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Enhancement of the light-extraction efficiency of light-emitting diodes with SiO2 photonic crystals
Optik 161 (2018) 27–37
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Original research article
Enhancement of the light-extraction efficiency of light-emitting diodes with SiO2 photonic crystals Meng Liu a,b , Kang Li a,∗ , Fan-min Kong a , Jia Zhao a , Hao-tian Meng a a b
School of Information Science and Engineering, Shandong University, Jinan 250100, China School of Physics and Electronics Engineering, Qilu Normal University, Jinan 250200, China
a r t i c l e
i n f o
Article history: Received 28 September 2016 Received in revised form 12 December 2017 Accepted 31 January 2018 Keywords: SiO2 Photonic crystals (PhC) Light-extraction efficiency (LEE) Light-emitting diodes (LEDs) Finite-difference time-domain (FDTD)
a b s t r a c t In this paper, we proposed a method of using SiO2 photonic crystals (PhC) to improve the light-extraction efficiency (LEE) of light-emitting diodes (LEDs). Numerical simulations based on the finite-difference time-domain (FDTD) algorithm were performed to reveal the mechanism of using SiO2 PhC to improve the light extraction of LEDs. The effects of several critical parameters, including the depth, the filling factor, and the radius of SiO2 PhC on the enhancement of LEE were investigated. The rigorous coupled-wave analysis (RCWA) method was utilized to verify the variation trends we got from the FDTD simulations. The LEE of the LEDs with normal air-hole PhC structures and the conventional planar LEDs were also studied for comparison. According to our calculations, more than 37% improvement has been achieved in the LEE of the SiO2 PhC LEDs in comparison to that of the conventional planar LEDs. And SiO2 PhC LEDs obtained more light extraction than normal air-hole PhC LEDs. The influences of the SiO2 PhC on the current density and the temperature distributions in the active layer of LEDs have also been discussed in this paper. Results demonstrated no noticeable degradation in electrical and thermal characteristics under high current injections. © 2018 Elsevier GmbH. All rights reserved.
1. Introduction In recent years, GaN-based LEDs are widely used in flat-panel displays, optical communications, automobile lighting and other applications [1,2]. And they are expected to replace the conventional light sources in the near future. The critical issue in achieving this destination is to improve the internal quantum efficiency (IQE) and the LEE. Nowadays, the IQE has been improved significantly with the development of the crystal quality and the epitaxial growth technology [3]. On the other hand, the LEE is still very low due to the total internal reflection (TIR) and the Fresnel reflection [4], especially the TIR. For example, for GaN planar LEDs, that is, there is no additional structure on the top of the LEDs, the LEE is only about 4%. Aiming to increase the LEE of LEDs, numerous methods have been implemented, such as the nano-patterned sapphire substrates (NPSS) [5], nano-array surfaces[6,7], surface roughing [8], and PhC [9–12]. In particular, PhC structures as an effective way to increase the LEE of LEDs have received great attention. In general, the PhC structures can be used to prevent emission into guided modes (deep etched holes) or to couple light from the guided modes into radiation modes (shallow etched holes) [13,14]. And systematical investigations have been carried out on the dependences of LEE on various structural parameters such as the filling factor, the PhC depth, and the radius to get an optimal structure [15,16]. However, the material
∗ Corresponding author. E-mail address: [email protected] (K. Li). https://doi.org/10.1016/j.ijleo.2018.01.128 0030-4026/© 2018 Elsevier GmbH. All rights reserved.
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Fig. 1. (a) The cross section schematic of the SiO2 PhC LEDs for FDTD simulations; (b) The schematic diagram of three typical dipole sources location in the x–y plane. A, B, and C represents the position that between two PhCs, in the center of three PhCs, and under one PhC, respectively; (c) The schematic model of SiO2 PhCs LEDs used in the current density and the temperature distributions simulations.
filling the PhC holes, which is another important parameter has been rarely considered, since most PhC used in the previous researches are air-holes. Recently, Huang et al. [17] fabricated a NPSS and a SiO2 photonic quasi-crystal on an n-GaN layer of LEDs through nanoimprinting technique and achieved a significantly greater light output power than that of the conventional LEDs. Wei et al. [18] have embedded 2D SiO2 PhC in p-GaN through a method of nano-spherical-lens photolithography and found the light output power (at 350 mA) of LEDs with SiO2 PhC was enhanced by 71.3% comparing to the planar LEDs, while that of normal air-hole PhC LEDs was enhanced by 49.3%. In their ensuing research [19], they embedded large-scale SiO2 PhC in the nGaN and p-GaN layers of LEDs to improve the efficiency of LEDs. Results showed that at 350 mA current injection, the light output power of bottom, top, and double SiO2 PhC LEDs was enhanced by 74.5%, 60.1%, and 88.2%, respectively, comparing to that of the conventional planar LEDs. Wu et al. [20] fabricated wafer-scale SiO2 PhC on indium tin oxide (ITO) layer of LEDs via novel nanospherical-lens lithography. In their proposed method, 300 nm thick SiO2 layer was deposited onto the ITO transparent conductive layer using plasma enhanced chemical vapor deposition (PECVD), and nanoscale polystyrene spheres were self-assembled into a hexagonal closed-packed monolayer array acting as convex lens for exposure to fabricate the SiO2 PhC. And results indicated that the light out power was enhanced by as 40.5% over those of as-grown LEDs. There might be many reasons for these enhancements, such as improvements of the LEE and the IQE. In order to have a deep insight of the mechanism that SiO2 PhC improving the light out power, we investigated the LEE of the SiO2 PhC LEDs in detail and compared it with the air-hole PhC LEDs. Furthermore, theoretical optimization of the structural parameters was still a requisite for the LEE improvement in the experimental fabrication. In this paper, 2D SiO2 PhC was fabricated on the top surface of LEDs, which gave more than 37% enhancement of LEE comparing to the conventional planar LEDs and provided more than 10% enhancement of LEE comparing to the normal airhole PhC LEDs. To find the optical performances of these aforementioned structures, we used 3D FDTD method to calculate the LEE. The reflections based on RCWA calculations in combination with the far-field distributions based on FDTD method were demonstrated to verify the simulation results and to further reveal the emission characteristics of SiO2 PhC LEDs. Moreover, the electrical and thermal performances of the proposed SiO2 PhC LEDs were also presented and investigated in this paper. 2. Simulation model and numerical method In order to investigate the effects of SiO2 PhC on the light extraction of LEDs, 3D FDTD method was used to calculate the LEE of the PhC LEDs and the planar LEDs. Here, both the SiO2 PhC LEDs and the air-hole PhC LEDs were calculated for comparison. The LEDs epitaxial layer structures were grown on a 1-m-thick sapphire substrate and were consisted of a 1.8-m-thick n-GaN layer, a 200-nm-thick p-GaN layer and a 250-nm-thick ITO current spreading layer from bottom to top as shown in Fig. 1(a). Balancing the calculation time and the results accuracy, a computational domain of 4 m × 4 m in the x-y plane was chosen during the simulations, since it has been demonstrated that a bigger calculated field size would have little effect on the LEE [21]. The active layer was embedded between the n-GaN layer and p-GaN layers, and was represented by a point dipole source with wavelength of 450 nm [22,23]. In order to present the random electron-hole pair combinations in the MQW layer, the typical locations and polarizations of the dipole sources were needed in each simulation. In 3D FDTD method, three polarizations of dipole sources along the x axis, y axis, and z axis were considered in the simulation. However, since it has been proved that dipoles polarized in the xy-plane were responsible for most LEDs emission [24], and there was no anisotropy in the xy-plane [15,25,26], so in order to reduce the computational cost, only E//x polarization was calculated during the simulations, although the results might be more precise when both E//x and E//y polarization were considered. Usually, the LEE would increase under the influences of the PhC. However, with the variation of the relative position between the dipole source and the PhC, the enhancement of LEE changed. In order to get a precise result, we have located the dipole in three typical positions as shown in Fig. 1(b), that was, between two PhCs, in the center of three PhCs, and under one PhC. And the final results were gotten by averaging the results of these three separate simulations. Since FDTD method was
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Fig. 2. (a) The refractive index (n) of GaN, ITO, and SiO2 ; (b) the extinction coefficient (k) of GaN, ITO, and SiO2 .
intrinsically a coherent simulation method, multi-reflection of the light inside the LEDs chip would result in an unphysical interference pattern. This would further influence the simulation results, especially the far-field pattern. For this reason, the Berenger perfectly matched layer (PML) [27] was added to the edge of the simulation domain as the absorbing boundary during the simulations, which could absorb the incident light with zero reflection. And the width of PML was set as 100 nm which could effectively absorb all incident energy. A homogeneous mesh-grid of 10 nm was used during the simulations, which was about/18n, and n was the refractive index of the materials. This meant about 10 spatial grids in the PML. Furthermore, although the PhC was periodical, periodic boundary conditions were not suitable in the simulations, since the periodic continuation of the simulation domain would replicate the dipole and interfere with other dipoles [28]. As far as the refractive index (n) of the materials were concerned, the refractive index of GaN at 450 nm was set as nGaN = 2.5, and those of ITO and SiO2 were taken to be nITO = 2.0 and nSiO2 = 1.5, respectively, as shown in Fig. 2(a). In addition, we could find from Fig. 2(b) that the extinction coefficient (k) of GaN, ITO, and SiO2 were closed to zero at the wavelength of 450 nm, then we ignored the material absorption during the simulations [29–31]. A power monitor was placed above the surface of LEDs to measure the power flux extracted from the top side of LEDs (Pout ), and a box monitor enclosing the dipole source was used to calculate the whole power emitted from the dipole source (Psource ). Then the LEE was defined as [13]: extr = Pout /Psource
(1)
And the LEE enhancement factorFFwas defined as extr − 0 × 100% F= 0
(2)
where extr was the LEE of LEDs with PhC structures, and 0 was the LEE of the conventional planar LEDs. In addition, the current density and the temperature distributions in the active region of LEDs at high current density injections (about 125 A/cm2 ) were also investigated through the finite-element method (FEM). And the schematic model of SiO2 PhCs LEDs used in the current density and the temperature distributions simulations was shown in Fig. 1(c). For the sake of simplicity, we ignored the details of the MQW and barriers, since it has been proved by Huang et al. [32], the resistance characteristic of the p-n junction dominated at high current density injection. Concerning the other epi-layers, their electronic characteristics followed the Ohm’s law:
J(r) = − · ∇ ϕ
(3)
where was the electrical conductivity, and ϕ denoted the electric potential. And the electrical conductivity of the p-/ncontact, SiO2 , ITO, p-GaN, and n- GaN were set as 1e15, 1e12, 1e7, 35, and 1e4 s/m, respectively. Insulated boundary conditions have been chosen during the simulations except for the p- and n-contacts which were set as metal contact boundary conditions. And all interfaces between the epi-layers and contacts were assumed to be Ohmic contacts. 3. Results and discussion At the beginning, we calculated the LEE of the planar LEDs with ITO placed on the top of GaN. Under the influence of TIR, the LEE of LEDs can be defined as extr
Pout = = Psource
c 0
2r 2 sin d 4r 2
=
1 (1 − cos c ) 2
(4)
where c = arcsin(n1/n2) is the critical angle. For GaN planar LEDs, the LEE is about 4%, while adding ITO on the top of GaN, the LEE of the top surface is about 6.7%. However, because of the TIR between the GaN and ITO layer, the overall LEE of LEDs
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Fig. 3. (a) LEE enhancement factor F as a function of the depth of the SiO2 PhC; Polar projection of the far-field intensities of SiO2 PhC LEDs with depth equals (b) 240 nm, (c) 320 nm and (d) 420 nm, respectively.
used in our simulations will be between 4% and 6.7%. Moreover, as far as the Fresnel reflection is concerned, the reflection ratio of the top surface of the ITO planar LEDs is: R=
n
− nair nITO + nair ITO
2
≈ 0.11
(5)
This will further reduce the LEE. According to our simulation, the LEE of planar ITO LEDs is about 4.6%, which can be reliable. 3.1. Effect of the SiO2 PhC depth on the LEE of LEDs Then the simulation of effect of the SiO2 PhC depth on the LEE of LEDs was conducted. Here, the depth of the SiO2 PhC was defined as the depth of SiO2 PhC embedded into the ITO layer, however, sometimes it might penetrate the ITO layer and embedded into the GaN layer. It was worth mention that, since it was still very difficult to fabricate PhC etching through the active layer, only shallow SiO2 PhC which could not penetrate the active layer was considered during the simulations. Since triangular lattice could offer more directions for light extraction, light incoming from more azimuthal angle in the GaN (ITO) layer could be extracted than square ones and 1D grating, we chose triangular lattice PhC in the simulations. This has also been proved in Ref. [24,33]. Then, the filling factor could be defined by: √ 2 ftriangle = 2RPhCs / 3a2PhCs (6) Here, RPhCs was the radius of PhC, and aPhCs was the PhC lattice constant, i.e., center-to-center distance between the neighboring PhC. Then the lattice constant of the SiO2 PhC was kept at 900 nm and the radius was 200 nm for the time being, which have been used to improve the LEDs light output performance in Ref. [18]. Using Eq. (6), we could calculate the filling factor, that was, about 0.18. Then the LEE of SiO2 PhC LEDs with PhC depth varied from 240 nm to 440 nm in step of 20 nm were calculated, and the results were shown in Fig. 3(a). From Fig. 3(a), it is clearly visible that with the increase of PhC etching depth, the LEE increases dramatically. However, this trend stops at some depth about 320 nm and begins to decrease as the depth increasing. The far-field radiation patterns were investigated to verify the above results. Here, the far-field radiation patterns of LEDs with depth of 240 nm, 320 nm, and 420 nm were demonstrated in Fig. 3(b), (c) and (d), respectively. We can see that when the PhC depth is 240 nm, the center intensity is a little higher than that of 320 nm. However, the whole intensity of LEDs with 320 nm depth PhC is significantly higher than that of 240 nm. Meanwhile, when the PhC depth equals 420 nm, the power intensity is more higher than that of 240 nm PhC depth LEDs, however, it is lower than that of LEDs with 320 nm depth PhC. This is in good agree with the variation trends of the LEE.
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Fig. 4. Effects of the SiO2 PhC radius r and the filling factor f on the LEE.
Fig. 5. (a) The reflection and transmission of the planar LEDs and the SiO2 PhC LEDs with different filling factors; (b) The calculated reflection at normal incidence as a function of wavelength.
3.2. Effects of the SiO2 PhC radius and the filling factor on the LEE of LEDs Then the effects of the PhC radius r and the filling factor f on the LEE of SiO2 PhC LEDs were investigated. During the simulations, the PhC depth was kept at 320 nm which has been obtained from above simulations, while the other two parameters, the radius and the filling factor, were varied to get the highest LEE. During the simulations, the radius was varied from 160 nm to 400 nm, and the filling factor was varied from 0.2 to 0.4. The results were shown in Fig. 4. From the viewpoint of LEE enhancement, these five lines in Fig. 4 have the similar variation trends. As the radius of PhC increasing, the LEE first increases and then decreases. We can also find that when the filling factor is smaller, a smaller radius is preferable to obtain larger LEE enhancement. On the other hand, when the radius is larger, a larger filling factor is suitable. As shown in Fig. 4, when the filling factor f equals 0.4, and the radius equals 380 nm, the highest LEE enhancement is achieved, that is, more than 37% enhancement comparing to the conventional planar LEDs. In order to verify the variation trend we got from the FDTD algorithm, we utilized the RCWA method to calculate the reflection and the transmission of the planar LEDs and the SiO2 PhC LEDs with different filling factors. Here, the wavelength of incident light was 450 nm, and the PhC radius was set to be 380 nm which has been obtained from the above calculations, and the results were shown in Fig. 5(a). As displayed in Fig. 5(a), the reflection and transmission of the SiO2 PhC LEDs are much better than that of the planar LEDs, while the SiO2 PhC LEDs with f = 0.4 are even better than the other SiO2 PhC LEDs. And the average reflection in the extraction cone (about 23◦ ) of the SiO2 PhC LEDs with filling factor varies from 0.4 to 0.2 are 5.7%, 8.3%, and 0.1%, respectively, while that of the planar LEDs is 11.4%. The calculated reflection at normal incidence as a function of wavelength is also shown in Fig. 5(b). From Fig. 5(b), we can find that the SiO2 PhC LEDs with f = 0.2 and f = 0.3exhibit higher reflection than planar LEDs in the wavelength scope of blue light, while the SiO2 PhC LEDs with f = 0.4 is a little better than the planar LEDs. The reflection at normal incidence of the SiO2 PhC LEDs with filling factor varies from 0.4 to 0.2 are 11.6%, 14.6%, and 15.6%, respectively, while that of the planar LEDs is 13.4%. That means the Fresnel reflection has also been reduced to a certain extent. In view of these, low TIR and Fresnel reflection enables better extraction of light, thereby enhancing the LEE. Notably, the value of reduction in the TIR and Fresnel reflection loss is much lower than the LEE enhancement that shown in Fig. 4. So we can infer that the enhancement of the light extraction may have something to do with the diffraction properties of the PhC.
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Fig. 6. The far-field power distributions of the SiO2 PhC LEDs with different configurations; the green dashed line indicates the far-field power distribution of the planar LEDs.
Fig. 7. The enhancement of LEE over the whole visible spectrum.
In order to show the application of PhC as a light extractor of light emission, we plotted the far-field power distributions of LEDs in Fig. 6. Here, the far-field distribution of the planar LEDs was also given for comparison. From Fig. 6, it can be seen that under the diffraction effect of the SiO2 PhC, as the filling factor of SiO2 PhC increasing, the far-field distribution is well modified. The power flux between angular −90◦ to 90◦ can be collected by the monitor placed above the top side of LEDs. So the area under the far-field curve can represent the output power of LEDs, that is, Pout . From Fig. 6, we can find that the emission intensities of SiO2 PhC LEDs are much stronger than that of planar LEDs in all directions. That means the incorporation of the SiO2 PhC is inclined to diffract much more emission energy out of the LEDs. As demonstrated in Fig. 6, the area under the far-field curve of LEDs with SiO2 PhC f = 0.4 and r = 380 nmis larger than the other SiO2 PhC configurations, and this implies more interaction with the guided modes and then more LEE enhancement can be achieved. The green dash line in Fig. 6 is the far-field power distribution of the dipole in planar LEDs, and its far-field pattern is near anisotropic. Under the diffraction of the SiO2 PhC, the power of LEDs is concentrated in the region between −30◦ to 30◦ . From Fig. 6, we can find that the main lobe of the radiation pattern is relatively wide, and the side lobes become weaker, which can benefit the extraction of light from the LEDs. And when the SiO2 PhC filling factor f = 0.4 and radius r = 380nm, we can find that more power is concentrated between the angular of −20◦ to 20◦ , that means better directional properties have been obtained. Until now, we have discussed the LEE of SiO2 PhC LEDs at a certain wavelength, i.e. 450 nm. However, LEDs have a wide emission wavelength range actually. Accordingly, we also calculated the LEE enhancement of the optimized structure along the whole visible spectral wavelengths, and the results were shown in Fig. 7. As can be seen from Fig. 7, the LEE spectrum of SiO2 PhC LEDs shows strong and broadband visible spectrum comparing with that of the normal GaN-based LEDs, not only at the 450 nm wavelength of interest. That is to say, the optimized structure can be used to increase the LEE in a broadband visible spectrum. 3.3. Effect of the air-hole PhC depth on the LEE of LEDs Then the simulations of the LEDs with air-hole PhC were carried out for comparison. Similar as that of the SiO2 PhC LEDs, the lattice constant of the PhC was kept at 900 nm and the radius was 200 nm. Then the LEE of normal air-hole PhC LEDs with PhC depth varied from 160 nm to 440 nm were calculated. Fig. 8(a) shows the variation of LEE for different depths of the air-hole PhC structure. As shown in Fig. 8(a), with the increase of the PhC depth, the LEE increases intensively, especially when the PhC depth is smaller than 200 nm. This can be explained by that the interaction between the PhC and the guided modes becomes stronger and stronger with the etching depth of the PhC increasing. However, this trend stops at some depth about 220 nm and begins to fluctuate as the depth increasing. This is analogous to that of the SiO2 PhC LEDs. As pointed by David [34], when the PhC depth was about /nPhC (nPhC is the
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Fig. 8. (a) LEE enhancement of LEDs with air-hole PhC as a function of the depth of PhC. Polar projection of far-field intensities of air-hole PhC LEDs with depth equals (b) 160 nm, (c) 220 nm and (d) 340 nm.
effective refractive index of the PhC layer), most guided modes will be diffracted by PhC, then the highest LEE will be gotten. With the PhC etching deeper, the LEE of PhC LEDs varies periodical fluctuation. This can be explained by the Fabry-Perot resonator theory [35]. k⊥ × 2dGaN + ϕPhC (m ) + ϕsapphire (m ) = 2m
(7)
where m is the mode number, ϕPhC (m ) and ϕsapphire (m ) are the phase changes reflected from the GaN-PhC and GaN-sapphire interfaces, respectively, dGaN is the thickness of un-etched GaN layer, and k⊥ is the perpendicular wave vector. As the PhC is etched deeper, the thickness of un-etched GaN layer decreases and it causes that the LEE appears periodical fluctuation. And the far-field distribution pattern of LEDs with SiO2 PhC depth equals 160 nm, 220 nm and 340 nm are also demonstrated here to verify the simulation results. From Fig. 8(b), (c), and (d), we can find that the far-field distribution pattern of LEDs with SiO2 PhC depth equals 220 nm is significantly higher than that of LEDs with SiO2 PhC depth equals 160 nm and 340 nm. 3.4. Effects of the air-hole PhC radius and the filling factor on the LEE of LEDs Then the effects of the PhC radius r and the filling factor f on the LEE of air-hole PhC LEDs were investigated. The PhC depth was kept at 220 nm as has been obtain from above simulation, while the other two parameters, the radius and filling factor, were varied to get the best LEE enhancement. The radius was varied from 160 nm to 520 nm and the filling factor was varied from 0.2 to 0.4. The results were shown in Fig. 9, and a similar phenomenon as the SiO2 PhC LEDs could be found. As presented in Fig. 9, when the filling factor f equals 0.4, and the radius equals 500 nm, more than 27% enhancement of LEE is achieved comparing to that of the conventional planar LEDs. Then, we utilized the RCWA method to calculate the reflection and the transmission of the planar LEDs, the air-hole PhC LEDs with different filling factors, and the results were shown in Fig. 10(a). As displayed in Fig. 10(a), with the filling factor of the air-hole PhC increasing, the reflection and the transmission of LEDs become better, and when f = 0.4, the highest transmission has been obtained. The average reflection in the extraction cone of the air-hole PhC LEDs with f varies from 0.4 to 0.2 are 4.6%, 7.7%, and 10.1%, respectively, while that of the planar LEDs is 11.4%. We also calculated the reflection at normal incidence as a function of wavelength and the results were shown in Fig. 10(b). From Fig. 10(b), we can find that the air-hole PhC LEDs with f = 0.4 exhibited lower reflection than planar LEDs in the wavelength scope of blue light. The reflection at normal incidence of the air-hole PhC LEDs with filling factor varies from 0.4 to 0.2 are 9.4%, 13.8%, and 15.7%, respectively, while that of the planar LEDs is 13.4%.
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Fig. 9. Effects of the air-hole PhC radius and the filling factor f on the LEE.
Fig. 10. (a) The reflection and the transmission of the planar LEDs and the air-hole PhC LEDs with different filling factors; (b) The calculated reflection at normal incidence as a function of wavelength.
Fig. 11. The far-field power distributions of LEDs with different PhC configurations; the green dashed line indicates that of planar LEDs.
Comparing with the average reflection in the extraction cone and the reflection at normal incidence of the SiO2 PhC LEDs, we can find that the air-hole PhC LEDs have even lower reflection; however, the SiO2 PhC LEDs have higher LEE. So we can infer that it must have something to do with the diffraction properties of the PhC. Then, as we have done in the previous SiO2 PhC LEDs simulations, the diffraction properties of the air-hole PhC were investigated, and the far-field power distributions were demonstrated in Fig. 11. Here, the far-field distribution of the optimized SiO2 PhC LEDs was also shown for comparison. From Fig. 11, it can be seen that the pattern of the far-field is well modified by the air-hole PhC comparing to that of the planar LEDs structure. When f = 0.4and r = 500 nmmore strong diffraction of the guided modes can be found. However, the SiO2 PhC LEDs have obtained more light diffracted out of the LEDs, especially between the angle −20◦ to 20◦ . That is to say, more light output power has been harvested when the normal air-hole PhC was replace by SiO2 PhC. Although the SiO2 PhC LEDs have only 10% enhancement of LEE than normal air-hole LEDs, we still believe that more enhancement of light output power will be gotten, since it has been proved in [18] that the SiO2 PhC can also exhibit partial compression strain release and reduced emission divergence which can improve the IQE. 3.5. The current density and the temperature distributions In order to get a deeper insight into the specific features of the LEDs operation, the current density and the temperature distributions in the active region of SiO2 PhC LEDs and the planar LEDs at high current density injections (about 125 A/cm2 )
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Fig. 12. The current density (dot) and the temperature distributions (hue) in the active layer of (a) the optimal SiO2 PhC LEDs and (b) the planar LEDs.
Fig. 13. The normalized current density along the line between two electrodes of the planar LEDs and the SiO2 PhC LEDs.
were shown in Fig. 12. As displayed in Fig. 12, both the SiO2 PhC and the planar LEDs demonstrate a uniform current density distribution in the active region. This is mainly because of the choice of the simulation domain is a few times less than the current spreading length in virtual LEDs. However, from the temperature distributions, the area near the n-contact has a little higher temperature, that means more current has crowded near the n-contact as a result of the current spreading effect of the ITO layer. This can be further explained by the normalized current density along the line between two electrodes. Form Fig. 13, we can find that because of the effect of ITO current spreading layer, the SiO2 PhC LEDs and the planar LEDs have similar current density distribution in the active layer, and have a current crowding near the n-contact. Although the current density distribution of the SiO2 PhC LEDs appears a little fluctuation, we can still find that the current density near the p-contact increases while that near the n-contact decreases, so a little more uniform current density distribution than the planar ITO LEDs will be obtained. Further more, we calculated the standard deviation of the normalized current density of these two kinds of LEDs, and found that the standard deviation of the normalized current density of SiO2 PhC LEDs was 0.032, while that of the planar ITO LEDs was 0.061, this meant that the current density of SiO2 PhC LEDs had a little improvement than the normal planar ITO LEDs. And in our previous paper [36], we have proved that current crowding near n-contact had little influence on the LEE. That is to say, the current and the temperature distributions here have little effect on the LEE. In a word, the high similarity of the current density and the temperature distributions of the SiO2 PhC LEDs and the planar LEDs means no noticeable degradation in the SiO2 PhC LEDs electrical and thermal properties. This conclusion is in line with the experiment observations which made in [37]. 4. Conclusion In the present study, the LEE of SiO2 PhC LEDs was systematically investigated with the help of 3D FDTD simulations. Through optimization, more than 37% enhancement of LEE has been achieved in case of a PhC depth h equaled 320 nm, a filling factor f equaled 0.4, and a radius r equaled 380 nm. The RCWA method was utilized to verify the variation trend gotten
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from the FDTD algorithm. For comparison, the normal air-hole PhC LEDs was also investigated, and the results indicated that SiO2 PhC LEDs had higher extraction efficiency. At last, the current density and the temperature distributions in the active region of SiO2 PhC LEDs and the planar LEDs at high current density injections were investigated. Results showed that there was no noticeable degradation in the SiO2 PhC LEDs electrical and thermal properties comparing with the conventional planar LEDs. These analyses suggested that SiO2 PhC LEDs could be envisioned to a promising candidate to replace the air-hole PhC LEDs and the presented results offered practical guidelines for the design of high efficiency SiO2 PhC LEDs. Acknowledgments This work is supported by the National Natural Science Foundation of China (61475084, 61327808) and the ScienceTechnology Foundation of the Higher Education Institutions of Shandong Province, China (J17KA054). References [1] E.F. 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Optik journal homepage: www.elsevier.de/ijleo
Original research article
Enhancement of the light-extraction efficiency of light-emitting diodes with SiO2 photonic crystals Meng Liu a,b , Kang Li a,∗ , Fan-min Kong a , Jia Zhao a , Hao-tian Meng a a b
School of Information Science and Engineering, Shandong University, Jinan 250100, China School of Physics and Electronics Engineering, Qilu Normal University, Jinan 250200, China
a r t i c l e
i n f o
Article history: Received 28 September 2016 Received in revised form 12 December 2017 Accepted 31 January 2018 Keywords: SiO2 Photonic crystals (PhC) Light-extraction efficiency (LEE) Light-emitting diodes (LEDs) Finite-difference time-domain (FDTD)
a b s t r a c t In this paper, we proposed a method of using SiO2 photonic crystals (PhC) to improve the light-extraction efficiency (LEE) of light-emitting diodes (LEDs). Numerical simulations based on the finite-difference time-domain (FDTD) algorithm were performed to reveal the mechanism of using SiO2 PhC to improve the light extraction of LEDs. The effects of several critical parameters, including the depth, the filling factor, and the radius of SiO2 PhC on the enhancement of LEE were investigated. The rigorous coupled-wave analysis (RCWA) method was utilized to verify the variation trends we got from the FDTD simulations. The LEE of the LEDs with normal air-hole PhC structures and the conventional planar LEDs were also studied for comparison. According to our calculations, more than 37% improvement has been achieved in the LEE of the SiO2 PhC LEDs in comparison to that of the conventional planar LEDs. And SiO2 PhC LEDs obtained more light extraction than normal air-hole PhC LEDs. The influences of the SiO2 PhC on the current density and the temperature distributions in the active layer of LEDs have also been discussed in this paper. Results demonstrated no noticeable degradation in electrical and thermal characteristics under high current injections. © 2018 Elsevier GmbH. All rights reserved.
1. Introduction In recent years, GaN-based LEDs are widely used in flat-panel displays, optical communications, automobile lighting and other applications [1,2]. And they are expected to replace the conventional light sources in the near future. The critical issue in achieving this destination is to improve the internal quantum efficiency (IQE) and the LEE. Nowadays, the IQE has been improved significantly with the development of the crystal quality and the epitaxial growth technology [3]. On the other hand, the LEE is still very low due to the total internal reflection (TIR) and the Fresnel reflection [4], especially the TIR. For example, for GaN planar LEDs, that is, there is no additional structure on the top of the LEDs, the LEE is only about 4%. Aiming to increase the LEE of LEDs, numerous methods have been implemented, such as the nano-patterned sapphire substrates (NPSS) [5], nano-array surfaces[6,7], surface roughing [8], and PhC [9–12]. In particular, PhC structures as an effective way to increase the LEE of LEDs have received great attention. In general, the PhC structures can be used to prevent emission into guided modes (deep etched holes) or to couple light from the guided modes into radiation modes (shallow etched holes) [13,14]. And systematical investigations have been carried out on the dependences of LEE on various structural parameters such as the filling factor, the PhC depth, and the radius to get an optimal structure [15,16]. However, the material
∗ Corresponding author. E-mail address: [email protected] (K. Li). https://doi.org/10.1016/j.ijleo.2018.01.128 0030-4026/© 2018 Elsevier GmbH. All rights reserved.
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Fig. 1. (a) The cross section schematic of the SiO2 PhC LEDs for FDTD simulations; (b) The schematic diagram of three typical dipole sources location in the x–y plane. A, B, and C represents the position that between two PhCs, in the center of three PhCs, and under one PhC, respectively; (c) The schematic model of SiO2 PhCs LEDs used in the current density and the temperature distributions simulations.
filling the PhC holes, which is another important parameter has been rarely considered, since most PhC used in the previous researches are air-holes. Recently, Huang et al. [17] fabricated a NPSS and a SiO2 photonic quasi-crystal on an n-GaN layer of LEDs through nanoimprinting technique and achieved a significantly greater light output power than that of the conventional LEDs. Wei et al. [18] have embedded 2D SiO2 PhC in p-GaN through a method of nano-spherical-lens photolithography and found the light output power (at 350 mA) of LEDs with SiO2 PhC was enhanced by 71.3% comparing to the planar LEDs, while that of normal air-hole PhC LEDs was enhanced by 49.3%. In their ensuing research [19], they embedded large-scale SiO2 PhC in the nGaN and p-GaN layers of LEDs to improve the efficiency of LEDs. Results showed that at 350 mA current injection, the light output power of bottom, top, and double SiO2 PhC LEDs was enhanced by 74.5%, 60.1%, and 88.2%, respectively, comparing to that of the conventional planar LEDs. Wu et al. [20] fabricated wafer-scale SiO2 PhC on indium tin oxide (ITO) layer of LEDs via novel nanospherical-lens lithography. In their proposed method, 300 nm thick SiO2 layer was deposited onto the ITO transparent conductive layer using plasma enhanced chemical vapor deposition (PECVD), and nanoscale polystyrene spheres were self-assembled into a hexagonal closed-packed monolayer array acting as convex lens for exposure to fabricate the SiO2 PhC. And results indicated that the light out power was enhanced by as 40.5% over those of as-grown LEDs. There might be many reasons for these enhancements, such as improvements of the LEE and the IQE. In order to have a deep insight of the mechanism that SiO2 PhC improving the light out power, we investigated the LEE of the SiO2 PhC LEDs in detail and compared it with the air-hole PhC LEDs. Furthermore, theoretical optimization of the structural parameters was still a requisite for the LEE improvement in the experimental fabrication. In this paper, 2D SiO2 PhC was fabricated on the top surface of LEDs, which gave more than 37% enhancement of LEE comparing to the conventional planar LEDs and provided more than 10% enhancement of LEE comparing to the normal airhole PhC LEDs. To find the optical performances of these aforementioned structures, we used 3D FDTD method to calculate the LEE. The reflections based on RCWA calculations in combination with the far-field distributions based on FDTD method were demonstrated to verify the simulation results and to further reveal the emission characteristics of SiO2 PhC LEDs. Moreover, the electrical and thermal performances of the proposed SiO2 PhC LEDs were also presented and investigated in this paper. 2. Simulation model and numerical method In order to investigate the effects of SiO2 PhC on the light extraction of LEDs, 3D FDTD method was used to calculate the LEE of the PhC LEDs and the planar LEDs. Here, both the SiO2 PhC LEDs and the air-hole PhC LEDs were calculated for comparison. The LEDs epitaxial layer structures were grown on a 1-m-thick sapphire substrate and were consisted of a 1.8-m-thick n-GaN layer, a 200-nm-thick p-GaN layer and a 250-nm-thick ITO current spreading layer from bottom to top as shown in Fig. 1(a). Balancing the calculation time and the results accuracy, a computational domain of 4 m × 4 m in the x-y plane was chosen during the simulations, since it has been demonstrated that a bigger calculated field size would have little effect on the LEE [21]. The active layer was embedded between the n-GaN layer and p-GaN layers, and was represented by a point dipole source with wavelength of 450 nm [22,23]. In order to present the random electron-hole pair combinations in the MQW layer, the typical locations and polarizations of the dipole sources were needed in each simulation. In 3D FDTD method, three polarizations of dipole sources along the x axis, y axis, and z axis were considered in the simulation. However, since it has been proved that dipoles polarized in the xy-plane were responsible for most LEDs emission [24], and there was no anisotropy in the xy-plane [15,25,26], so in order to reduce the computational cost, only E//x polarization was calculated during the simulations, although the results might be more precise when both E//x and E//y polarization were considered. Usually, the LEE would increase under the influences of the PhC. However, with the variation of the relative position between the dipole source and the PhC, the enhancement of LEE changed. In order to get a precise result, we have located the dipole in three typical positions as shown in Fig. 1(b), that was, between two PhCs, in the center of three PhCs, and under one PhC. And the final results were gotten by averaging the results of these three separate simulations. Since FDTD method was
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Fig. 2. (a) The refractive index (n) of GaN, ITO, and SiO2 ; (b) the extinction coefficient (k) of GaN, ITO, and SiO2 .
intrinsically a coherent simulation method, multi-reflection of the light inside the LEDs chip would result in an unphysical interference pattern. This would further influence the simulation results, especially the far-field pattern. For this reason, the Berenger perfectly matched layer (PML) [27] was added to the edge of the simulation domain as the absorbing boundary during the simulations, which could absorb the incident light with zero reflection. And the width of PML was set as 100 nm which could effectively absorb all incident energy. A homogeneous mesh-grid of 10 nm was used during the simulations, which was about/18n, and n was the refractive index of the materials. This meant about 10 spatial grids in the PML. Furthermore, although the PhC was periodical, periodic boundary conditions were not suitable in the simulations, since the periodic continuation of the simulation domain would replicate the dipole and interfere with other dipoles [28]. As far as the refractive index (n) of the materials were concerned, the refractive index of GaN at 450 nm was set as nGaN = 2.5, and those of ITO and SiO2 were taken to be nITO = 2.0 and nSiO2 = 1.5, respectively, as shown in Fig. 2(a). In addition, we could find from Fig. 2(b) that the extinction coefficient (k) of GaN, ITO, and SiO2 were closed to zero at the wavelength of 450 nm, then we ignored the material absorption during the simulations [29–31]. A power monitor was placed above the surface of LEDs to measure the power flux extracted from the top side of LEDs (Pout ), and a box monitor enclosing the dipole source was used to calculate the whole power emitted from the dipole source (Psource ). Then the LEE was defined as [13]: extr = Pout /Psource
(1)
And the LEE enhancement factorFFwas defined as extr − 0 × 100% F= 0
(2)
where extr was the LEE of LEDs with PhC structures, and 0 was the LEE of the conventional planar LEDs. In addition, the current density and the temperature distributions in the active region of LEDs at high current density injections (about 125 A/cm2 ) were also investigated through the finite-element method (FEM). And the schematic model of SiO2 PhCs LEDs used in the current density and the temperature distributions simulations was shown in Fig. 1(c). For the sake of simplicity, we ignored the details of the MQW and barriers, since it has been proved by Huang et al. [32], the resistance characteristic of the p-n junction dominated at high current density injection. Concerning the other epi-layers, their electronic characteristics followed the Ohm’s law:
J(r) = − · ∇ ϕ
(3)
where was the electrical conductivity, and ϕ denoted the electric potential. And the electrical conductivity of the p-/ncontact, SiO2 , ITO, p-GaN, and n- GaN were set as 1e15, 1e12, 1e7, 35, and 1e4 s/m, respectively. Insulated boundary conditions have been chosen during the simulations except for the p- and n-contacts which were set as metal contact boundary conditions. And all interfaces between the epi-layers and contacts were assumed to be Ohmic contacts. 3. Results and discussion At the beginning, we calculated the LEE of the planar LEDs with ITO placed on the top of GaN. Under the influence of TIR, the LEE of LEDs can be defined as extr
Pout = = Psource
c 0
2r 2 sin d 4r 2
=
1 (1 − cos c ) 2
(4)
where c = arcsin(n1/n2) is the critical angle. For GaN planar LEDs, the LEE is about 4%, while adding ITO on the top of GaN, the LEE of the top surface is about 6.7%. However, because of the TIR between the GaN and ITO layer, the overall LEE of LEDs
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Fig. 3. (a) LEE enhancement factor F as a function of the depth of the SiO2 PhC; Polar projection of the far-field intensities of SiO2 PhC LEDs with depth equals (b) 240 nm, (c) 320 nm and (d) 420 nm, respectively.
used in our simulations will be between 4% and 6.7%. Moreover, as far as the Fresnel reflection is concerned, the reflection ratio of the top surface of the ITO planar LEDs is: R=
n
− nair nITO + nair ITO
2
≈ 0.11
(5)
This will further reduce the LEE. According to our simulation, the LEE of planar ITO LEDs is about 4.6%, which can be reliable. 3.1. Effect of the SiO2 PhC depth on the LEE of LEDs Then the simulation of effect of the SiO2 PhC depth on the LEE of LEDs was conducted. Here, the depth of the SiO2 PhC was defined as the depth of SiO2 PhC embedded into the ITO layer, however, sometimes it might penetrate the ITO layer and embedded into the GaN layer. It was worth mention that, since it was still very difficult to fabricate PhC etching through the active layer, only shallow SiO2 PhC which could not penetrate the active layer was considered during the simulations. Since triangular lattice could offer more directions for light extraction, light incoming from more azimuthal angle in the GaN (ITO) layer could be extracted than square ones and 1D grating, we chose triangular lattice PhC in the simulations. This has also been proved in Ref. [24,33]. Then, the filling factor could be defined by: √ 2 ftriangle = 2RPhCs / 3a2PhCs (6) Here, RPhCs was the radius of PhC, and aPhCs was the PhC lattice constant, i.e., center-to-center distance between the neighboring PhC. Then the lattice constant of the SiO2 PhC was kept at 900 nm and the radius was 200 nm for the time being, which have been used to improve the LEDs light output performance in Ref. [18]. Using Eq. (6), we could calculate the filling factor, that was, about 0.18. Then the LEE of SiO2 PhC LEDs with PhC depth varied from 240 nm to 440 nm in step of 20 nm were calculated, and the results were shown in Fig. 3(a). From Fig. 3(a), it is clearly visible that with the increase of PhC etching depth, the LEE increases dramatically. However, this trend stops at some depth about 320 nm and begins to decrease as the depth increasing. The far-field radiation patterns were investigated to verify the above results. Here, the far-field radiation patterns of LEDs with depth of 240 nm, 320 nm, and 420 nm were demonstrated in Fig. 3(b), (c) and (d), respectively. We can see that when the PhC depth is 240 nm, the center intensity is a little higher than that of 320 nm. However, the whole intensity of LEDs with 320 nm depth PhC is significantly higher than that of 240 nm. Meanwhile, when the PhC depth equals 420 nm, the power intensity is more higher than that of 240 nm PhC depth LEDs, however, it is lower than that of LEDs with 320 nm depth PhC. This is in good agree with the variation trends of the LEE.
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Fig. 4. Effects of the SiO2 PhC radius r and the filling factor f on the LEE.
Fig. 5. (a) The reflection and transmission of the planar LEDs and the SiO2 PhC LEDs with different filling factors; (b) The calculated reflection at normal incidence as a function of wavelength.
3.2. Effects of the SiO2 PhC radius and the filling factor on the LEE of LEDs Then the effects of the PhC radius r and the filling factor f on the LEE of SiO2 PhC LEDs were investigated. During the simulations, the PhC depth was kept at 320 nm which has been obtained from above simulations, while the other two parameters, the radius and the filling factor, were varied to get the highest LEE. During the simulations, the radius was varied from 160 nm to 400 nm, and the filling factor was varied from 0.2 to 0.4. The results were shown in Fig. 4. From the viewpoint of LEE enhancement, these five lines in Fig. 4 have the similar variation trends. As the radius of PhC increasing, the LEE first increases and then decreases. We can also find that when the filling factor is smaller, a smaller radius is preferable to obtain larger LEE enhancement. On the other hand, when the radius is larger, a larger filling factor is suitable. As shown in Fig. 4, when the filling factor f equals 0.4, and the radius equals 380 nm, the highest LEE enhancement is achieved, that is, more than 37% enhancement comparing to the conventional planar LEDs. In order to verify the variation trend we got from the FDTD algorithm, we utilized the RCWA method to calculate the reflection and the transmission of the planar LEDs and the SiO2 PhC LEDs with different filling factors. Here, the wavelength of incident light was 450 nm, and the PhC radius was set to be 380 nm which has been obtained from the above calculations, and the results were shown in Fig. 5(a). As displayed in Fig. 5(a), the reflection and transmission of the SiO2 PhC LEDs are much better than that of the planar LEDs, while the SiO2 PhC LEDs with f = 0.4 are even better than the other SiO2 PhC LEDs. And the average reflection in the extraction cone (about 23◦ ) of the SiO2 PhC LEDs with filling factor varies from 0.4 to 0.2 are 5.7%, 8.3%, and 0.1%, respectively, while that of the planar LEDs is 11.4%. The calculated reflection at normal incidence as a function of wavelength is also shown in Fig. 5(b). From Fig. 5(b), we can find that the SiO2 PhC LEDs with f = 0.2 and f = 0.3exhibit higher reflection than planar LEDs in the wavelength scope of blue light, while the SiO2 PhC LEDs with f = 0.4 is a little better than the planar LEDs. The reflection at normal incidence of the SiO2 PhC LEDs with filling factor varies from 0.4 to 0.2 are 11.6%, 14.6%, and 15.6%, respectively, while that of the planar LEDs is 13.4%. That means the Fresnel reflection has also been reduced to a certain extent. In view of these, low TIR and Fresnel reflection enables better extraction of light, thereby enhancing the LEE. Notably, the value of reduction in the TIR and Fresnel reflection loss is much lower than the LEE enhancement that shown in Fig. 4. So we can infer that the enhancement of the light extraction may have something to do with the diffraction properties of the PhC.
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Fig. 6. The far-field power distributions of the SiO2 PhC LEDs with different configurations; the green dashed line indicates the far-field power distribution of the planar LEDs.
Fig. 7. The enhancement of LEE over the whole visible spectrum.
In order to show the application of PhC as a light extractor of light emission, we plotted the far-field power distributions of LEDs in Fig. 6. Here, the far-field distribution of the planar LEDs was also given for comparison. From Fig. 6, it can be seen that under the diffraction effect of the SiO2 PhC, as the filling factor of SiO2 PhC increasing, the far-field distribution is well modified. The power flux between angular −90◦ to 90◦ can be collected by the monitor placed above the top side of LEDs. So the area under the far-field curve can represent the output power of LEDs, that is, Pout . From Fig. 6, we can find that the emission intensities of SiO2 PhC LEDs are much stronger than that of planar LEDs in all directions. That means the incorporation of the SiO2 PhC is inclined to diffract much more emission energy out of the LEDs. As demonstrated in Fig. 6, the area under the far-field curve of LEDs with SiO2 PhC f = 0.4 and r = 380 nmis larger than the other SiO2 PhC configurations, and this implies more interaction with the guided modes and then more LEE enhancement can be achieved. The green dash line in Fig. 6 is the far-field power distribution of the dipole in planar LEDs, and its far-field pattern is near anisotropic. Under the diffraction of the SiO2 PhC, the power of LEDs is concentrated in the region between −30◦ to 30◦ . From Fig. 6, we can find that the main lobe of the radiation pattern is relatively wide, and the side lobes become weaker, which can benefit the extraction of light from the LEDs. And when the SiO2 PhC filling factor f = 0.4 and radius r = 380nm, we can find that more power is concentrated between the angular of −20◦ to 20◦ , that means better directional properties have been obtained. Until now, we have discussed the LEE of SiO2 PhC LEDs at a certain wavelength, i.e. 450 nm. However, LEDs have a wide emission wavelength range actually. Accordingly, we also calculated the LEE enhancement of the optimized structure along the whole visible spectral wavelengths, and the results were shown in Fig. 7. As can be seen from Fig. 7, the LEE spectrum of SiO2 PhC LEDs shows strong and broadband visible spectrum comparing with that of the normal GaN-based LEDs, not only at the 450 nm wavelength of interest. That is to say, the optimized structure can be used to increase the LEE in a broadband visible spectrum. 3.3. Effect of the air-hole PhC depth on the LEE of LEDs Then the simulations of the LEDs with air-hole PhC were carried out for comparison. Similar as that of the SiO2 PhC LEDs, the lattice constant of the PhC was kept at 900 nm and the radius was 200 nm. Then the LEE of normal air-hole PhC LEDs with PhC depth varied from 160 nm to 440 nm were calculated. Fig. 8(a) shows the variation of LEE for different depths of the air-hole PhC structure. As shown in Fig. 8(a), with the increase of the PhC depth, the LEE increases intensively, especially when the PhC depth is smaller than 200 nm. This can be explained by that the interaction between the PhC and the guided modes becomes stronger and stronger with the etching depth of the PhC increasing. However, this trend stops at some depth about 220 nm and begins to fluctuate as the depth increasing. This is analogous to that of the SiO2 PhC LEDs. As pointed by David [34], when the PhC depth was about /nPhC (nPhC is the
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Fig. 8. (a) LEE enhancement of LEDs with air-hole PhC as a function of the depth of PhC. Polar projection of far-field intensities of air-hole PhC LEDs with depth equals (b) 160 nm, (c) 220 nm and (d) 340 nm.
effective refractive index of the PhC layer), most guided modes will be diffracted by PhC, then the highest LEE will be gotten. With the PhC etching deeper, the LEE of PhC LEDs varies periodical fluctuation. This can be explained by the Fabry-Perot resonator theory [35]. k⊥ × 2dGaN + ϕPhC (m ) + ϕsapphire (m ) = 2m
(7)
where m is the mode number, ϕPhC (m ) and ϕsapphire (m ) are the phase changes reflected from the GaN-PhC and GaN-sapphire interfaces, respectively, dGaN is the thickness of un-etched GaN layer, and k⊥ is the perpendicular wave vector. As the PhC is etched deeper, the thickness of un-etched GaN layer decreases and it causes that the LEE appears periodical fluctuation. And the far-field distribution pattern of LEDs with SiO2 PhC depth equals 160 nm, 220 nm and 340 nm are also demonstrated here to verify the simulation results. From Fig. 8(b), (c), and (d), we can find that the far-field distribution pattern of LEDs with SiO2 PhC depth equals 220 nm is significantly higher than that of LEDs with SiO2 PhC depth equals 160 nm and 340 nm. 3.4. Effects of the air-hole PhC radius and the filling factor on the LEE of LEDs Then the effects of the PhC radius r and the filling factor f on the LEE of air-hole PhC LEDs were investigated. The PhC depth was kept at 220 nm as has been obtain from above simulation, while the other two parameters, the radius and filling factor, were varied to get the best LEE enhancement. The radius was varied from 160 nm to 520 nm and the filling factor was varied from 0.2 to 0.4. The results were shown in Fig. 9, and a similar phenomenon as the SiO2 PhC LEDs could be found. As presented in Fig. 9, when the filling factor f equals 0.4, and the radius equals 500 nm, more than 27% enhancement of LEE is achieved comparing to that of the conventional planar LEDs. Then, we utilized the RCWA method to calculate the reflection and the transmission of the planar LEDs, the air-hole PhC LEDs with different filling factors, and the results were shown in Fig. 10(a). As displayed in Fig. 10(a), with the filling factor of the air-hole PhC increasing, the reflection and the transmission of LEDs become better, and when f = 0.4, the highest transmission has been obtained. The average reflection in the extraction cone of the air-hole PhC LEDs with f varies from 0.4 to 0.2 are 4.6%, 7.7%, and 10.1%, respectively, while that of the planar LEDs is 11.4%. We also calculated the reflection at normal incidence as a function of wavelength and the results were shown in Fig. 10(b). From Fig. 10(b), we can find that the air-hole PhC LEDs with f = 0.4 exhibited lower reflection than planar LEDs in the wavelength scope of blue light. The reflection at normal incidence of the air-hole PhC LEDs with filling factor varies from 0.4 to 0.2 are 9.4%, 13.8%, and 15.7%, respectively, while that of the planar LEDs is 13.4%.
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Fig. 9. Effects of the air-hole PhC radius and the filling factor f on the LEE.
Fig. 10. (a) The reflection and the transmission of the planar LEDs and the air-hole PhC LEDs with different filling factors; (b) The calculated reflection at normal incidence as a function of wavelength.
Fig. 11. The far-field power distributions of LEDs with different PhC configurations; the green dashed line indicates that of planar LEDs.
Comparing with the average reflection in the extraction cone and the reflection at normal incidence of the SiO2 PhC LEDs, we can find that the air-hole PhC LEDs have even lower reflection; however, the SiO2 PhC LEDs have higher LEE. So we can infer that it must have something to do with the diffraction properties of the PhC. Then, as we have done in the previous SiO2 PhC LEDs simulations, the diffraction properties of the air-hole PhC were investigated, and the far-field power distributions were demonstrated in Fig. 11. Here, the far-field distribution of the optimized SiO2 PhC LEDs was also shown for comparison. From Fig. 11, it can be seen that the pattern of the far-field is well modified by the air-hole PhC comparing to that of the planar LEDs structure. When f = 0.4and r = 500 nmmore strong diffraction of the guided modes can be found. However, the SiO2 PhC LEDs have obtained more light diffracted out of the LEDs, especially between the angle −20◦ to 20◦ . That is to say, more light output power has been harvested when the normal air-hole PhC was replace by SiO2 PhC. Although the SiO2 PhC LEDs have only 10% enhancement of LEE than normal air-hole LEDs, we still believe that more enhancement of light output power will be gotten, since it has been proved in [18] that the SiO2 PhC can also exhibit partial compression strain release and reduced emission divergence which can improve the IQE. 3.5. The current density and the temperature distributions In order to get a deeper insight into the specific features of the LEDs operation, the current density and the temperature distributions in the active region of SiO2 PhC LEDs and the planar LEDs at high current density injections (about 125 A/cm2 )
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Fig. 12. The current density (dot) and the temperature distributions (hue) in the active layer of (a) the optimal SiO2 PhC LEDs and (b) the planar LEDs.
Fig. 13. The normalized current density along the line between two electrodes of the planar LEDs and the SiO2 PhC LEDs.
were shown in Fig. 12. As displayed in Fig. 12, both the SiO2 PhC and the planar LEDs demonstrate a uniform current density distribution in the active region. This is mainly because of the choice of the simulation domain is a few times less than the current spreading length in virtual LEDs. However, from the temperature distributions, the area near the n-contact has a little higher temperature, that means more current has crowded near the n-contact as a result of the current spreading effect of the ITO layer. This can be further explained by the normalized current density along the line between two electrodes. Form Fig. 13, we can find that because of the effect of ITO current spreading layer, the SiO2 PhC LEDs and the planar LEDs have similar current density distribution in the active layer, and have a current crowding near the n-contact. Although the current density distribution of the SiO2 PhC LEDs appears a little fluctuation, we can still find that the current density near the p-contact increases while that near the n-contact decreases, so a little more uniform current density distribution than the planar ITO LEDs will be obtained. Further more, we calculated the standard deviation of the normalized current density of these two kinds of LEDs, and found that the standard deviation of the normalized current density of SiO2 PhC LEDs was 0.032, while that of the planar ITO LEDs was 0.061, this meant that the current density of SiO2 PhC LEDs had a little improvement than the normal planar ITO LEDs. And in our previous paper [36], we have proved that current crowding near n-contact had little influence on the LEE. That is to say, the current and the temperature distributions here have little effect on the LEE. In a word, the high similarity of the current density and the temperature distributions of the SiO2 PhC LEDs and the planar LEDs means no noticeable degradation in the SiO2 PhC LEDs electrical and thermal properties. This conclusion is in line with the experiment observations which made in [37]. 4. Conclusion In the present study, the LEE of SiO2 PhC LEDs was systematically investigated with the help of 3D FDTD simulations. Through optimization, more than 37% enhancement of LEE has been achieved in case of a PhC depth h equaled 320 nm, a filling factor f equaled 0.4, and a radius r equaled 380 nm. The RCWA method was utilized to verify the variation trend gotten
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from the FDTD algorithm. For comparison, the normal air-hole PhC LEDs was also investigated, and the results indicated that SiO2 PhC LEDs had higher extraction efficiency. At last, the current density and the temperature distributions in the active region of SiO2 PhC LEDs and the planar LEDs at high current density injections were investigated. Results showed that there was no noticeable degradation in the SiO2 PhC LEDs electrical and thermal properties comparing with the conventional planar LEDs. These analyses suggested that SiO2 PhC LEDs could be envisioned to a promising candidate to replace the air-hole PhC LEDs and the presented results offered practical guidelines for the design of high efficiency SiO2 PhC LEDs. Acknowledgments This work is supported by the National Natural Science Foundation of China (61475084, 61327808) and the ScienceTechnology Foundation of the Higher Education Institutions of Shandong Province, China (J17KA054). References [1] E.F. 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