light extraction enhancement can be achieved easily by controlling the ITO thickness without needing to modify the epitaxial layers.The contrast of the oscillating optical power becomes reduced compared to that of the nonpatterned structure in the simulation of Fig. 2(c).Figure 3(b) shows the near-field images captured by a coupled-charged device (CCD) camera in the LEDs with different ITO thicknesses, 20 nm and 60 nm, at 350 mA.The current was injected using a contact probe tip.A brighter image was observed in the LED at d ITO = 20 nm due to constructive interference.Even at a low current of 20 µA, the light emission was distributed uniformly over the entire surface of each device [11,17].The forward and backward current-voltage (I-V) curves of the devices were measured [Fig.3(c)].The I-V characteristics were all identical regardless of d ITO showing an operation voltage of ~3.2 V, which is lower than those in conventional vertical LEDs [12].This suggests that the electrical properties are not affected by d ITO and the enhanced light extraction was demonstrated without electrical degradation.
Figure 3(d) shows the measured output power as a function of the current in the LEDs with and without the random patterns on the top surface (red and black lines, respectively).The samples were mounted on a lead frame and encapsulated with a transparent Si-gel flat mould with a refractive index of 1.42.The EL intensities were measured using an integration sphere.d ITO was fixed to 20 nm for constructive interference.The reference (green line) was assumed to be a non-patterned LED with d ITO = 40 nm, which exhibited intermediate It is surprising that a significant quantity of photons were extracted even without the top-surface patterns (black line) compared to the reference.This clearly shows how efficiently this LED structure employing the vertically directional emitter works.As shown in the red line, the introduction of a randomly textured surface provided additional momentum to the photons near the light cone [19], which further increased the output power.The output power was increased ~1.4 fold compared to the reference at a standard current of 350 mA and a large wall-plug efficiency of ~29% was achieved.In addition, the ratio of the output power in this LED to the power of the reference increased with increasing current or increasing absorption of the MQWs [26,27].This suggests that the reduced travel distance of light by the vertical emission yielded a large output power despite the large absorption of the MQWs.Therefore, one can take full advantage of this LED structure for the high-current applications required in bright illumination and large size displays.

Discussion
To further understand the enhanced light extraction, the extraction efficiency was calculated using a 3D FDTD simulation.We modeled a LED structure identical to the fabricated one as shown in Fig. 4(a).The randomly textured top surface and the absorption of MQWs were considered in the simulation [17,26].The GaN slab with a refractive index and thickness of 2.46 and 4 µm, respectively, and Si-gel with a respective refractive index and thickness of 1.4 and 1 µm were introduced in the calculation domain with a size of 12 µm x 12 µm x 6 µm and a computation grid size of 5 nm.The side boundaries consisted of perfect electric conductors to describe the indefinite light propagation and the upside boundary consisted of a perfectly matched layer (PML) to eliminate reflected light.Randomly polarized volume dipole sources with a central wavelength of 450 nm and a spectral width of 25 nm were excited in the position of the quantum wells in the slab.In the case where a perfect metal was used as a bottom mirror, two absorptive layers with a thickness of 45 nm and an extinction coefficient (k) were introduced to the upper and lower sides of the dipole sources to consider the absorption of the quantum wells and metal loss.Note that The absorption coefficient, α, is related to the extinction coefficient, k, by the formula, α = 4πk/λ, where λ is the wavelength.In fact, the field profile of a guided mode and overlap of the mode with the two absorbing layers should be considered to reflect the real absorption losses faithfully in the simulation.The randomly textured surface consisting of cones of various sizes was also introduced in the simulation based on the fabricated structure in Fig. 1(b).Note that we do not consider the effect of the package shape and its sidewall angle.Apprently, the extraction efficiency of nonpatterned devices can be underestimated over that of the experimental values.The vertical component of the Poynting vector was then accumulated in front of the PML and the extraction efficiency was calculated by dividing the extracted energy by the total energy generated.In this simulation, we did not consider the shape and sidewall angle of the package in which the device was mounted and thus the calculated extraction efficiency of the nonpatterned device can be underestimated.Finally, we suggest several ideas to further increase the extraction efficiency in our LED structure.First, light extraction will be enhanced if the emitter thickness can be reduced whilst preserving the internal quantum efficiency and the emitter can be located in a position satisfying the constructive interference condition.For example, the introduction of a single quantum well instead of MQWs will lead to better extraction efficiency.Secondly, in a point of view of the light extractor, a proper periodic pattern on the top surface could be introduced to extract the wavevectors outside the light cone [8,11], e.g. the second lobe of the field profile in the top of Fig. 1(c).The efficient extraction of the second lobe becomes more important because the photons inside the light cone can be extracted naturally, without substantial absorption, when the constructive interference condition is satisfied.Furthermore, we expect that an optimum periodic pattern combined with the directional emitter can offer a way to exhibit a narrow directionality of the emission.

Conclusions
In summary, a large wall-plug efficiency ~29% was demonstrated in a GaN slab LED using the vertical emission profile of MQWs.The far-field measurements showed that the desired radiation pattern can be obtained by controlling the thickness of the ITO layer between the MQWs and Ag mirror.The introduction of a randomly textured surface further increased the output optical power.With the optimization of a light extractor and reduction of internal absorption loss, this promising approach to realizing the highly efficient, large size LEDs without electrical degradation will be more powerful in practical illumination applications.

Fig. 1 .
Fig. 1.The vertical GaN slab LED with a randomly textured surface and a bottom Ag mirror.(a) Schematic diagram of the LED structure.The distance between the MQWs and Ag mirror is denoted by d.(b) SEM image of a cross-section of the fabricated LED structure with a scale bar of 5 µm (left).A magnified SEM image of the randomly textured top surface with a scale car of 5 µm (top) and a TEM image of the heterostructure of the n-GaN/three pairs of MQWs/p-GaN/ITO/Ag with a scale bar of 20 nm (bottom).(c) The calculated field profiles (log E 2 ) using a 3D FDTD simulation.Dipole sources with identical oscillation intensities in all three directions are located in the GaN slab and separated from the bottom Ag mirror by d = 2.6•(λ/4n) (top) and d = 1.6•(λ/4n) (bottom).The blue dotted lines indicate the critical angle (37°) of the total internal reflection between GaN and the Si-gel.

Fig. 2 .
Fig. 2. The far-field measurement of the emission profiles.(a) Schematic diagram of the farfield measurement setup.The light intensity was recorded in the θand φ-directions by rotating both sample and photodetector.(b) The output intensities measured in the non-patterned LEDs with different ITO thicknesses of 20 nm, 40 nm and 60 nm are plotted as a function of θ (top).The thickness of p-GaN was 97 nm.In the bottom, the 2D angular distributions measured in both θand φ-directions are shown for the ITO thicknesses of 20 nm and 60 nm.The narrow and vertical emission profile was observed at an ITO thickness of 20 nm due to constructive interference.(c) The relative enhancement was calculated using the 3D FDTD simulation as a function of the distance between the dipole source and Ag, d.A non-patterned LED structure was introduced with an ambient medium, Si-gel, with a refractive index of 1.4.The relative enhancement is defined by the extraction efficiency normalized by the calculated efficiency in the case that the dipole source with the isotropic emission profile located infinitely far from the Ag mirror.In addition, the output powers measured in the non-patterned devices with the ITO thicknesses of 20 nm, 40 nm, 60 nm and 80 nm are introduced for comparison (black dots).These output powers were normalized by the average power showing no interference effect.
(b) were carried out on LED structures without a randomly textured surface to clearly observe the interference effects.#125217 -$15.00USD Received 9 Mar 2010; revised 25 Apr 2010; accepted 4 May 2010; published 11 May 2010 (C) 2010 OSA It should be noted that the distinguishable far-field distributions were measured with different ITO thicknesses [Fig.2(b)].At d ITO = 20 nm, a narrow and vertically concentrated emission profile was observed due to constructive interference.On the other hand, the emission pattern spread widely with increasing d ITO , showing a local minimum in the normal direction.An emission profile modified by destructive interference was observed at d ITO = 60 nm.The twodimensional (2D) angular distributions measured in the θand φ-directions clearly show these characteristic emission profiles [bottom, Fig.2(b)].In addition, the optical power at d ITO = 20 nm was twice that at d ITO = 60 nm, demonstrating the significant effect of interference.The dispersive three-dimensional (3D) finite-difference time-domain (FDTD) simulation strongly supports these far-field measurement results.In Fig.2(c), the relative enhancement was calculated as a function of the distance between the dipole source and real Ag mirror, d.Note that d corresponds to total optical thickness taking refractive indices into account.For example, d ITO = 20 nm in Fig.2bcorresponds to d of ~2.4•(λ/4n), which meets the constructive interference conditions in the simulation, where λ and n are the centre wavelength and refractive index of GaN, respectively.On the other hand, d ITO = 60 nm corresponds to d of ~3.1•(λ/4n), which meets the conditions for destructive interference.

Fig. 3 .
Fig. 3. Measurement of the optical and electrical properties of the LEDs with randomly textured surfaces.(a) The output powers were measured at a standard current of 350 mA with varying ITO thickness from 20 nm to 80 nm.The two LEDs with p-GaN thicknesses of 97 nm (black line) and 80 nm (red line) were used.The graph is plotted as a function of the total distance between the MWQs and Ag mirror, d, that includes the p-GaN and ITO thicknesses.(b) CCD images at 350 mA of the LEDs with dITO = 20 nm (left) and dITO = 60 nm (right).In both images, identical neutral density filters were used to avoid intensity saturation.(c) Current-voltage characteristics measured in the LEDs with dITO = 20 nm (black line) and dITO = 60 nm (blue line).(d) The output power-current characteristics measured in the LEDs with and without the random patterns on the top surface at dITO = 20 nm (red and black lines, respectively).The reference (green line) is the non-patterned LED with dITO = 40 nm.In (b), (c), and (d), the p-GaN thickness was 97 nm.

Fig. 4 .
Fig. 4. The 3D FDTD simulation of the LEDs with and without a randomly textured surface.(a) Schematic diagram of the patterned LED structure used in the simulation.The random patterns were introduced based on the SEM image in Fig. 1(b).A perfect metal was used as the bottom mirror.(b) The extraction efficiencies were calculated as a function of the extinction coefficient, k, of the absorptive layers introduced in the GaN slab.The red line and dot show the efficiencies in the patterned LED under constructive and destructive interference conditions, respectively.On the other hand, the black line and dot show the efficiencies in the non-patterned LED under constructive and destructive interference conditions, respectively.The green line is the efficiency of the reference.In Fig. 4(b), the extraction efficiencies in the patterned and non-patterned LED structures were plotted as a function of the extinction coefficient (red and black lines and dots, respectively).Obviously, light extraction was increased by constructive interference.In addition, the introduction of random patterns on the top surface caused a further increase in light extraction.The results showed that the extraction efficiency of the patterned devices depends strongly on the absorption because the trapped photons can be extracted more effectively by the top-surface pattern with decreasing propagation distance or decreasing absorption [26].The extinction coefficient and extraction efficiency in the fabricated LED device were estimated by comparing the ratio of the measured output powers of the patterned devices at d ITO = 20 nm and d ITO = 60 nm with the ratio of the extraction efficiencies in Fig. 4(b) (red line and dot).An extraction efficiency of >40% was estimated at a standard current of 350 mA, which can be further increased by reducing internal absorption of the device.This simple estimation shows a lower boundary of the extraction efficiency and can be substantially changed by the extinction coefficient of the internal layer.Finally, we suggest several ideas to further increase the extraction efficiency in our LED structure.First, light extraction will be enhanced if the emitter thickness can be reduced whilst preserving the internal quantum efficiency and the emitter can be located in a position satisfying the constructive interference condition.For example, the introduction of a single