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Optimization design of holographic photonic crystal for improved light extraction efficiency of GaN LED
Superlattices and Microstructures 64 (2013) 303–310
Contents lists available at ScienceDirect
Superlattices and Microstructures journal homepage: www.elsevier.com/locate/superlattices
Optimization design of holographic photonic crystal for improved light extraction efficiency of GaN LED X.X. Shen a,⇑, Y.Z. Ren a, G.Y. Dong b, X.Z. Wang a, Z.W. Zhou a a b
Shen Zhen Institute of Information and technology, ShenZhen 518072, China College of Materials Science and Opto-Electronic Technology, University of Chinese Academy of Sciences, BeiJing 100084, China
a r t i c l e
i n f o
Article history: Received 4 September 2013 Accepted 27 September 2013 Available online 6 October 2013 Keywords: Photonic crystals Holographic interferometry Light emitting diode
a b s t r a c t A study on improved light extraction efficiency (LEE) of LEDs with photonic crystals formed by holographic lithography (HL) was present. The propagation and extraction of light in LEDs were simulated using FDTD method for LED structures with top HL PC and embedded HL PC respectively. By optimizing the design parameters of the HL PC, the best value of 88.3% enhancement of LEE were obtained. Result also revealed that the scattering and diffraction of photonic lattices play a more important role in the increased light extraction of HL PC LEDs than photonic band gap effects. Ó 2013 Elsevier Ltd. All rights reserved.
1. Introduction GaN-based LEDs play an important role recently in many fields, since they can be widely used in medical operations, traffic lights, mobile devices, flat panel displays, general lighting, and many other fields. However, external quantum efficiency of LEDs is still not high enough to realize LED-based solid state lighting, even the internal quantum efficiency is relatively high [1,2]. The external quantum efficiency is mainly limited by low light extraction efficiency (LEE). And one of the primary reasons for low LEE is the total reflection at the interface of the semiconductor and the outer medium. In order to improve the LEE, a number of approaches have been applied, such as LEDs grown over patterned sapphire substrates, shaped LED ships, photon recycling, coupling to surface plasmon modes [3], surface roughening [4] and photonic crystals [5–8]. The aims of surface roughening and photonic crystals
⇑ Corresponding author. E-mail address: [email protected] (X.X. Shen). 0749-6036/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.spmi.2013.09.043
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used in LEDs are both to avoid total internal reflection and prevent the lateral propagation of lightwaveguide effect. Though the randomizing light reflection at roughed surface destroyed the light propagation in straight paths and made light escaped from the LEDs through the critical cone, yet it provides little control on the direction of the light emission, which result in Lambertian radiation patterns. Compared with surface roughening method, PCs used in LEDs have been researched in many works and demonstrated to provide superior light extraction and directional light emissions. Most studies used 2-D PCs with regular circle columns formed by RIE or electron beam lithography. Since the holographic lithography (HL) approach for PCs fabrication has its unique advantages such as one step recording in large scale [9,10], which made the industrialization of production low cost and easy; And holographic structures usually have irregular atoms or columns, the light propagation properties of PCs are closely related to their specific structures [11,12], we may expect some difference in light extraction behavior between LED structures with regular and holographic photonic crystals. The fabrication of a PC on the top of an LED degrades the Ohmic contact between the P-GaN and the Ohmic metals, and the low interaction of the PCs with some of the guided modes limits the potential enhancement in extraction efficiency, as these modes are not well diffracted by shallow PCs due to their poor overlap with the etch region [13]. Thus LEDs with embedded PC inserted below the active layer were researched to improve the light extraction efficiency [14]. The embedded PC was fabricated in highly conductive N-GaN cladding, and both p-type and n-type Ohmic performance were not degraded. To fully utilize the advantage of an LED with embedded PC, structures of LEDs with top or embedded PCs are researched. In our study, we used the finite-difference time-domain (FDTD) method to study the light extraction characteristics of LEDs with various PC structures formed by holographic lithography and compared the improved enhancement results. The HL PC structures were introduced in Section 2; the enhancements of light extraction of LEDs with top and embedded HL PCs were analyzed and compared in Section 3, We also analysized the distribution of band gap for HL PC structures using the plane wave method (PWM) [15] with the wave number of 729 in Section 3, to demonstrate the point that the increased light extraction of HL PC LEDs was mainly due to lattices scattering and diffraction more than photonic band gap effects. 2. Structures and FDTD method In our analysis, there are two steps carried out to fabricate holographic PCs onto the LED structures: (1) Fabricating triangular pattern in photo resist layer using holographic lithography; (2) Transferring the pattern into GaN layer. We used an interference technique of three non-coplanar beams (ITNB) to fabricate the 2-D triangular lattices. The intensity distribution of the holographic structure we adopt can be expressed as [16]
2p 2p 3 2p 3 I ¼ 3 þ cos pffiffiffi ð2yÞ þ cos pffiffiffi pffiffiffi x þ y þ cos pffiffiffi pffiffiffi x y : 3a 3a 3a 3 3
ð1Þ
By controlling the exposure intensity, introducing an intensity threshold It, (here It e(1.5, 6) for Eq. (1)), which is a specific value the region with light intensity below it can be removed and the region above it will remain due to photo polymerization for negative photoresist, we may wash away the region of I < It to get a normal structure. By filling this structure with a material of high dielectric constant and then removing the template, an inverse structure can be obtained [17]. In our situation, we used the inverse structure which means that the dielectric constant distribution e(x, y) of result lattice should be 1 in the region I(x, y) > It, represented by the white part (air); and 5.86 in the region I(x,y) < It, represented by black part (GaN with the refractive index of 2.42 at a wavelength of 465 nm). To find the difference between the holographic structures and the regular ones, we chose several lattices shown in Fig. 1 for investigation, here (a), (b) and (c) are the shape and size of the cross section of air columns with different intensity threshold It and filling ratio FR. The relation between It and FR of the air column is shown in Fig. 2, to optimize the structures so as to maximize the LEE of LEDs, the effect of different threshold and corresponding FR has been examined. Light extraction characteristics of LEDs with various PC structures formed by holographic lithography were studied using FDTD method with the calculation domain shown in Fig. 3. The simulated LED
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Fig. 1. Variation of the shape and size of the cross section of air columns with different It and filling ratio FR. (a) It = 1.9, FR = 83.10%; (b) It = 2.4, FR = 57.68%; (c) It = 3.5, FR = 32.74%.
100
Filling Ratio (%)
80
60
40
20 Threshold It 0 2
3
4
5
6
Fig. 2. The relation between filling ratio of air columns and intensity threshold It.
Z X
Perfect mirror
Detected surface
PML
P-GaN
PC
MQW
P-GaN MQW
PC
N-GaN
N-GaN
Sapphire
Sapphire
(a)
(b)
Fig. 3. FDTD simulation domain and LED structure with (a) top HL PC and (b) embedded HL PC.
structure is composed of a P-GaN layer, a multi-quantum-well (MQW) active layer, an N-GaN layer, and a sapphire substrate. And a 2D triangular HL PC with the shape of air columns described in Fig. 1 was formed on the top surface of the LED or located below the MQW active layer, as shown
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in Fig. 3(a) and (b) respectively. To solve the calculation problems of FDTD simulation for any realistic LED device, we used a simplified LED with a cross section of smaller size and applied perfect mirrors at four lateral sides (shown as blue1 line in Fig. 3), and the calculation domain was chosen as 4 lm 4 lm. The radiating source of LED was represented by a point dipole located in the middle of active region, and we assume the emitted radiation has TE polarization since the point dipole was allowed to move in the xy-plane of MQW [18]. The radiate spectrum of this dipole was centered at 465 nm with a full-width at half-maximum of 10 nm. In our simulation the refractive indexes of GaN and sapphire at a wavelength of 465 nm were 2.42 and 1.77 respectively [19]. Perfect matched layer was used outside the calculation region in order to suppress the reflection at the boundary. The energy of extracted light was measured by the integration of Poynting vectors at the detected surfaces surrounding all sides of the LED [20], which were shown in Fig. 3 using red dashed line rectangular. 3. FDTD results and discussion The enhancements of the LEDs were calculated in this section, when using various PC structures with HL triangular patterns. PC parameters such as the PC thickness d, the filling ratio of air columns FR, and the position of PC located were considered either, to find the optimal design of a HL PC LED for improved light extraction and compare the results of enhancement when using top and embedded HL PCs. The enhancement factor genhance can be represented as:
genhance ¼
EPC E0 E0
ð2Þ
where EPC is the integrated energies of light escaped from the LED with PC structures, and E0 for the ordinary LED. The power loss in GaN during the simulation was ignored since the imaginary part of the GaN index is closed to zero at the wavelength of 465 nm [21]. 3.1. LED with top HL PC structure As described in Fig. 3, the simulated LED structures with a top HL PC consisted of a P-GaN layer with the thickness of 200 nm, a MQW active layer, an N-GaN layer of 800 nm, and the sapphire substrate 1 lm, with a cross-sectional area of 4 lm 4 lm, and the grid size for FDTD was Dx = Dy = Dz = 20 nm. The relativity between the improvement of LEE and the PC parameters was studied using a standard top HL PC LED with a = 300 nm, It = 3.5, FR = 32.74%, and the thickness of PC slab d = 150 nm. When the enhancement of LEE was calculated each time, other parameters of PC were kept the same as mentioned. Only one situation of dipole source has y-direction polarization was concerned, since the simulation results were similar with x-polarization [5]. The relativity between the improvement of LEE and the top HL PC parameters is shown in Fig. 4. The thickness of HL PC was varied from 0.1a to 0.8a, and the filling ratio of air columns was 0 to 1, respectively. From Fig. 4(a), we see that the enhance factor of LEE increased with the varying thickness of PC. However, the fabrication of PC with a large thickness was very difficult in experiment, the thickness of PC is smaller than the lattice constant a ordinarily. So in this case the PC thickness of 0.4–0.7a is enough for the improvement of genhance. In Fig. 4(b), the enhancement of LEE was high when the filling ratio changes from 0.3 to 0.75, but dropped quickly when FR became too small or too large. The peak value was archived when FR = 0.58, and the It of HL PC was 2.4, the corresponding lattice pattern was given in Fig. 1(b). This result was reasonable due to the contrast of index. 3.2. LED with embedded HL PC structure For an LED with an embedded HL PC as shown in Fig. 3(b), the parameters of simulated LED structure were almost the same as LED with top HL PC, only the thickness of N-GaN layer changed to 4 lm in order to locate the embedded PC. The standard embedded HL PC with the same parameters as top 1
For interpretation of color in Fig. 3, the reader is referred to the web version of this article.
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Ehancement ηenhance (%)
Enhancement ηenhance (%)
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80 60 40 20
80 60 40 20
Thickness of Holographic PC (a) 0
0.2
0.3
0.4
0.5
(a)
0.6
0.7
Filling ratio of air column FR 0.8
0 0.0
0.2
0.4
0.6
0.8
1.0
(b)
Fig. 4. Enhancement of light extraction efficiency as a function of (a) PC thickness, and (b) Filling ratio of air columns for the top HL PC LED.
PC: a = 300 nm, It = 3.5, FR = 32.74% and the thickness d = 150 nm, the PC was 8a below the MQW at first. We changed PC thickness, filling ratio, PC location and the lattice constant in turn, and kept the other parameters the same as beginning each time. The relation between the enhancement of light extraction efficiency and the embedded PC parameters is shown in Fig. 5. From Fig. 5(a), we can see the relation between the enhancement of LEE and the thickness of HL PC, LEEs of LED increase with the thickness of PC from 0 to 0.6a, and the largest enhancement was obtained when d was 0.4–0.6a, however this ascending trend stops at this thickness and changes to fluctuation as the thickness of PCs getting bigger. This was caused by the confinement effect in the cavity between the surface of the LED and the PC. In this case, the embedded PC acted as a mirror, the reflected waves of light incident on the top surface of PC and light incident on the bottom of PC may have interference effect, and when the interference were constructive the enhancement of LEE would be high. The HL PC can be considered as an isotropic thin film with an effective refractive index neff, which can be calculated as: neff = FRnair + (1 FR)nGaN, and the thickness of PC for constructive interference can be estimated by d = (m + 1/2)k/2neff (m = 1,2. . .), in our case for the standard PC structure, neff = 1.955, for the wavelength of 465 nm, d 180 nm, 300 nm, and 420 nm when m = 1, 2, 3 respectively, corresponding to 0.6a, 1.0a,1.4a in Fig. 5(a) where the highest enhancements were obtained. In Fig. 5(b), the simulation result of relation between genhance and FR was close to that of LED with top PC. We obtained the highest enhancement of LEE at a filling ratio of 0.32 (It = 3.5, and the corresponding lattice pattern was given in Fig. 1(c)), LEE then dropped fast when the filling ratio became too small or too large. The relation between genhance and the location of PC was also analyzed. The embedded PC was formed and covered before MQW growth, so the distance would influenced the internal quantum efficiency, usually for a high quality MQW a thickness of several micrometers for GaN layer was needed [14]. And most of energy radiate from the active region was concentrated in the cavity formed by the embedded PC and LED surface, and the smaller distance from the top of embedded PC to MQW means more radiate energy near the LED surface, which results in a bigger chance for photons to escape from the LED. Therefore, the location of embedded PC should be considered and make compromises between internal quantum efficiency and light extraction efficiency. From Fig. 5(c) we can see the simulation result proved our analysis that when the distance was varied from 0 to 12a, the enhancement of LEE almost decreased linearly. At last before the lattice constant was considered, we know that there are three main mechanisms of using PC to increase LEE: First, the existence of photonic band gap (PBG), light with frequencies within the band gap cannot propagate laterally and was coupled into radiation modes, result in an enhancement of the extraction in the vertical direction from an LED; Second, the diffraction effect
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Enhancement ηenhance (%)
Enhancement ηenhance (%)
40 35 30 25 20 15 10 5
Thickness of Holographic PC (a)
0 0.0
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35 30 25 20 15 10 5 The filling ratio of air column FR
1.4
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Enhancement ηenhance (%)
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(b)
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60
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20
50 40 30 20 10
Distance from the top of the PC to the MQW(a) 0
0.6
0
2
4
6
(c)
8
10
12
0
Lattice constant a (nm) 0
100
200
300
400
500
600
700
(d)
Fig. 5. Enhancement of light extraction efficiency as a function of (a) embedded PC thickness, (b) filling ratio of air columns for the embedded HL PC LED. (c) Distance from the top of the PC to the MQW, and (d) lattice constant for the embedded PC.
when PC acting as a Bragg grating; Third, the diffused scattering by PC structure, which broke the total internal reflection condition of guided light. In order to make out which mechanism play the most important role in enhancement of LEE, we calculated the photonic band diagrams for the triangular holographic PC with varied It, Fig. 6 shows the dependence of the PBG on the It, extracted from band structure calculations when It changes from 1.5 to 5.5. The blue dashed area represented the distribution of PBG between TE1 and TE2 using normalized frequency units (xa/2pc), and the red dotted line indicate the corresponding relative band gap (measured by gap to mid-gap ratio Dx/x0). From Fig. 6 the PBG can be observed for a wide region when It varied from 1.9 to 4.8((the corresponding FR: 0.8310–0.1335), and the relative band gap can be as high as 29.92% when It = 2.5. For the standard HL PC with It = 3.5 we simulated, the PBG appears from 0.2916 to 0.3477, which corresponded to 136–162 nm for lattice constant a with the wavelength of 465 nm. And the central normalized frequency is 0.3196, corresponded to 149 nm. We suggested that the LEE should be highest when light in the PBG for the first mechanism mentioned before. However, from Fig. 5(d) when a was small the enhancement of LEE was small and then getting higher with increased a, though for a = 150 nm when light in the PBG LEE had a little rise, the highest enhancement appeared when a was 450–650 nm. It is obvious that the existence of a photonic band gap was not the main reason for the increased light extraction of HL PC LEDs, since the strong reduction in spontaneous radiative emission rate for photos within the band gap requires low temperature operation to diminish the effect of competing non-radiative recombination and maintain good internal quantum efficiency. Enhancement of LEE would mainly due to lattices scattering more than photonic band gap effects.
X.X. Shen et al. / Superlattices and Microstructures 64 (2013) 303–310 40
0.7
30 Relative bandgap (%)
Normalized frequency (ωa/2πc)
0.8
309
0.6
0.5
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20
10
0
0.3 1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
Threshold It Fig. 6. TE gap map and the relative band gap with varied It for the triangular holographic PC structure.
3.3. Comparisons To get a comprehensive understanding for the holographic PC to improve the LEE of LEDs, we compared the improvement of the LEDs with a top and embedded HL PC, and LED with both top and embedded PCs. For FDTD simulations, the same PC structure was used with a = 300 nm, a filling ratio of air column FR = 0.3274 when It = 3.5, and a PC thickness of 0.5a. The locations of embedded PCs were at the distance of 200 nm below the MQW. The integrated emitted energy were calculated with increasing simulated time steps for three LED structures, and the enhancements compared with ordinary LED were given in Fig. 7. Here the time step dt = Dx/2c (c is the speed of light), and n is the integrated steps, 5000 steps is enough for the accuracy of the simulation since the results almost keep the same when integrated time steps increased from 5000 to 10,000. The black, red, and blue dotted lines represent LEDs with top PC, with embedded PC, and with both top and embedded PCs, respectively. At the extracted time step n = 5000, compared with traditional LEDs without PCs, the calculated radiative energies of the LEDs with top and embedded PCs were enhanced by 71.5% and 82.0% respectively, and 88.3% for LED with both top and embedded PCs. Since the fabrication of LEDs with both top and embedded PCs is much more expensive and complicated, and the improvement is inconsiderably, to achieve a high light extraction efficiency using LEDs with top or embedded PC only is quite enough.
Enhancement ηenhance (%)
100
80
60
40 LED with top PC LED with embedded PC LED with both top and embedded PCs
20
0
0
2000
4000
6000
8000
10000
Time (nδt) Fig. 7. Enhancement of integrated total emitted energies with increasing simulated time steps for LEDs with three different structures.
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4. Conclusions We have investigated the improvement of light extraction efficiency of GaN LED with PC structure formed by holographic lithography. The simulation result had given the optimized design of top and embedded HL PCs for LEDs to achieve the highest LEE. Results showed that the embedded PC was more effective in improving the LEE, because embedded PC has interaction with all guided modes in the LEDs, since most of the radiative energy was confined in the cavity between the top surface of the LED and the embedded PC, though the distance between the MQW and the embedded had to be considered and make compromise between IQE and LEE. The study also revealed that the improvement of LEE for PC LEDs was mainly due to lattices scattering and diffraction more than photonic band gap effects. And considering that HL has its unique advantages such as one-step recording, large scale and low cost fabrication, holographic structures may have a promising potential when fabricating PC LEDs in practice. The more comprehensive study in this field will be our next task. Acknowledgements This work is supported by the National Natural Science Foundation (61240015, 51102148), the National Science Foundation of GuangDong Province (S2012010010030), and Shenzhen Institute of Information and Technology Project (YB201007), Shenzhen Science and Technology plan Project (JCYJ20120615101957810, JCYJ20120821162230170). References [1] C.C. Liu, Y.H. Chen, M.P. Houng, Improved light-output power of GaN LEDs by selective region activation, IEEE Photon. Technol. Lett 16 (6) (2004) 1444–1446. [2] T. Nishida, H. Saito, Efficient and high-power AlGaN- based ultraviolet light-emitting diode grown on bulk GaN, Appl. Phys. Lett. 79 (6) (2001) 711–712. [3] A.I. Zhmakin, Enhancement of light extraction from light emitting diodes, Phys. Rep. 498 (2011) 189–241. [4] T. Fujii, Y. Gao, R. Sharma, E.L. Hu, S.P. DenBaars, S. Nakamura, Increase in the extraction efficiency of GaN-based lightemitting diodes via surface roughening, Appl. Phys. Lett. 84 (2004) 855–857. [5] Dang Hoang Long, In-Kag Hwang, Sang-Wan Ryu, Design optimization of photonic crystal structure for improved light extraction of GaN LED, IEEE J. Sel. Top. Quantum Electron. 15 (4) (2009) 1257–1263. [6] H. Gao, K. Li, Improving light extraction efficiency of GaN-Based LEDs by AlxGa1xN confining layer and embedded photonic crystals, IEEE J. Sel. Top. Quantum Electron. 18 (6) (2012) 1650–1660. [7] E. Matioli, Impact of photonic crystals on LED light extraction efficiency: approaches and limits to vertical structure designs, J. Phys. D: Appl. Phys. 43 (2010) 354005. [8] Kyeong-Jae Byeon, Joong-Yeon Cho, Fabrication of SiNx-based photonic crystals on GaN-based LED devices with patterned sapphire substrate by nanoimprint lithography, Opt. Express 20 (10) (2012) 11423–11432. [9] S. Foteinopoulou1, C.M. Soukoulis, Electromagnetic wave propagation in two-dimensional photonic crystals: a study of anomalous refractive effects, Phys. Rev. B 72 (2005) 165112-1–165112-20. [10] R. Gajic´, R. Meisels, F. Kuchar, K. Hingerl, Refraction and rightness in photonic crystals, Opt. Express 13 (2005) 8596–8605. [11] E. Yablonovitch, T.J. Gmitter, K.M. Leung, Photonic band structure: the face-centered-cubic case employing nonspherical atoms, Phys. Rev. Lett. 67 (1991) 2295–2298. [12] X.Y. Ao, S.L. He, Three-dimensional photonic crystal of negative refraction achieved by interference lithography, Opt. Lett. 29 (2004) 2542–2544. [13] A. David, High-Efficiency GaN-Based Light-Emitting Diodes: Light Extraction by Photonic Crystals and Microcavities, Ph.D. Thesis, Ecole Polytechnique, Paris, France, 2006, pp. 91–109 (Chapter 4). [14] J. Park, J.-K. Oh, K.W. Kwon, Y.H. Kim, S.S. Jo, J.K. Lee, S.W. Ryu, Improved light output of photonic crystal light-emitting diode fabricated by anodized aluminum oxide aano-patterns, IEEE Photon. Technol. Lett. 20 (4) (2008) 321–323. [15] K.M. Ho, C.T. Chan, C.M. Soukoulis, Existence of a photonic gap in periodic dielectric structures, Phys. Rev. Lett. 65 (1990) 3152–3155. [16] X.L. Yang, L.Z. Cai, Q. Liu, Theoretical bandgap modeling of two-dimensional triangular photonic crystals formed by interference technique of three-noncoplanar beams, Opt. Express 11 (9) (2003) 1050–1055. [17] M. Campbell, D.N. Sharp, M.T. Harrison, R.G. Denning, A.J. Turberfield, Fabrication of photonic crystals for the visible spectrum by holographic lithography, Nature 404 (2000) 53–56. [18] S. Manak, D.V. Karasev, V.K. Kononenko, K. Valerii, S.V. Nalivko, A.A. Romanenko, A.A. Vitalisov, Polarization characteristics of quantum-well semiconductor structures, Proc. SPIE 3094, 1997, 2–17. [19] G.M. Laws, E.C. Larkins, I. Harrison, C. Molloy, D. Somerford, Improved refractive index formulas for the AlxGa1–xN and InyGa1-yN alloys, J. Appl. Phys. 89 (2001) 1108–1115. [20] C. Wiesmann, Nano-Structured LEDs-Light Extraction Mechanisms and Applications, Ph.D. Thesis, Science Faculty, University Regensburg, Regensburg, Germany, pp. 41–45 (Chapter 4: 32). [21] U. Köhler, D.J. As, B. Schöttker, T. Frey, Optical constants of cubic GaN in the energy range of 1.5–3.7 eV, J. Appl. Phys. 85 (1999) 404–407.
Contents lists available at ScienceDirect
Superlattices and Microstructures journal homepage: www.elsevier.com/locate/superlattices
Optimization design of holographic photonic crystal for improved light extraction efficiency of GaN LED X.X. Shen a,⇑, Y.Z. Ren a, G.Y. Dong b, X.Z. Wang a, Z.W. Zhou a a b
Shen Zhen Institute of Information and technology, ShenZhen 518072, China College of Materials Science and Opto-Electronic Technology, University of Chinese Academy of Sciences, BeiJing 100084, China
a r t i c l e
i n f o
Article history: Received 4 September 2013 Accepted 27 September 2013 Available online 6 October 2013 Keywords: Photonic crystals Holographic interferometry Light emitting diode
a b s t r a c t A study on improved light extraction efficiency (LEE) of LEDs with photonic crystals formed by holographic lithography (HL) was present. The propagation and extraction of light in LEDs were simulated using FDTD method for LED structures with top HL PC and embedded HL PC respectively. By optimizing the design parameters of the HL PC, the best value of 88.3% enhancement of LEE were obtained. Result also revealed that the scattering and diffraction of photonic lattices play a more important role in the increased light extraction of HL PC LEDs than photonic band gap effects. Ó 2013 Elsevier Ltd. All rights reserved.
1. Introduction GaN-based LEDs play an important role recently in many fields, since they can be widely used in medical operations, traffic lights, mobile devices, flat panel displays, general lighting, and many other fields. However, external quantum efficiency of LEDs is still not high enough to realize LED-based solid state lighting, even the internal quantum efficiency is relatively high [1,2]. The external quantum efficiency is mainly limited by low light extraction efficiency (LEE). And one of the primary reasons for low LEE is the total reflection at the interface of the semiconductor and the outer medium. In order to improve the LEE, a number of approaches have been applied, such as LEDs grown over patterned sapphire substrates, shaped LED ships, photon recycling, coupling to surface plasmon modes [3], surface roughening [4] and photonic crystals [5–8]. The aims of surface roughening and photonic crystals
⇑ Corresponding author. E-mail address: [email protected] (X.X. Shen). 0749-6036/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.spmi.2013.09.043
304
X.X. Shen et al. / Superlattices and Microstructures 64 (2013) 303–310
used in LEDs are both to avoid total internal reflection and prevent the lateral propagation of lightwaveguide effect. Though the randomizing light reflection at roughed surface destroyed the light propagation in straight paths and made light escaped from the LEDs through the critical cone, yet it provides little control on the direction of the light emission, which result in Lambertian radiation patterns. Compared with surface roughening method, PCs used in LEDs have been researched in many works and demonstrated to provide superior light extraction and directional light emissions. Most studies used 2-D PCs with regular circle columns formed by RIE or electron beam lithography. Since the holographic lithography (HL) approach for PCs fabrication has its unique advantages such as one step recording in large scale [9,10], which made the industrialization of production low cost and easy; And holographic structures usually have irregular atoms or columns, the light propagation properties of PCs are closely related to their specific structures [11,12], we may expect some difference in light extraction behavior between LED structures with regular and holographic photonic crystals. The fabrication of a PC on the top of an LED degrades the Ohmic contact between the P-GaN and the Ohmic metals, and the low interaction of the PCs with some of the guided modes limits the potential enhancement in extraction efficiency, as these modes are not well diffracted by shallow PCs due to their poor overlap with the etch region [13]. Thus LEDs with embedded PC inserted below the active layer were researched to improve the light extraction efficiency [14]. The embedded PC was fabricated in highly conductive N-GaN cladding, and both p-type and n-type Ohmic performance were not degraded. To fully utilize the advantage of an LED with embedded PC, structures of LEDs with top or embedded PCs are researched. In our study, we used the finite-difference time-domain (FDTD) method to study the light extraction characteristics of LEDs with various PC structures formed by holographic lithography and compared the improved enhancement results. The HL PC structures were introduced in Section 2; the enhancements of light extraction of LEDs with top and embedded HL PCs were analyzed and compared in Section 3, We also analysized the distribution of band gap for HL PC structures using the plane wave method (PWM) [15] with the wave number of 729 in Section 3, to demonstrate the point that the increased light extraction of HL PC LEDs was mainly due to lattices scattering and diffraction more than photonic band gap effects. 2. Structures and FDTD method In our analysis, there are two steps carried out to fabricate holographic PCs onto the LED structures: (1) Fabricating triangular pattern in photo resist layer using holographic lithography; (2) Transferring the pattern into GaN layer. We used an interference technique of three non-coplanar beams (ITNB) to fabricate the 2-D triangular lattices. The intensity distribution of the holographic structure we adopt can be expressed as [16]
2p 2p 3 2p 3 I ¼ 3 þ cos pffiffiffi ð2yÞ þ cos pffiffiffi pffiffiffi x þ y þ cos pffiffiffi pffiffiffi x y : 3a 3a 3a 3 3
ð1Þ
By controlling the exposure intensity, introducing an intensity threshold It, (here It e(1.5, 6) for Eq. (1)), which is a specific value the region with light intensity below it can be removed and the region above it will remain due to photo polymerization for negative photoresist, we may wash away the region of I < It to get a normal structure. By filling this structure with a material of high dielectric constant and then removing the template, an inverse structure can be obtained [17]. In our situation, we used the inverse structure which means that the dielectric constant distribution e(x, y) of result lattice should be 1 in the region I(x, y) > It, represented by the white part (air); and 5.86 in the region I(x,y) < It, represented by black part (GaN with the refractive index of 2.42 at a wavelength of 465 nm). To find the difference between the holographic structures and the regular ones, we chose several lattices shown in Fig. 1 for investigation, here (a), (b) and (c) are the shape and size of the cross section of air columns with different intensity threshold It and filling ratio FR. The relation between It and FR of the air column is shown in Fig. 2, to optimize the structures so as to maximize the LEE of LEDs, the effect of different threshold and corresponding FR has been examined. Light extraction characteristics of LEDs with various PC structures formed by holographic lithography were studied using FDTD method with the calculation domain shown in Fig. 3. The simulated LED
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Fig. 1. Variation of the shape and size of the cross section of air columns with different It and filling ratio FR. (a) It = 1.9, FR = 83.10%; (b) It = 2.4, FR = 57.68%; (c) It = 3.5, FR = 32.74%.
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Fig. 3. FDTD simulation domain and LED structure with (a) top HL PC and (b) embedded HL PC.
structure is composed of a P-GaN layer, a multi-quantum-well (MQW) active layer, an N-GaN layer, and a sapphire substrate. And a 2D triangular HL PC with the shape of air columns described in Fig. 1 was formed on the top surface of the LED or located below the MQW active layer, as shown
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in Fig. 3(a) and (b) respectively. To solve the calculation problems of FDTD simulation for any realistic LED device, we used a simplified LED with a cross section of smaller size and applied perfect mirrors at four lateral sides (shown as blue1 line in Fig. 3), and the calculation domain was chosen as 4 lm 4 lm. The radiating source of LED was represented by a point dipole located in the middle of active region, and we assume the emitted radiation has TE polarization since the point dipole was allowed to move in the xy-plane of MQW [18]. The radiate spectrum of this dipole was centered at 465 nm with a full-width at half-maximum of 10 nm. In our simulation the refractive indexes of GaN and sapphire at a wavelength of 465 nm were 2.42 and 1.77 respectively [19]. Perfect matched layer was used outside the calculation region in order to suppress the reflection at the boundary. The energy of extracted light was measured by the integration of Poynting vectors at the detected surfaces surrounding all sides of the LED [20], which were shown in Fig. 3 using red dashed line rectangular. 3. FDTD results and discussion The enhancements of the LEDs were calculated in this section, when using various PC structures with HL triangular patterns. PC parameters such as the PC thickness d, the filling ratio of air columns FR, and the position of PC located were considered either, to find the optimal design of a HL PC LED for improved light extraction and compare the results of enhancement when using top and embedded HL PCs. The enhancement factor genhance can be represented as:
genhance ¼
EPC E0 E0
ð2Þ
where EPC is the integrated energies of light escaped from the LED with PC structures, and E0 for the ordinary LED. The power loss in GaN during the simulation was ignored since the imaginary part of the GaN index is closed to zero at the wavelength of 465 nm [21]. 3.1. LED with top HL PC structure As described in Fig. 3, the simulated LED structures with a top HL PC consisted of a P-GaN layer with the thickness of 200 nm, a MQW active layer, an N-GaN layer of 800 nm, and the sapphire substrate 1 lm, with a cross-sectional area of 4 lm 4 lm, and the grid size for FDTD was Dx = Dy = Dz = 20 nm. The relativity between the improvement of LEE and the PC parameters was studied using a standard top HL PC LED with a = 300 nm, It = 3.5, FR = 32.74%, and the thickness of PC slab d = 150 nm. When the enhancement of LEE was calculated each time, other parameters of PC were kept the same as mentioned. Only one situation of dipole source has y-direction polarization was concerned, since the simulation results were similar with x-polarization [5]. The relativity between the improvement of LEE and the top HL PC parameters is shown in Fig. 4. The thickness of HL PC was varied from 0.1a to 0.8a, and the filling ratio of air columns was 0 to 1, respectively. From Fig. 4(a), we see that the enhance factor of LEE increased with the varying thickness of PC. However, the fabrication of PC with a large thickness was very difficult in experiment, the thickness of PC is smaller than the lattice constant a ordinarily. So in this case the PC thickness of 0.4–0.7a is enough for the improvement of genhance. In Fig. 4(b), the enhancement of LEE was high when the filling ratio changes from 0.3 to 0.75, but dropped quickly when FR became too small or too large. The peak value was archived when FR = 0.58, and the It of HL PC was 2.4, the corresponding lattice pattern was given in Fig. 1(b). This result was reasonable due to the contrast of index. 3.2. LED with embedded HL PC structure For an LED with an embedded HL PC as shown in Fig. 3(b), the parameters of simulated LED structure were almost the same as LED with top HL PC, only the thickness of N-GaN layer changed to 4 lm in order to locate the embedded PC. The standard embedded HL PC with the same parameters as top 1
For interpretation of color in Fig. 3, the reader is referred to the web version of this article.
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Fig. 4. Enhancement of light extraction efficiency as a function of (a) PC thickness, and (b) Filling ratio of air columns for the top HL PC LED.
PC: a = 300 nm, It = 3.5, FR = 32.74% and the thickness d = 150 nm, the PC was 8a below the MQW at first. We changed PC thickness, filling ratio, PC location and the lattice constant in turn, and kept the other parameters the same as beginning each time. The relation between the enhancement of light extraction efficiency and the embedded PC parameters is shown in Fig. 5. From Fig. 5(a), we can see the relation between the enhancement of LEE and the thickness of HL PC, LEEs of LED increase with the thickness of PC from 0 to 0.6a, and the largest enhancement was obtained when d was 0.4–0.6a, however this ascending trend stops at this thickness and changes to fluctuation as the thickness of PCs getting bigger. This was caused by the confinement effect in the cavity between the surface of the LED and the PC. In this case, the embedded PC acted as a mirror, the reflected waves of light incident on the top surface of PC and light incident on the bottom of PC may have interference effect, and when the interference were constructive the enhancement of LEE would be high. The HL PC can be considered as an isotropic thin film with an effective refractive index neff, which can be calculated as: neff = FRnair + (1 FR)nGaN, and the thickness of PC for constructive interference can be estimated by d = (m + 1/2)k/2neff (m = 1,2. . .), in our case for the standard PC structure, neff = 1.955, for the wavelength of 465 nm, d 180 nm, 300 nm, and 420 nm when m = 1, 2, 3 respectively, corresponding to 0.6a, 1.0a,1.4a in Fig. 5(a) where the highest enhancements were obtained. In Fig. 5(b), the simulation result of relation between genhance and FR was close to that of LED with top PC. We obtained the highest enhancement of LEE at a filling ratio of 0.32 (It = 3.5, and the corresponding lattice pattern was given in Fig. 1(c)), LEE then dropped fast when the filling ratio became too small or too large. The relation between genhance and the location of PC was also analyzed. The embedded PC was formed and covered before MQW growth, so the distance would influenced the internal quantum efficiency, usually for a high quality MQW a thickness of several micrometers for GaN layer was needed [14]. And most of energy radiate from the active region was concentrated in the cavity formed by the embedded PC and LED surface, and the smaller distance from the top of embedded PC to MQW means more radiate energy near the LED surface, which results in a bigger chance for photons to escape from the LED. Therefore, the location of embedded PC should be considered and make compromises between internal quantum efficiency and light extraction efficiency. From Fig. 5(c) we can see the simulation result proved our analysis that when the distance was varied from 0 to 12a, the enhancement of LEE almost decreased linearly. At last before the lattice constant was considered, we know that there are three main mechanisms of using PC to increase LEE: First, the existence of photonic band gap (PBG), light with frequencies within the band gap cannot propagate laterally and was coupled into radiation modes, result in an enhancement of the extraction in the vertical direction from an LED; Second, the diffraction effect
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Fig. 5. Enhancement of light extraction efficiency as a function of (a) embedded PC thickness, (b) filling ratio of air columns for the embedded HL PC LED. (c) Distance from the top of the PC to the MQW, and (d) lattice constant for the embedded PC.
when PC acting as a Bragg grating; Third, the diffused scattering by PC structure, which broke the total internal reflection condition of guided light. In order to make out which mechanism play the most important role in enhancement of LEE, we calculated the photonic band diagrams for the triangular holographic PC with varied It, Fig. 6 shows the dependence of the PBG on the It, extracted from band structure calculations when It changes from 1.5 to 5.5. The blue dashed area represented the distribution of PBG between TE1 and TE2 using normalized frequency units (xa/2pc), and the red dotted line indicate the corresponding relative band gap (measured by gap to mid-gap ratio Dx/x0). From Fig. 6 the PBG can be observed for a wide region when It varied from 1.9 to 4.8((the corresponding FR: 0.8310–0.1335), and the relative band gap can be as high as 29.92% when It = 2.5. For the standard HL PC with It = 3.5 we simulated, the PBG appears from 0.2916 to 0.3477, which corresponded to 136–162 nm for lattice constant a with the wavelength of 465 nm. And the central normalized frequency is 0.3196, corresponded to 149 nm. We suggested that the LEE should be highest when light in the PBG for the first mechanism mentioned before. However, from Fig. 5(d) when a was small the enhancement of LEE was small and then getting higher with increased a, though for a = 150 nm when light in the PBG LEE had a little rise, the highest enhancement appeared when a was 450–650 nm. It is obvious that the existence of a photonic band gap was not the main reason for the increased light extraction of HL PC LEDs, since the strong reduction in spontaneous radiative emission rate for photos within the band gap requires low temperature operation to diminish the effect of competing non-radiative recombination and maintain good internal quantum efficiency. Enhancement of LEE would mainly due to lattices scattering more than photonic band gap effects.
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3.3. Comparisons To get a comprehensive understanding for the holographic PC to improve the LEE of LEDs, we compared the improvement of the LEDs with a top and embedded HL PC, and LED with both top and embedded PCs. For FDTD simulations, the same PC structure was used with a = 300 nm, a filling ratio of air column FR = 0.3274 when It = 3.5, and a PC thickness of 0.5a. The locations of embedded PCs were at the distance of 200 nm below the MQW. The integrated emitted energy were calculated with increasing simulated time steps for three LED structures, and the enhancements compared with ordinary LED were given in Fig. 7. Here the time step dt = Dx/2c (c is the speed of light), and n is the integrated steps, 5000 steps is enough for the accuracy of the simulation since the results almost keep the same when integrated time steps increased from 5000 to 10,000. The black, red, and blue dotted lines represent LEDs with top PC, with embedded PC, and with both top and embedded PCs, respectively. At the extracted time step n = 5000, compared with traditional LEDs without PCs, the calculated radiative energies of the LEDs with top and embedded PCs were enhanced by 71.5% and 82.0% respectively, and 88.3% for LED with both top and embedded PCs. Since the fabrication of LEDs with both top and embedded PCs is much more expensive and complicated, and the improvement is inconsiderably, to achieve a high light extraction efficiency using LEDs with top or embedded PC only is quite enough.
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4. Conclusions We have investigated the improvement of light extraction efficiency of GaN LED with PC structure formed by holographic lithography. The simulation result had given the optimized design of top and embedded HL PCs for LEDs to achieve the highest LEE. Results showed that the embedded PC was more effective in improving the LEE, because embedded PC has interaction with all guided modes in the LEDs, since most of the radiative energy was confined in the cavity between the top surface of the LED and the embedded PC, though the distance between the MQW and the embedded had to be considered and make compromise between IQE and LEE. The study also revealed that the improvement of LEE for PC LEDs was mainly due to lattices scattering and diffraction more than photonic band gap effects. And considering that HL has its unique advantages such as one-step recording, large scale and low cost fabrication, holographic structures may have a promising potential when fabricating PC LEDs in practice. The more comprehensive study in this field will be our next task. Acknowledgements This work is supported by the National Natural Science Foundation (61240015, 51102148), the National Science Foundation of GuangDong Province (S2012010010030), and Shenzhen Institute of Information and Technology Project (YB201007), Shenzhen Science and Technology plan Project (JCYJ20120615101957810, JCYJ20120821162230170). References [1] C.C. Liu, Y.H. Chen, M.P. Houng, Improved light-output power of GaN LEDs by selective region activation, IEEE Photon. Technol. Lett 16 (6) (2004) 1444–1446. [2] T. Nishida, H. Saito, Efficient and high-power AlGaN- based ultraviolet light-emitting diode grown on bulk GaN, Appl. Phys. Lett. 79 (6) (2001) 711–712. [3] A.I. 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