LED-FDTD LED时域有限差分方法

Efficiency enhancement of homoepitaxialInGaN/GaN light-emitting diodes on free-standing GaN substrate with double embeddedSiO2 photonic crystalsTongbo Wei,* Ziqiang Huo, Yonghui Zhang, Haiyang Zheng, Yu Chen, Jiankun Yang, Qiang Hu, Ruifei Duan, Junxi Wang, Yiping Zeng, and Jinmin Li Semiconductor Lighting Technology Research and Development Center, Institute of Semiconductors, ChineseAcademy of Sciences, Beijing 100083, China*tbwei@Abstract: Homoepitaxially grown InGaN/GaN light emitting diodes(LEDs) with SiO2 nanodisks embedded in n-GaN and p-GaN as photoniccrystal (PhC) structures by nanospherical-lens photolithography arepresented and investigated. The introduction of SiO2 nanodisks doesn’tproduce the new dislocations and doesn’t also result in the electricaldeterioration of PhC LEDs. The light output power of homoepitaxial LEDswith embedded PhC and double PhC at 350 mA current is increased by29.9% and 47.2%, respectively, compared to that without PhC. Thecorresponding light radiation patterns in PhC LEDs on GaN substrate showa narrow beam shape due to strong guided light extraction, with a viewangle reduction of about 30°. The PhC LEDs are also analyzed in detail byfinite-difference time-domain simulation (FDTD) to further reveal theemission characteristics.©2014 Optical Society of AmericaOCIS codes: (230.0230) Optical devices; (230.3670) Light-emitting diodes; (160.5298)Photonic crystals; (220.4241) Nanostructure fabrication.References and links1. B. Monemar and B. E. Sernelius, “Defect related issues in the “current roll-off” in InGaN based light emittingdiodes,” Appl. Phys. Lett. 91(18), 181103 (2007).2. G. Verzellesi, D. Saguatti, M. Meneghini, F. Bertazzi, M. Goano, G. Meneghesso, and E. Zanoni, “Efficiencydroop in InGaN/GaN blue light-emitting diodes: Physical mechanisms and remedies,” J. Appl. Phys. 114(7), 071101 (2013).3. K. Akita, T. Kyono, Y. Yoshizumi, H. Kitabayashi, and K. 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M.Sigalas, “InGaN/GaN quantum-well heterostructure light-emitting diodes employing photonic crystal structures,”Appl. Phys. Lett. 84(19), 3885 (2004).1. IntroductionIII-nitride wide bandgap light-emitting diodes (LEDs) have recently attracted considerable interest due to their various applications, such as traffic signals, back-side lighting in liquid crystal display and illumination lighting by white light LEDs. Nevertheless, up to now, all commercial LEDs are grown on foreign substrates such as sapphire, GaAs, SiC and silicon due to the lack of availability of a native substrate. Such heteroepitaxial growth typically leads to high density of threading dislocations (108-1010 cm−2), which are detrimental to the LED’s internal quantum efficiency (ηint) and reliability. The development of high-brightness LEDs suffers from the non-thermal rollover of ηint at high current density, known as the efficiency droop [1,2]. To solve the above problems, the homoepitaxially grown LEDs have been presented with low dislocation density and high thermal conductivity [3–5], as a result of recent progress in production of free-standing GaN (FS-GaN) substrate grown hydride vapor phase epitaxy (HVPE). Furthermore, the availability of FS-GaN is also advantageous for LED device processing when FS-GaN can be made electrically conductive, eliminating the etching step for contact and increasing the emission areas. However, the production cost of FS-GaN substrate is still too high for a broader commercialization, which limits the further investigation of homoepitaxial LEDs. Recently, it is heart-stirring that Cich et al. has shown the good performance of GaN LEDs on bulk GaN substrates with very high external quantum efficiency (ηext) up to high current density [6].It is known that the extraction efficiency of LEDs is limited by high refractive index contrast between the GaN (2.5) and air (1.0). For conventional LED on sapphire, smaller refractive index (1.78) and higher transparency of sapphire compared to bulk GaN are favor of light extraction. In contrast, a considerable amount of downward light in homoepitaxial #209568 - $15.00 USD Received 4 Apr 2014; revised 23 May 2014; accepted 26 May 2014; published 2 Jun 2014 (C) 2014 OSA30 June 2014 | Vol. 22, No. S4 | DOI:10.1364/OE.22.0A1093 | OPTICS EXPRESS A1094LED is absorbed by the FS-GaN substrate [7]. Thus, the problems about ηextraction for the LEDs on FS-GaN are more serious than the counterpart on sapphire. Currently, it has been demonstrated that several methods are used to improve ηextraction in GaN-based LEDs on FS-GaN substrate, such as etching roughness of N-face GaN [8,9], geometric die shaping [10,11] and vertically mounted configuration [12]. The N-face GaN roughness on the backside of FS-GaN substrate may effectively increase the light extraction, but severe absorption losses also occur since some of the backside light is absorbed by mechanical support of chips due to the lack of metal reflector. In contrast, the die shaping and vertically mounted configuration open possibilities to enhance light extraction from LEDs sidewalls. However, the laser shaping process for the chips with thick bulk GaN easily causes undesirable damages to the LEDs properties. In general, until now there has still been very limited literature on how ηextraction of homoepitaxial LEDs is increased, while a majority of work is concentrated on the research of ηint and droop effect. Therefore, more efforts are needed to gain the high ηextraction for LEDs grown on FS-GaN substrate.To enhance ηextraction of LEDs, photonic crystal (PhC) structures have drawn much attention, which could lead to efficiently coupling light from the dielectric-guided modes into air [13–16]. In addition to increasing the extraction efficiency of LEDs, periodic PhC structures have the ability to enhance the directionality, especially along the vertical orientation. Recently, Weisbuch et al. demonstrated two air-gap embedded PhCs, which created a waveguide with highly confined and well-extracted mode while exhibiting no significant deleterious effects on the LEDs [17,18]. In our previous report [19], we have employed a low-cost and high-throughput method of nanospherical-lens photolithography (NLP) to fabricate two-dimensional SiO2 PhC embedded in p-GaN to improve the light extraction of LEDs on sapphire substrate. In this work, we report on the development and analysis of improved extraction efficiency of homoepitaxial LEDs on FS-GaN substrate with double SiO2 PhC structures by NLP and overgrowth. The effects of the double SiO2 PhC on the light propagation of homoepitaxial LEDs are analyzed and discussed in detail. The finite-difference time-domain (FDTD) is also used to simulate the optical field distributions to verify the experimental results.2. FabricationThe blue InGaN/GaN LEDs were grown on c-plane FS-GaN substrate with a dislocation density of about 2 × 107 cm−2 by a veeco metal-organic chemical vapor deposition (MOCVD) system at a growth pressure of 200 mbar. Figure 1 shows the fabrication process flow for embedded and double SiO2 PhC LEDs. The details of the SiO2 nanodisk structures fabricated on n-GaN had been described in our previous reports [19]. Following the SiO2 nanodisks, the regrown structure consisted of 2.5 µm n-GaN layer at 1030 °C, eight periods of In0.2GaN0.8/GaN multiple quantum wells (MQWs) at 740 °C, 40 nm thick Al0.2Ga0.8N electron-blocking layer (EBL) and a 100 nm thick p-GaN layer. Subsequently, the same SiO2 nanodisks and regrowth of p-GaN with 150 nm thickness were carried out to fulfill the double PhC LEDs. Here, the height of p-GaN and top SiO2 PhC is designed as the sameness to keep the low surface roughness of double PhC LED. For comparison, the LEDs with PhC structure embedded in n-GaN and without PhC structure were also prepared. Finally, the LEDs were fabricated with a conventional square mesa (1 × 1 mm2) using indium tin oxide (ITO) with a thickness of 200 nm as a transparent current spreading layer (TCL) and Cr/Pt/Au as the n- and p-electrodes by e-beam evaporation. To avoid the impact of light extraction, the backside of all the chips was polished and without the reflectivity mirror. The light output-current-voltage characteristics of the LEDs were measured using an Everfin-PMS50 optical spectrum analyzer and a HAAS-2000 integrating sphere at a direct current (DC) mode. Far-field radiation patterns of the LEDs were also measured in LSA 3000 LED spatial analyzer with the angular resolution of 0.1°.#209568 - $15.00 USD Received 4 Apr 2014; revised 23 May 2014; accepted 26 May 2014; published 2 Jun 2014 (C) 2014 OSA30 June 2014 | Vol. 22, No. S4 | DOI:10.1364/OE.22.0A1093 | OPTICS EXPRESS A1095Fig. 1. Schematic illustration of the process for the fabrication of embedded PhC and doublePhC LEDs.3. Results and discussionFigure 2(a) demonstrates the scanning electron microscope (SEM) image of cross-sectional view of the n-GaN laterally reovergrown over the SiO2 nanodisks in the embedded PhC LED. It is noted that the SiO2 nanodisks are fully surrounded by the GaN layer, without leaving the voids. The diameter, period and height of the embedded SiO2 nanodisk are 400, 900 and 200 nm, respectively. According to the top-view of PhC structure, there is a uniform hexagonal-lattice distribution of SiO2 nanodisks as shown in Fig. 2(b). Selectively regrowth of p-GaN with a thickness of 150 nm is carried out to fill the space between SiO2 nanodisks. Furthermore, transmission electron microscopy (TEM) is employed to investigate the crystalline quality of GaN layers that are homoepitaxially grown on the SiO2 PhC structure. As shown in Figs. 2(c) and 2(d), almost no threading dislocations can be observed in both n-GaN and MQWs structures, implying the high quality growth of GaN on FS-GaN substrate. In the epitaxial lateral overgrowth (ELOG) on sapphire, Wuu et al. reported the SiO2 array could block the dislocation propagation, but new dislocations may be introduced in the lateral coalescence region during the second growth [20]. Unlike the heteroepitaxial growth, there are also no new dislocations formed on the SiO2 nanodisks in the grown process.#209568 - $15.00 USD Received 4 Apr 2014; revised 23 May 2014; accepted 26 May 2014; published 2 Jun 2014(C) 2014 OSA30 June 2014 | Vol. 22, No. S4 | DOI:10.1364/OE.22.0A1093 | OPTICS EXPRESS A1096Fig. 2. (a) Cross-sectional view of embedded PhC of SiO 2 nanodisks surrounded by n -GaN and(b) tilted top-view of p -GaN surface with top SiO 2 PhC structure. (c) Cross-sectional TEMimage of the LED with embedded SiO 2 PhC. (d) is the magnified region of MQWs from PhCLED in (c).The logarithmic I -V curves of the LEDs without and with PhC structures are shown in Fig. 5(a). At an injection current of 350 mA, the forward bias voltages of LEDs without PhC, with an embedded PhC and double PhC are 3.57 V, 3.64 V and 3.77 V, respectively. The slight increase in forward voltage, especially for the double PhC LED due to enhanced surface roughness is acceptable for practical application. In addition, it is found that the leakage currents of these LEDs on FS-GaN without and with PhC are almost identical, about 8.2 × 10−8 A at the reverse voltage of 10 V. The reverse leakage current of InGaN/GaN has been attributed to the electron tunneling from p -GaN to n -GaN through dislocation or defects [21]. Therefore, the low and accordant reverse leakage currents of these LEDs imply comparable dislocation density of GaN for LEDs without and with SiO 2 nanodisks, consistent with the above TEM results. Furthermore, the turn-on voltage of the aforementioned LEDs is almost same, about 1.9 V as shown in the inset of Fig. 3(a), suggesting that the carrier transport characteristics are not injured by embedded SiO 2 PhC structures. As compared with the LED without PhC, the electroluminescence (EL) intensities of LED with PhC are obviously increased in Fig. 3(b). The peak wavelength of EL spectra in conventional, embedded PhC and double PhC LEDs is measured as 456.4, 455.2 and 454.1 nm at 350 mA current, respectively. The slight blue-shift phenomenon in the EL spectra is caused by a partial compression strain release in the InGaN active layer through selective regrowth on SiO 2 nanodisks. Figure 3(c) shows the light output power as functions of current for the PhC LEDs. At 350 mA current, the light output power of LEDs with embedded PhC and double PhC is increased by 29.9% and 47.2%, respectively, compared to that without PhC. Based on the observed increases of 47.2% for double PhC and 29.9% for embedded PhC, the increase of ηextraction is estimated to be only 13.3% for top SiO 2 PhC due to diffused scattering effect. In fact, light extraction of surface PhC is to do rather more than that. The overlap of photon escape probability from the surface PhC and embedded PhC structures weakens the contribution of double SiO 2 PhC.#209568 - $15.00 USDReceived 4 Apr 2014; revised 23 May 2014; accepted 26 May 2014; published 2 Jun 2014(C) 2014 OSA 30 June 2014 | Vol. 22, No. S4 | DOI:10.1364/OE.22.0A1093 | OPTICS EXPRESS A1097Fig. 3. (a) The reverse and forward I-V characteristics of the LEDs without and with PhCstructures on a logarithmic scale. Inset: corresponding enlarged forward I-V curves closed tothe turn-on voltage. (b) Peak wavelength of the EL emission spectra of the LEDs at a current of350 mA. (c) Optical output power (L-I) of these LEDs as a function of injection current.We measure the light output radiation patterns of the LEDs with and without PhC structures at a driving current of 200 mA. Here, the chips are Au-wire bonded and loaded on an aluminium leaded chip carrier without epoxy encapsulation. The far-field emission patterns from the PhC LEDs show much smaller view angles but obvious enhancement in the overall integrated emission intensity. In order to scrutinize the effect of the PhCs, the normalized relative radiation profiles of different LEDs are plotted in Fig. 4. It is found that the full-width-at-half maximum (FWHM) of emission divergence for the embedded and double PhC LEDs are 128.1° and 131.6°, respectively, compared to that of 159.4° without SiO2 PhC structure. Here, the errors of the measured divergence values are ± 0.1°. In general, the conventional LED on sapphire substrate has a divergent angle of about 151° on the same LED structure [19]. Here, the larger divergent angle in LED without PhC on FS-GaN substrate implies that the light confined in the LED chip is extracted from edge of the chip or of the FS-GaN substrate after multiple scattering or reflection [22], corresponding to the low light extraction efficiency (LEE). In the PhC LEDs, the light beam shaping of SiO2 nanodisks is highly remarkable with a view angle reduction of about 30°, which helps to confine the light to radiate in the vertical direction for the suppression of total internal reflection. Especially, in the double PhC LED, the light is further redirected to the top escape cone through the twice transmission of embedded and top SiO2 arrays, resulting in the most significant focusing effect and more photon capable of escaping from the chips.#209568 - $15.00 USD Received 4 Apr 2014; revised 23 May 2014; accepted 26 May 2014; published 2 Jun 2014 (C) 2014 OSA30 June 2014 | Vol. 22, No. S4 | DOI:10.1364/OE.22.0A1093 | OPTICS EXPRESS A1098Fig. 4. Normalized relative far-field emission patterns of the LEDs without and with SiO2 PhCstructures at a driving current of 200 mA.To further understand the influence of embedded PhC and double PhC patterns on the performance of LEDs, a two-dimensional (2D) finite difference time domain (FDTD) simulation is used. Here, considering the plane isotropy of hexagonal PhC structures, the simulation model is simplified from 3D to 2D to reduce the calculation time. We use the perfectly matched layer (PML) boundary condition for the simulation and a point dipole polarized along the x, y and z directions is used as radiation source. The computational domains are 42 µm in the x-direction and 16 µm in the y-direction. The simulated LED structure consists of 250 nm thick p-GaN/150 nm thick MQWs/4.2 µm thick n-GaN/10 µm FS-GaN substrate, as shown in Fig. 5(a). The shape and size of the SiO2 PhC solid model for FDTD simulation are determined are exactly the same as those in the SEM images in Fig. 2 and scarce non-uniformities in PhC are ignored to simplify the simulation. Figures 5(b)-5(d) compare the propagation of electro-magnetic waves passing through SiO2 PhC structures and hybrid surface. The sole GaN-air interface produces the torch-like radiation pattern for LED without PhC on FS-GaN, resulting in the stronger electric field distribution in the FS-GaN and lower LEE. In contrast, part of optical energy for LED on sapphire is radiated to air through light incidence at the mesa sidewall due to the diffraction of interface between GaN and sapphire [19]. In the PhC LEDs on FS-GaN, the incorporation of SiO2 nanodisks is seen to suppress the internal reflection and diffract the optical energy to the surface normal. Due to the suited dimension of SiO2 with wavelength, wave-like features such as interference and diffraction dominate the interface between GaN and air. Especially, the PhC converging effect of embedded and top SiO2 structures in double PhC LED is coupled and causes the smallest view angle, consistent with the observation far-field emission patterns in Fig. 4.#209568 - $15.00 USD Received 4 Apr 2014; revised 23 May 2014; accepted 26 May 2014; published 2 Jun 2014(C) 2014 OSA30 June 2014 | Vol. 22, No. S4 | DOI:10.1364/OE.22.0A1093 | OPTICS EXPRESS A1099Fig. 5. (a) The schematic representation of the 2D FDTD simulation for the double PhC LED.FDTD simulation of light propagation in (b) LED without PhC, (c) LED with embedded PhCand (d) LED with double PhC on FS-GaN substrate.4. ConclusionIn summary, we fabricate the SiO2 nanodisk arrays to form PhC structures, which are embedded in n-GaN and p-GaN of homoepitaxially grown LEDs by NLP and overgrowth. Significant improvements on light extraction of the embedded PhC and double PhC LED at 350 mA current have been observed of up to 29.9% and 47.2% over that without PhC structure, respectively. Furthermore, the view angle of PhC LEDs is obviously reduced, which confines the light to radiate in the vertical direction for the suppression of total internal reflection. The work offers a promising potential to reduce the severe internal reflection and increase the light output powers of homoepitaxial LEDs on FS-GaN substrate. AcknowledgmentThis work was supported by the National Natural Sciences Foundation of China under Grant 61274040, 61274008 and 51102226, the National Basic Research Program of China under Grant 2011CB301902, the National High Technology Program of China under Grant 2014AA032605 and Youth Innovation Promotion Association, Chinese Academy of Sciences.#209568 - $15.00 USD Received 4 Apr 2014; revised 23 May 2014; accepted 26 May 2014; published 2 Jun 2014(C) 2014 OSA30 June 2014 | Vol. 22, No. S4 | DOI:10.1364/OE.22.0A1093 | OPTICS EXPRESS A1100。