APPLIED PHYSICS LETTERS 96, 031108 2010

High extraction efﬁciency light-emitting diodes based on embedded air-gap photonic-crystals
Elison Matioli,1,a Elizabeth Rangel,1 Micheal Iza,1 Blaise Fleury,1 Nathan Pfaff,1 James Speck,1 Evelyn Hu,2 and Claude Weisbuch1,3
1 2

Department of Materials, University of California, Santa Barbara, California 93106-5050, USA School of Engineering and Applied Physics, Harvard University, Cambridge, Massachusetts 02138, USA 3 Laboratoire de Physique de la Matière Condensée, CNRS, Ecole Polytechnique, 91128 Palaiseau, France

Received 16 November 2009; accepted 21 December 2009; published online 22 January 2010 This letter reports on high extraction efﬁciency light-emitting diodes LEDs based on embedded two-dimensional air-gap photonic crystals PhCs . High refractive index contrast provided by the air gaps along with high interaction of the embedded PhCs with the guided light resulted in an efﬁcient extraction of all guided modes in the LED, in contrast to the common surface PhC conﬁguration. Embedded PhC LEDs presented an enhanced directional light emission compared to non-PhC LEDs. High extraction efﬁciency, close to unity, provided by the encapsulated embedded PhC LEDs demonstrates the capability of this approach to achieve high efﬁciency devices with directional light emission. © 2010 American Institute of Physics. doi:10.1063/1.3293442 The application of photonic crystals PhCs as light extractors in light-emitting diodes LEDs has evoked increased interest over recent years. Several groups1–5 demonstrated the efﬁcacy of PhCs in controlling the direction of light emission and enhancing the extraction efﬁciency of LEDs. A number of different schemes are commonly applied to increase the extraction efﬁciency in LEDs. While surface roughening, which is among the most widely used methods, has demonstrated extraction efﬁciencies as high as 80% in encapsulated LEDs,6 it offers no control over the direction of the emitted light, resulting in a Lambertian far ﬁeld emission. The most straightforward design of PhCs is on the surface of the LEDs, however the observed enhancement in light extraction, mainly in thick LED structures, is usually signiﬁcantly lower than the theoretical limit, due to the limited interaction of the surface PhCs with some of the guided modes, notably the low order modes.2 The poor extraction of a relatively high portion of the guided light carried by these low order modes7 limits the enhancement on extraction efﬁciency by the surface PhCs in such structures. The alternative approach presented in this letter is to utilize embedded air-gap PhCs within the LEDs. The greater interaction of the guided light with the embedded PhCs not only allows extraction of the low order modes but also improves the extraction of high order modes, compared to surface PhCs.8 In addition, the high refractive index contrast between GaN and air in these air-gap structures yields an enhanced PhC diffraction strength, compared to embedded dielectric-based gratings,9 and the two-dimensional 2D nature of the PhC results in omnidirectional light extraction. Furthermore, the planar top surface of the embedded PhC LED simpliﬁes device fabrication, and, in particular, eases issues related to making the best electrical contacts to the device. Finally, this approach mitigates possible etch-related damage to the quantum wells QWs , since the embedded PhCs are fabricated before the growth of the LED active region. These devices demonstrated close to unity extraction efﬁciency and highly directional light emission.
a

The schematic of the embedded PhC LED presented in this letter is shown in Fig. 1 a . Several electromagnetic guided modes are supported in such a structure, due to the fairly thick GaN slab 4 m , these are designated as low order modes, high order modes and cap-layer mode CLM . The latter is the mode conﬁned in the top layer above the embedded air-gap PhCs, due to their lower effective index of refraction. A thorough optimization of the embedded PhC LED structure would require consideration of the extraction of every single supported mode in the structure; this is quite tedious due to the large number of modes. A sufﬁcient analysis can be done by optimizing the extraction of the poorest extracted mode. In simple and general terms, all the guided modes extend spatially over the entire GaN layer, resulting in a good interaction with the embedded PhCs, except the CLM which is the only mode conﬁned above the embedded PhCs. The CLM is not only the mode with the lowest interaction with the PhCs, but also the best excited by the QWs, justifying the importance of its optimization.

Electronic mail: elison.matioli@polytechnique.org.

FIG. 1. Color online a Schematic of the embedded PhC LED supporting following three different families of modes: low order, high order, and CLMs. b Simulated extraction length of the CLM as a function of the cap-layer and embedded PhC thicknesses for 35% PhC ﬁll factor, 4 m-thick GaN layer and = 460 nm. c Cross-sectional SEM image of the embedded air-gap PhC LED. © 2010 American Institute of Physics

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FIG. 2. Color online a Low resolution angle-resolved EL measurement, where k0 = 2 / , showing the diffraction of the guided modes by the embedded PhCs. b High-resolution angle-resolved measurement revealing the presence of many more diffracted modes.

The critical vertical dimensions of this structure, such as thickness of the cap-layer and embedded air-gap PhCs, were theoretically optimized by calculating the extraction length Lextraction of the CLM, which corresponds to the distance traveled by the mode after which the fraction 1 − e−1 of its energy is diffracted to air by the PhCs. The modal extraction length is related to the imaginary component of the wave vector k of the guided mode or more precisely, Bloch mode supported by the structure as Lextraction = 1 / 2k , where k is due only to the PhC diffraction of this guided mode. The imaginary component of the CLM wave vector was calculated based on a full three-dimensional scattering matrix formalism2,10 considering the PhCs with 35% ﬁll factor deﬁned as the fraction of the PhC surface occupied by air holes above a 4 m-thick GaN layer and wavelength = 460 nm. The dependence of the calculated CLM extraction length on the cap layer and PhC thicknesses is shown on Fig. 1 b . The shortest extraction length of the CLM is achieved for the thinnest possible cap layer and a relatively thin PhC layer 100 nm , which produces a weaker conﬁnement of the CLM, resulting in a higher interaction with the embedded PhCs. The discontinuities at the dashed lines shown in Fig. 1 b are due to the change on the mode order of the CLM as the thickness of the cavity varies and the oscillations represent variations in the vertical resonances of the Bloch mode with the PhC layer.11 The optimal PhC ﬁll factor for a 540 nm-thick cap layer and 100 nm-thick embedded PhC layer was found to be around 14%. Both low ﬁll factor and thin embedded PhCs result in weak conﬁnement of modes in the cap layer or equivalently, in the bottom GaN layer below the PhCs . Therefore, the modes spatially extend across the PhC layer, which increases their diffraction strength resulting in shorter extraction lengths. These optimal values guided the fabrication of the structure. The GaN-based embedded PhC LED was grown by metalorganic chemical vapor deposition on a sapphire substrate. The LED structure consists of a 3 m-thick n-GaN followed by a 100 nm-thick layer of air-gap PhCs, with 230 nm period, and 540 nm-thick active region comprised of a 300 nm-thick n-GaN layer, 6x-InGaN QWs emitting at = 445 nm and a 110 nm-thick p-GaN layer Fig. 1 c . The 2D triangular-lattice air-gap PhCs were embedded within the GaN layer by the growth method described in Ref. 12 with a 12% ﬁll factor. The device size was 800 800 m2 and the current was injected through a circular p-contact diameter of 100 m in the center of the device to separate the

metal absorption from the PhC extraction of the guided modes. Although this choice of contact scheme offers poor current spreading in the p-GaN layer, it is optically equivalent to a perfectly reﬂecting metal deposited over the entire surface in ﬂip-chip LEDs. The measurement of the extracted guided modes was performed by an angle-resolved electroluminescence EL setup where the spectrum of the LED under electric bias was measured for all angles from 0° to 180°. The collection of all the spectra versus angle, along the K direction of symmetry of the PhC,13 reveals the dispersion relation of the extracted guided modes represented by the sharp lines in Fig. 2 a , where k0 = 2 / . The comparison of the high-resolution angular spectra of the LEDs with embedded PhCs Fig. 2 b to the one with surface PhCs,13 under similar conditions, reveals a higher number of modes diffracted by the embedded PhCs. In particular, well diffracted modes were observed between 80° and 20° Fig. 2 b which were not observed from the surface PhC LEDs. The extraction length of the low order modes, determined from the linewidth of the high-resolution angular spectra13 Fig. 2 b , was in the range of 64– 80 m which is lower than the extraction lengths of the same modes in a similar structure with surface PhCs.13 Additionally, the extraction of all low order modes was observed, in contrast to the surface PhCs.2,3,13 The PhC period a = 230 nm was designed to enhance the LED vertical emission, which can be seen from the angleresolved measurements of Fig. 2 a , where the diffracted modes are mostly concentrated at angles between 30° and 30°. The vertically emitted power of the LEDs as a function of the current was measured by placing a power meter 5 mm above the device, with a full collection angle of 53° and the result is shown in Fig. 3 a . The red curves correspond to the non-PhC LEDs and the blue to the embedded PhC LEDs. The dotted curves represent the extreme performances obtained among all measured devices. Average performing devices solid lines on Fig. 3 a were used for comparison, to exclude the effect of the internal quantum efﬁciencies IQE variation over the wafer, showing a 3.5-fold enhancement in the vertical output power by the embedded PhCs. This is a rather qualitative result because the present contact scheme blocks most of the direct emitted light from the non-PhC LEDs, therefore the top emitted output power cannot be fairly compared between these devices. However, it demonstrates the PhC ability to vertically extract the guided modes. The I-V characteristics were not modiﬁed by the inclusion of

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FIG. 3. Color online a Vertically emitted output power versus current for the embedded PhC LEDs and non-PhC LED. The dotted curves represent the extreme behaving and the solid line the average behaving devices. b I-V characteristics of the embedded PhC and non-PhC LEDs. c EQE and total output power vs current of the unencapsulated embedded PhC and encapsulated embedded PhC LEDs.

the embedded PhCs. Hence no additional series resistance was introduced into the device Fig. 3 b . An important ﬁgure of merit to quantify the total light extraction in the LED is the extraction efﬁciency, deﬁned as extraction = EQE/ IQE, where EQE and IQE are, respectively, the external and internal quantum efﬁciencies. The EQE as a function of current density was determined from the measurement of the total output power of the average-performing unencapsulated embedded PhC LED, using an integrating sphere blue curve in Fig. 3 c . The total output power of the same devices after encapsulation with a silicone dome is shown by the black line in Fig. 3 c . The peak IQE of these devices LEDs was estimated using a room temperature RT EL method. The output power was measured from a well deﬁned surface of a single facet of the LED, where the extraction efﬁciency extraction f of the non-PhC LED is well known theoretically,14 and the rest of the chip was covered with light absorbing material. Non-PhC LEDs from the same wafer with similar output power were processed speciﬁcally for the IQE measurement, using the same processing method described in Ref. 14. The IQE was determined as IQEpeak = EQEpeak / extraction f resulting in 7.9% for the non-PhC LED. The extraction of the unencapsulated embedded PhC LED was then estimated to be 73% assuming that the IQE does not vary considerably with the introduction of embedded PhCs in the structure. Although the embedded PhC efﬁciently extracts all guided modes from the GaN slab, it does not extract the modes guided in the sapphire substrate corresponding to 22% of the emitted energy from the QWs Ref. 7 plus some guided modes diffracted from GaN to sapphire by the PhCs . To increase the extraction of the sapphire modes to air, the same embedded PhC LED was encapsulated with a silicone dome yielding an extraction efﬁciency of 94%. The IQE was also estimated by the widely used temperature-dependent photoluminescence PL method,

where the IQE at RT is determined from the ratio of output powers at RT and low temperature LT , assuming the IQE at LT 4 K is 100%. However, we expect that our materials may contain a rather high density of non radiative centers which would not be completely suppressed at LT. Therefore use of this method allows us to only set an upper bound on the IQE; 12.6% for the embedded PhC LEDs, and 15.5% for non-PhC LEDs. The estimated lower bound for extraction of the unencapsulated devices was then 46% and 59% for the encapsulated embedded PhC LED. The high extraction efﬁciency obtained from the encapsulated embedded PhC LEDs is in agreement with the very good extraction of the guided modes in both GaN and sapphire slabs by the embedded PhCs, however the IQE estimation from both methods needs to be carefully considered. While the RT EL method is a more reliable technique, it was measured from different devices from the same wafer with similar output power , due to the different processing method required. On the other hand, the temperature dependent PL method, realized on the same devices used in the EQE measurement, overestimates the IQE and assumes similar carrier injection in QWs from PL and EL. In conclusion, the embedded PhC LEDs reported in this letter were designed to yield short extraction length of the guided modes, improving the competition between PhC assisted light extraction and dissipation mechanisms. The diffraction of all low order modes was observed in contrast to surface PhC LEDs. High extraction efﬁciency devices, close to unity, were demonstrated with directional light emission, which makes the embedded air-gap PhCs an excellent candidate for high efﬁciency and high brightness LEDs. This work was supported by DOE under Project No. DE-FC26-06NT42857 and DOE-EFRC under Project No. DE-SC0001009.
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