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Chinese Journal of ElectronicsVol.25, No.4, July 2016

Current Spreading Effects in Vertical GaN-Based

Light-Emitting Diode on Si(111) Substrate∗

WEI Jingting1,2, ZHANG Baijun2 and WANG Gang2

(1. Guangdong Polytechnic Institute, The Open University of Guangdong, Guangzhou 510091, China)

(2. School of Microelectronics, State Key Laboratory of Optoelectronic Materials and Technologies, Sun Yat-sen University,

Guangzhou 510275, China)

Abstract — The optimal design of GaN-based Light-emitting diode (LED) is important for its reliability. In

this work, a new three-Dimensional (3D) circuit modelwith a resistor network is developed to study the current

distribution in the active layer of vertical conducting GaN-

based LED grown on Si(111) substrate with different struc-tures and electrode patterns. It consists of resistance of

Transparent conductive layer (TCL), resistance of epitax-ial layer, intrinsic diodes presenting the active layer, and

AlN/Si junction as which the multilayer of AlN/Si is as-

sumed. Simulations results of current distribution in activelayers of two kinds of LED structures show that current

distribution uniformity is greatly affected by the electrode

pattern and the LED structure. Furthermore, the exper-imentally measured light emission uniformity agrees well

with simulation results. The electrical and optical char-acteristics of LED are obviously affected by the current

distribution uniformity.

Key words — Light-emitting diodes, Current distribu-

tion uniformity, Circuit model.

I. Introduction

GaN-based Light-emitting diodes (LEDs) have seen arapid development recently because of their widespreadapplications in many fields such as solid-state lighting,backlight of liquid crystal display and mobile phones, traf-fic lights, display units, and so on[1]. For many of theseapplications, the development of high-brightness or high-power GaN-based LED is required. Thermal effect plays acrucial role in the reliability and durability of high-powerLEDs[2]. It originates from two aspects: nonradiative re-combination in the active layer at low injection currentand Joule heating generated by current crowding at highinjection current[3]. In order to reduce the current crowd-ing effect, which also obstructs the uniformity of illumi-

nation in large-area LED devices[4], several circuit mod-els have been proposed. Guo et al. analyzed the currentcrowding effect on LEDs grown on sapphire substratein terms of a quantitative model, assuming that the p-contact was equal potential[4,5]. They concluded that thecurrent intensity decreased exponentially with distancefrom the edge of contact metal. Considering that the cir-cuit model proposed by Guo et al. was only valid for asufficiently bulky thickness of the transparent electrodeand the resistivity of thin metals was strongly dependenton the thickness, Kim et al. proposed an advance modelby including the resistance component of p-type trans-parent electrodes[6]. Ebong presented an electro-opticalmodel to evaluate the relationship between uniformity ofcurrent spreading and LED structures[7,8]. Shim et al. de-veloped a 3D electrical circuit model to analyze the cur-rent spreading in the active layer influenced by electrodepatterns[9−12]. Chen et al. systematically analyzed the ef-fects of current distribution in LED chips in the fields ofelectrical potential, optical light extraction efficiency, andthermal effects[13−15]. Many models have been reportedto study the current spreading effects that fit for theLED grown on sapphire substrate. However, these modelssuffer difficulties applying to the LED grown on Si sub-strate. Firstly, the electrical properties of silicon are quitedifferent from that of sapphire. Secondly, the insertionof AlN between GaN and silicon to improve the epitax-ial quality introduces large band offset. A junction wasformed between the AlN and silicon substrate, which ob-structs the development of vertical conducting LED on Sisubstrate[16]. The current spreading of LED grown on Sisubstrate has been seldom reported previously. Compared

∗Manuscript Received May 28, 2015; Accepted Oct. 10, 2015. This work is supported by Research Program of The Open Universityof Guangdong (No.1318), the National Natural Science Foundation of China (No.61274039), and International Sci. & Tech. Collaboration

Program of Guangdong Province, China (No.2013B051000041).c© 2016 Chinese Institute of Electronics. DOI:10.1049/cje.2016.07.014

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Current Spreading Effects in Vertical GaN-Based Light-Emitting Diode on Si(111) Substrate 673

to sapphire substrate, Si substrate provides many advan-tages such as low cost, large diameter, better thermal andelectrical conductivity, vertical electrode capability, chip-level package, and especially the possibility for integra-tion Si-based electronics to create a monolithic Opticaland electronics integrated circuit (OEIC). It is believedthat Si would gradually surpass sapphire as substrates forLED. Therefore, it is essential to analyze how the currentspreads in the active layer of LED on Si substrate. In thisstudy, a 3-D equivalent circuit model, where the AlN/Sijunction was regarded as intrinsic diode, was developed tostudy the current distribution in the active layer of LEDwith different structures. The effect of the electrode pat-tern on the current distribution was investigated by simu-lation using this 3D circuit model. To test our model, wefabricated two kinds of GaN-based LED structures withchip dimension of 1mm × 1mm on Si substrate. The ex-perimental results on these chips showed good agreementswith the simulation results.

II. Experiments

The growth of InGaN/GaN MQWs LED on Si(111)substrate used in this work was carried out in Metal-organic chemical vapor deposition (MOCVD) system. Thedetails of LED structure and growth process can be foundin previous publications[17]. After epilayer growth, theLED chip was fabricated into two kinds of structures, withand without through-hole. Such fabrication process hasbeen reported in our previous work[18]. The LED struc-tures with through-hole and without through-hole weredenoted as LED I and LED II, respectively. Fig.1(a) and(b) show the schematic cross-section diagrams of LED Iand LED II with chip dimension of 1mm × 1mm, respec-tively.

Fig. 1. Cross-sectional schematic diagrams of vertical con-ducting LEDs. (a) LED with through-hole (LED I);

(b) Conventional LED (LED II)

III. Equivalent Circuit Model

Fig.2 shows LED chips with three different electrodepatterns denoted as Pattern 1, Pattern 2, and Pattern3, respectively. The gray pattern is cathode where thethrough-hole is and the else pattern is anode.

Fig.3(a) and (b) show the 3D schematic structures andthe related circuit models with electrode Pattern 2 usedin this study.

Fig. 2. LED chips with three different electrode patterns. (a)

Pattern 1; (b) Pattern 2; (c) Pattern 3

Fig. 3. The 3D schematic structures and the related circuit

models. (a) LED I; (b) LED II

Each structure was divided into a series of very smallhexahedron meshes and each hexahedron mesh was pre-sented by intrinsic diodes and resistors as follows: theactive layer and AlN/Si junction were expressed as in-trinsic diodes, whereas the epilayers and the contact be-tween metals and epilayer were expressed as resistors. Themodulation frequency of a LED is usually limited by afew tens kHz[9,10], so the effects of capacitances and in-ductances are neglected, which means capacitances wereopen and inductances were shorted. Specific contact resis-tivity was obtained from the experimental Transmissionline method (TLM). The epilayer and circuit parametersof a hexahedron mesh are showed in Table 1, where ρn,ρp, ρc, Rsh, and Vth were represented as electrical resis-tivity of n-GaN, electrical resistivity of p-GaN, specificcontact resistivity, sheet resistance and threshold voltage.As the resistivity in the p-electrode is much smaller thanthat in the Transparent conductive layer (TCL), the p-and n-electrodes are assumed to be equipotential, respec-tively. In addition, since the resistance of TCL is muchless than the lateral resistance of the p-GaN, the current

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674 Chinese Journal of Electronics 2016

spreading related to the lateral path in the p-GaN can beignored. It is worth noting that the difference between thetwo models is that the AlN/Si junction near the through-hole is shorted by the metals filling in the hole shown inFig.3(a).

Table 1. Circuit parameters of a fabricated LED chip

Layers Parameters Value

n-GaN ρn(Ω · cm) 0.004

p-GaN ρp(Ω · cm) 6.25

Ohmic contact ρc(Ω · cm2) 9e-3

TCL Rsh(Ω/�) 12

Intrinsic diode1 Active layer Vth1(V) 2.5

Intrinsic diode2 GaN/AlN/Si Vth2(V) 1[11]

IV. Results and Discussion

1. Study of current distribution in the activelayer of LED with different structure

To analyze the current distribution details, the 3Dcircuit model is performed by the P simulation pro-gram with integrated circuit emphasis (PSPICE) soft-ware. Fig.4 presents a series of simulated current distribu-tion as a function of position in the active layer of verticalconducting LED I with electrode Pattern 2, at differentinjection current. The coordinate origin is set as the chipcenter. As seen from the contour plots, current distribu-tion changes when the injection current varies from 20mAto 500mA. Current crowds only at the edge of the chipunder low injection current, while it mainly happens onthe edge and at the center of the chip under the largeinjection current. It is straightforward to find that cur-rent gradually extends to spread under the p-electrodewhen the injection current is larger than 200mA. Thisphenomenon becomes obvious when the injection currentis increased to 500mA, as shown in the Fig.4(f), where

the current distribution contour looks like the geomet-ric pattern of p-electrode. At the low injection current(I ≤ 200mA), current spreads more easily along Path Athan Path B represented in Fig.1. This is because metalfills in the through-hole, shortening the AlN/Si junction,and thus reducing the resistivity. However, when the injec-tion current is increased large enough to make the AlN/Sijunction conductive, current simultaneously spreads alongPath A and Path B and the two spreading path is underthe competition mechanism. The choice of spreading pathdepends on the sum of voltage drops across the n-GaN,TCL, p-GaN, lapped silicon substrate, and the turn onvoltage of AlN/Si junction. Current will distribute uni-formly when it spreads along Path A and Path B equally.

Fig.5 shows a series of simulated current distributionas a function of position in the active layer at differentinjection current in the vertical conducting LED II withelectrode Pattern 2. At low injection current (I = 20mA),current crowds at the four corners of the chip as shown inFig.5(a). When injection current increases to 100mA oreven larger, the current intensity in the active layer underthe p-electrode is larger than other region. When pumpedwith low current, the regions near the tips of p-electrodeare more easily conducted than others. This may be dueto the effect of high field point along the edges of theelectrode[19]. Due to the fact that the resistance of TCLis smaller than that of the n-GaN layer, current crowdingemerges at the four corners of the chip at injection currentvalue as low as 20mA. When injection current increases,current begins to spread along Path B shown in Fig.1(b)to crowd at the region under the p-electrode.

Fig.6(a) and (c) show the gray photos of the top viewof biased LED structures at 350mA took under a micro-scope while Fig.6(b) and (d) represent the cross-section ofthe light intensity profile corresponding to straight LineA and dotted Line B in Fig.6(a) and (c) respectively.

Fig. 4. A series of simulated current distribution in the active layer in the LED I with electrode Pattern 2 at different injection

current. (a) I = 20mA; (b) I = 100mA; (c) I = 200mA; (d) I = 300mA; (e) I = 350mA; (f) I = 500mA

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Current Spreading Effects in Vertical GaN-Based Light-Emitting Diode on Si(111) Substrate 675

Fig. 5. A series of simulated current distribution in the active layer in the LED II with electrode Pattern 2 at different injection

current. (a) I = 20mA; (b) I = 100mA; (c) I = 200mA; (d) I = 300mA; (e) I = 350mA; (f) I = 500mA

Fig. 6. Gray photos of the top view of biased LED took undermicroscope and the cross-section of the light intensity

profile corresponding to straight Line A and dotted

Line B. (a) and (b) related to LED I; (c) and (d) re-lated to LED II

The parts where the light intensity greatly decline inFig.6(b) and (d) are related to the p-electrode location.The uniformity percentage can be characterized using theratio of the minimum/maximum intensities. As seen fromthe Fig.6(b) and (d), the light uniformity percentage is60.5% and 83.5%, respectively. Since the optical emissionintensity of an LED is proportional to the current densityin the active region[13], these results agrees well with cur-rent distribution shown in Fig.4(e) and Fig.5(e), wherethe simulated uniformity percentage is 58.3% and 85.7%,respectively.

2. Influence of electrode pattern on the currentdistribution uniformity

The current distributions in the active layer of LEDwith different electrode patterns are simulated at injectioncurrent of 350mA as shown in Fig.7. The coordinate origin

is also set as the chip center. Fig.7(a), (b), and (c) showthe current spreading distributions in the active layer ofLED I whereas Fig.7(d), (e), and (f) show the currentdistribution in the active layer of conventional LED II.As shown in these figures, the effect of electrode patternon the current distribution in the active layer of LED withdifferent structures is conspicuous. The current distribu-tion uniformity in LED I with electrode Pattern 2 is betterthan that in LED I with electrode Pattern 1 and worsethan that in LED I with electrode Pattern 3, whereascurrent distribution uniformity in LED II with electrodePattern 2 is the best. However, the crowding in LED I ismore significant than that in LED II regardless the elec-trode pattern. This may due to the fact that AlN/Si junc-tion was partly shortened by metal filling in the through-hole. The voltage remained on such short-circuit area ismuch lower than that on the remaining AlN/Si junction,which causes enhanced current spreading along Path Aat low injection current. It was reported that a perfectlyuniform current distribution at the lateral geometric LEDstructure could be achieved at the critical condition whenρt/tt = ρn/tn, where ρt, tt, ρn, and tn are the electrical re-sistivity, thickness of the transparent conductive layer andn-GaN layer, respectively[6]. However, in this study, thethickness of n-GaN layer is too thin so that ρt/tt � ρn/tn.As a result, current prefers to spread in the TCL alongPath A and crowd near the edge of n-electrode at lowinjection current. Therefore, the introduction of through-hole structure reduces the current uniformity. To solvethis problem, n-GaN layer with enough thickness needsto be grown on Si substrate. In this case, as the injectioncurrent increases, AlN/Si junction is gradually turned onand current would consequently spread vertically alongPath B, providing more uniformed current spread. How-ever, the introduction of current spreading Path A affectsthe current spreading uniformity.

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676 Chinese Journal of Electronics 2016

Fig. 7. The current distributions in the active layer of LED with three electrode patterns at injection current of 350mA.(a), (b) and (c) related to LED I; (d), (e) and (f) related to LED II

Fig.8(a) and (b) show the electrical and optical char-acteristics of LED I and LED II, respectively. Comparedto LED II, the series resistance and operating voltage ofLED I were reduced and the light output was increased.This is due to the fact that the band offset of AlN/Sijunction and the interlayer is shortened by the metal fill-ing in the through-hole. The decrease in series resistanceresults in the reduction of thermal effect and increase ofthe internal quantum efficiency. Furthermore, the intro-duction of through-hole makes current easily crowd nearthe n-electrode, which effectively avoids the shadow effectof p-electrode. In addition, the current-light output andcurrent-voltage characteristics are influenced by the elec-trode patterns, since the electrode pattern affects the cur-rent spreading uniformity dramatically as shown in Fig.7.According to Fig.7(a), (b), and (c), the current distri-bution uniformity in LED I with electrode Pattern 2 issuperior to that with electrode Pattern 1 and inferior tothat with electrode Pattern 3. This result shows an agree-ment with the current-light output and current-voltagecharacteristics shown in Fig.8(a). Nevertheless, there is adiscrepancy between the current distribution uniformityof LED II and LED I. According to Fig.7(d), (e), and(f), the current distribution uniformity of LED II withelectrode Pattern 2 is the best. This is also consistent tothe current-light output and current-voltage characteris-tics presented in Fig.8(b). Therefore, the electrode patterneffect on the current spreading uniformity is distinguish-ing for different LED structures. Compared Fig.8(a) withFig.8(b), it can be found that light output intensity ofLED I is obviously higher than that of LED II. This maybe due to that the introduction of through-hole drainsthe current out of the region under p-electrode to avoidabsorption and reflection by p-electrode. This function ofthe through-hole is the same as the Current blocking layer(CBL) inserted beneath the p-pad electrode by means of

an insulating SiO2 layer[20].

Fig. 8. The electrical and optical characteristics of (a) LED Iand (b) LED II

V. Conclusion

In this paper, a 3D circuit model was developed to in-vestigate the current distribution effects in vertical GaN-based Light-emitting diode (LED) with different struc-tures and with different electrode patterns on Si(111) sub-strate. It showed that the current distribution uniformity

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Current Spreading Effects in Vertical GaN-Based Light-Emitting Diode on Si(111) Substrate 677

was greatly affected by the LED structure and electrodepattern. Additionally, it also can be found that the in-troduction of through-hole structure could reduce the se-ries resistance and turn-on voltage of the LED, on theother hand reducing the current distribution uniformity.However, the through-hole makes current easily flow nearthe n-electrode, which avoids the shadowing effect of p-electrode. The light output uniformity measured experi-mentally shows a good consistency with current distribu-tion uniformity by simulation. The circuit model devel-oped in this paper provides an effective method to eval-uate the state of current distribution in the active layerof various LED structures, especially those designed on Sisubstrate.

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[7] A. Ebong, S. Arthur, E. Downey, et al., “Modeling and circuit

simulation of GaN-based LEDs for optimum efficiency through

uniform current spreading”, Proc. SPIE, Solid State LightingII, Seattle, USA, pp.187–194, 2002.

[8] A. Ebong, E. Downey, S. Arthur, et al., “Simplified electro-

optical model for device and circuit simulations of LEDs”, Proc.

SPIE, Third International Conference on Solid State Lighting,San Diego, California, USA, pp.286–293, 2004.

[9] S. Hwang and J. Shim, “A method for current spreading analy-

sis and electrode pattern design in LEDs”, IEEE Transactions

on Electron Devices, Vol.55, No.5, pp.1123–1128, 2008.

[10] S. Hwang, J. Yoon, J. Shim, et al., “Effect of electrode pat-

tern on light emission distribution in InGaN/GaN light emittingdiode”, Physica Status Solidi (c), Vol.5, No.6, pp.2179–2182,

2008.

[11] J. Shim, J. Yun and H. Kim, “Current spreading and its re-

lated issues in GaN-based light emitting diodes”, Proc. SPIE,Gallium Nitride Materials and Devices IV, SanJose, USA,

pp.72160V-1–9, 2009.

[12] J.S. Yun, J.I. Shim and D.S. Shin, “Enhancing current spread-

ing by simple electrode pattern design methodology in lateral

GaN/InGaN LEDs”, Electronics Letters, Vol.45, No.13, pp.703–705, 2009.

[13] G.J. Sheu, F.S. Hwu, J.C. Chen, et al., “Effect of the elec-

trode pattern on current spreading and driving voltage in aGaN/sapphire LED chip”, Journal of the Electrochemical Soci-

ety, Vol.155, No.10, pp.H836–H840, 2008.

[14] J.C. Chen, G.J. Sheu, F.S. Hwu, et al., “Electrical-optical anal-ysis of a GaN/sapphire LED chip by considering the resistivity

of the current-spreading layer”, Optical Review, Vol.16, No.2,pp.213–215, 2009.

[15] F.S. Hwu, J.C. Chen, S.H. Tu, et al., “A numerical study of

thermal and electrical effects in a vertical LED chip”, Jour-nal of the Electrochemical Society, Vol.157, No.1, pp.H31–H37,

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[16] H. Kondo, N. Koide, Y. Honda, et al., “Series Resistance inn-GaN/AlN/n-Si Heterojunction Structure”, Japanese Journal

of Applied Physics, Vol.308, No.5726, pp.1274–1278, 2005.[17] B. J. Zhang, T. Egawa, H. Ishikawa, et al., “Thin-film InGaN

multiple-quantum-well light-emitting diodes transferred from

Si(111) substrate onto copper carrier by selective lift-off”, Ap-plied Physics Letters, Vol.86, No.7, pp.071113-1–3, 2005.

[18] J.T. Wei, B.J. Zhang, G. Wang, et al., “Vertical GaN-

based light-emitting diodes structure on Si(111) substrate withthrough-hole”, Japanese Journal of Applied Physics, Vol.49,

No.7R, pp.072104-1–3, 2010.[19] N.G. Green, A. Ramos and H. Morgan, “Ac electrokinetics:

a survey of sub-micrometre particle dynamics”, Journal of

Physics D: Applied Physics, Vol.33, No.6, pp.632–641, 2000.[20] C. Huh, K.S. Lee, E.J. Kang, et al., “Improved light-output

and electrical performance of InGaN-based light-emitting diodeby microroughening of the p-GaN surface”, Journal of applied

Physics, Vol.93, No.11, pp.9383–9385, 2003.

WEI Jingting was born in 1982. She

received the Ph.D. degree in optical engi-neering from Sun Yat-sen University. She

is now a lecturer in the Open University of

Guangdong, Guangdong Polytechnic Insti-tute. Her research interests include the fab-

rication and current spreading distributionanalysis of light emitting-diodes on Si(111)

substrate. (Email: migrant88@163.com)

ZHANG Baijun (corresponding au-

thor) was born in 1971. He received the

Ph.D. degree from Jilin University. He isa professor and doctor supervisor of op-

tical engineering and microelectronics at

Sun Yat-sen University. His research inter-ests include LED fabrication on Si sub-

strate and wide band semiconductor ma-terial growth on Si substrate. (Email: zh-

baij@mail.sysu.edu.cn)

WANG Gang was born in 1968.He received the Ph.D. degree from Nagoya

Institute of Technology, Japan. He is aprofessor and doctor supervisor of optical

engineering. His research interests include

growth of semiconductor materials for op-toelectronic compounds and devices de-

sign. (Email: stswangg@mail.sysu.edu.cn)

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Current spreading effects in vertical GaN-based light-emitting diode (LED) on

Si(111) substrate*

垂直结构 Si（111）衬底 GaN 基发光二极管（LED）有源区内的电流扩展效应

研究

卫静婷 1，2，张佰君 2，王钢 2

（1. 广东理工职业学院，广东开放大学，广州 510091，中国）

（2．微电子学院，光电材料与技术国家重点实验室，中山大学，广州 510275，

中国）

摘要：GaN 基 LED 的优化设计对它的稳定性至关重要。本论文提出了一种新的

三维的电阻网络的电路模型用以研究垂直导通结构的 Si 衬底 GaN 基 LED 有源

区内电流分布的情况，被研究的 LED 具有不同器件的结构和电极形状。这种电

路模型包含透明导电层（TCL）的电阻值，外延层的电阻值，代表有源层的理想

二极管以及 AlN/Si 也被认为是 AIN/Si 异质结。仿真结果表明，两种不同器件结

构的 LED 有源区内的电流分布均受到电极形状和器件结构的影响。同时，LED

芯片表面出光均匀性的实验结果与仿真结果高度吻合。LED 的电学性能和光学

性能都明显受到电流分布均匀性的影响。

关键词：发光二极管，电流分布均匀性，电路模型

* 这项工作受到广东开放大学校内科研项目（No.1318）、国家自然科学基金(No.61274039) 、

广东省国际科技合作项目(No.2013B051000041)等的资助。

11

Ⅰ 引言

GaN基LED近年来被广泛应用于固态照明、液晶显示和移动手机的背光源、

交通灯等众多领域，使得LED的发展迅猛。【1】在这众多的应用产品中，又需要开

发出高亮度和大功率的LED。对于大功率LED而言，热效应起着一个至关重要的

作用【2】，它源于两个方面，即有源区内小电流注入时的非辐射复合和大电流注入

时电流聚集引起的焦耳热【3】。电流聚集效应同样会影响大尺寸LED器件的出光均

匀性【4】，为了降低该效应，几种用于分析该效应的电路模型应运而生。Guo【4-5】

等人假设p接触电极是等势体，提出了一种用于分析蓝宝石衬底LED有源区内电

流聚集效应的模型，并得出结论：电流强度随着距离接触电极边缘的长度呈现出

e指数衰减的趋势。上述模型只适用于p型电流扩展金属层的厚度足够厚的条件，

而在实际生产中，为了保证电流扩展层的透过率，p型电流扩展金属层不宜过厚，

因此，p型电流扩展金属层的电阻不能够被忽略，也就是说，p型电流扩展金属上

各点不能被视为等势体。鉴于此，H. Kim【6】等人对Guo等人提出的上述模型进行

了修正，引入了p型透明导电层的电阻。Ebong【7，8】等人提出了一种电-光模型用

于评估电流扩展均匀性与LED器件结构之间的关系。Shim【9-12】等人则开发出一

种三维电路模型用于分析电极形状对LED有源区内的电流扩展情况造成的影响。

Chen【13-15】等人则系统地分析了电流扩展均匀性对LED的电特性、光萃取效率以

及热效应的影响。被报道的众多模型都仅仅适用于研究蓝宝石衬底的LED有源区

内的电流扩展效应，并不适合用于分析Si衬底GaN基LED有源区内的电流扩展效

应。首先，Si衬底与蓝宝衬底的电学性能不同。其次，为了改善外延层质量，Si

衬底与GaN之间引入ALN插入层，从而形成了一个更大的带隙，AlN和Si衬底之

间形成了一个异质结，从而限制了垂直导通结构的Si衬底LED的发展【16】。目前，

Si衬底GaN基LED有源区内的电流扩展效应的研究鲜有报道。同蓝宝石衬底相

比，Si衬底具有价格低、尺寸大、良好的导热和导电性能、芯片级别封装等优点，

尤其是成熟的Si电子器件集成工艺也促使其成为在同一芯片上实现光电集成的

焦点。Si衬底将逐渐取代蓝宝石衬底，因此，必须对Si衬底LED有源区内电流扩

展进行分析研究。本文提出了一种三维电路模型，用于分析具有不同器件结构的

LED有源区内的电流分布情况以及电极形状对电流分布均匀性的影响，在该电路

模型中，AlN/Si异质结被认为是理想二极管。为了验证模型的准确性，我们制作

12

了两种不同结构的Si衬底GaN基LED芯片，芯片尺寸大小为1mm×1mm，实验结

果与仿真结果进行对比之后，高度吻合。

Ⅱ 实验过程

本文中所用到的 Si 衬底 InGaN/GaN MQWs LED 是使用化学气相沉积系统

进行生长的。具体的材料生长细节已被发表【17】。外延层生长完成之后，LED 芯

片被制作成了两种垂直导电的结构，分别为带通孔的垂直结构和传统的垂直结

构，芯片尺寸为 1mm×1mm，具体的制作过程也已经作为论文发表【18】。带通孔

的垂直结构和传统的无通孔的垂直结构被分别记为。通孔内沉积有金属将 AlN/Si

异质结短路。图 1（a）和（b）是 LEDⅠ和 LEDⅡ的截面图。

图 1 两种垂直结构的 LED芯片（a）通孔结构 LEDⅠ；（b）传统结构 LEDⅡ

Ⅲ. 等效电路模型

图 2 为 LED 芯片的三种不同的电极形状，被记为 pattern1，pattern2 和 pattern3。

其中灰色的形状是阴极，通孔就在阴极区域内，另外一种形状为阳极。图 3（a）

和 3（b）是两种结构的 3 维电路模型图，该模型使用了电极形状 2。采用有限元

分析法，每层结构都被划分为一系列的六面体单元，每个六面体单元代表理想二

极管或者电阻，如下：有源层和 AlN/Si 异质结用理想二极管来表示，其他外延

层以及金属和外延层之间的接触用电阻来表示。由于 LED 的调制频率通常是有

限的几十千赫【9，10】，因此电感和电容效应被忽略，即电容相当于开路，电感相

当于短路。透明导电层与外延层之间的比接触电阻率则利用传输线模型（TLM）

由实验数据获取。六面体单元的外延层参数和电路参数在表 1 中列出。其中 ρn, ρp,

ρc, Rsh, 和 Vth 分别表示 n-GaN 的电阻率，p-GaN 的电阻率，比接触电阻率，面

电阻以及阈值电压。由于 p 电极的电阻率远小于透明导电层，p-和 n-电极被分别

13

假设为等势体。另外，由于透明导电层的电阻远小于 p-GaN 的横向电阻，因此

电流沿 p-GaN 横向扩展的路径被忽略。值得注意的是，两种电路模型的区别在

于图 3（a）中，贴近通孔的 AlN/Si 异质结被填入到通孔内的金属所短路。

图 2. LED 芯片的三种电极形状：（a）pattern1，（b）pattern2，（c）pattern3

图 3. Si 衬底 LED 的 3D 电流扩展分析的电路仿真模型：(a) LEDⅠ；（b）LEDⅡ.

表 1. 电路模型参数表

layers n-GaN p-GaN Ohmic

contact

TCL Intrinsic diode

active layer GaN/AlN/Si

Circuit

parameters

ρn(Ω·cm) ρp(Ω·cm) ρc(Ω·cm2) Rsh(Ω/□) Vth(V) Vth(V)

0.004 6.25 9e-3 12 2.5 1 [11]

Ⅳ. 结果和讨论

1．不同垂直结构的硅衬底 GaN 基 LED 的有源区中的电流分布情况的研究

本文利用 PSPICE 软件对所提出的 3 维电路模型进行仿真，从而获得 LED

有源区内电流分布的细节。图 4 表示出注入电流值不同时，在 LEDⅠ芯片（pattern

2）有源区内电流分布随芯片位置变化的一系列等高线仿真结果。坐标原点设置

在芯片的中心位置。注入电流值从 20mA 变化到 500mA，从图中可以发现，随

着注入电流值的变化，获得的电流分布的等高线仿真图也在不断发生变化。注入

电流值较小时，电流在靠近芯片边缘的地方聚集，随着注入电流值的增大，电流

(a) (b)

14

先继续在靠近芯片边缘的地方聚集，当电流增加到一定程度，电流开始在电极下

方或者靠近电极的区域聚集。可以直观的看到，当注入电流超过 200mA 时，电

流开始聚集在 p 电极下方，这种现象在注入电流为 500mA 时尤为明显，如图 4

（f）所示。低电流注入下（I≤200 mA），由于通孔内金属将 AlN/Si 异质结短路，

所以这种情况下，电流易于横向扩展，然后经过通孔内的金属垂直导通到硅衬底，

路径如同图 1（a）中的 pathA，但是随着注入电流的增大，由于 AlN/Si 异质结

的导通，电流逐渐沿图 1（a）中的 path B 流通，此时，电流扩展的两种路径处

于竞争机制，电流究竟沿 path A 还是 path B 进行流通，取决于 n-GaN, 透明导电

层, p-GaN, 减薄的硅衬底, 以及 AlN/Si 异质结上的总的电压降之和，当这两种

路径的总电压一致时，电流处于均匀扩展状态。

(a) I=20mA (b) I=100mA (c) I=200mA

(d) I=300mA (e) I=350mA (f) I=500mA

图 4. 注入不同电流值的 LEDⅠ（pattern 2）有源区内电流分布等高线图

图 5 表示出注入电流值不同时，在 LEDⅡ芯片（pattern 2）有源区内电流分

布随芯片位置变化的一系列等高线仿真结果。注入电流值较小时(I=20 mA)，电

流在靠近芯片四个角边缘的地方聚集，随着注入电流值的增大到 100mA 甚至更大

时，电流在电极下方或靠近电极的区域聚集。注入电流较小时，电流在电极的指

端附近产生高电场的现象较为明显【19】，因此，电流在靠近芯片边缘的地方聚集，

而当注入电流值增大后，虽然仍存在电流在电极的指端附近产生高电场的现象，

但是，这种现象已经不是很明显，电流在 LED 芯片内部，沿 Path B扩展。此时，

15

电流开始在 p电极下方聚集。

(a) I=20mA (b) I=100mA (c) I=200mA

(d) I=300mA (e) I=350mA (f) I=500mA

图 5. 注入不同电流值的 LEDⅡ（pattern 2）有源区内电流分布等高线图

图 6（a）和 6（c）为显微镜下拍摄的两种结构 Si 衬底 LED 在注入电流为 350

mA 时的发光照片灰度图，图 6（b）和 6（d）沿灰度图中的 A、B 两条直线路

径提取的相对发光强度图。图 6（b）和 6（d）中光强骤降那部分与 p 电极的位

置相对应，是由于 p 电极的挡光效应造成的。这里，我们定义最小光强值与最大

光强值的比值最为均匀性百分比。那么，从图（b）和 6（d）中可以计算出它们

相对应的光强均匀性分别为 60.5% 和 83.5%。由于 LED 的光输出强度正比于

LED 有源区内的电流密度【13】，因此，这个实验结果与图 4（e）和图 5（e）的仿

真结果中的电流均匀性百分比高度吻合，图 4（e）和图 5（e）的仿真结果中的

电流均匀性百分比分别为 58.3%和 85.7%。

16

图 6. 在注入电流为 350mA 下的发光照片灰度图以及沿灰度图中的 A、B 两条直线路径提取

的相对发光强度图：(a)&(c) LEDⅠ；(b)& (d) LEDⅡ

2．电极形状对电流分布均匀性的影响

图 7 分别为图 4 所示三种电极形状对应的注入电流为 350mA 时，两种垂直

结构 Si 衬底 LED 有源区内的电流分布等高线仿真图，坐标原点同样设置在芯片

的中心位置。其中图 7(a)，7(b)，7 (c)对应 LEDⅠ，图 7(d)，7(e)，7(f)对应 LED

Ⅱ。从图中可以看出，对于 LEDⅠ，电极 pattern3 对应的 LED 有源区内的电流分

布均匀性最好， pattern2 次之，pattern1 最差。对于 LEDⅡ，电极 pattern2 对应

的 LED 有源区内的电流分布均匀性最好，pattern3 次之，pattern1 最差。但是无

论对于哪个电极形状，LEDⅡ的有源区内的电流扩展均匀性都要好于 LEDⅠ有源

区内的电流扩展均匀性。这主要是由于 AlN/Si 异质结在通孔部分被填充在通孔

内的金属所短路。因此，被短路区域的电压要低于其他部位未被短路区域的电压，

造成在低电流注入下，电流更容易沿着 Path A 进行扩展。根据文献报道【6】，电

流横向扩展均匀性最佳的条件是 ρt/tt=ρn/tn，ρt, tt, ρn, 和 tn 分别代表透明导电层的

电阻率、透明导电层的厚度，n-GaN 的电阻率和 n-GaN 的厚度。然后，由于，

在本文的研究中，由于 n-GaN 的厚度过薄导致 ρt/tt << ρn/tn，导致注入电流小时，

电流更容易在透明导电层内沿着 path A 进行扩展然后聚集在 n 电极的边缘。因

此，通孔结构的引入降低了电流扩展均匀性。为了解决这个问题，必须增大 Si

衬底上生长的 n-GaN 的厚度。同时，由于注入电流的增加，AlN/Si 异质结逐渐

导通，电流逐渐沿着 path B 开始垂直扩展，使得电流的扩展均匀性逐渐变好。

但是，电流沿 path A 进行扩展的路径引入确实影响了电流扩展的均匀性。

17

(a) (b) (c)

(d) (e) (f)

图 7. 注入电流为 350mA 下不同电极形状 Si 衬底 LED 有源区内电流分布等高线图：(a)-(c)

LEDⅠ;(d)-(f) LEDⅡ

图 8（a）和图 8（b）分别为具有三种电极形状的 LEDⅠ和 LEDⅡ的 I-V 和 I-L

曲线图。由图可知，与 LEDⅡ相比，LEDⅠ的串联电阻降低同时出光强度增加了，

这是因为通孔内的金属短路了 AlN/Si 异质结，串联电阻的降低改善了芯片内的

热效应从而提高了芯片的内量子效应。同时，通孔的引入使得电流更易于聚集在

n电极的边缘，有效阻住了 p电极的挡光效应。除此之外，图 7所示的电极形状

对电流扩展均匀性造成的影响也可以在 I-V 和 I-L曲线中体现出来。根据图 7(a),

7(b), and 7(c)所示，对于 LEDⅠ，电极 pattern3 对应的 LED 芯片的电流扩展均匀性

最好，pattern2 次之，pattern1 最差。这一点同图 8(a)的 I-V、I-L 特性高度吻合。

然而，LED Ⅱ与 LED Ⅰ的电流扩展均匀性的情况有所不同，根据图 7(d), 7(e), 和

7(f)，对于 LEDⅡ，电极 pattern2 对应的 LED 芯片的电流扩展均匀性最好。这一

点也与图 8(b)展示的 I-V、I-L 特性保持一致。因此，对于不同器件结构的 LED，

其电流扩展均匀性受到电极形状影响的趋势不同。对比图 8(a) 和 8(b)，可以发

现，LED Ⅰ的光输出强度要明显高于 LED Ⅱ，这是由于通孔的作用，使电流避

免聚集在金属电极下方，相当于起到了阻挡层的作用，这样，出光效率更高，这

个作用等效于在 p 电极下方插入一层 SiO2作为绝缘阻挡层的效果【20】。但是其电

流扩展的不均匀性也影响了光衰减的快慢，可以看出，LEDⅡ的光衰电流要大于

18

LEDⅠ的衰减电流值。同时，对于同种结构的 LED 而言，电流扩展均匀性越好，

出光强度越高。

图 8. 三种电极形状的垂直结构 Si 衬底 LED 的 I-V 和 I-L 曲线图：(a) LEDⅠ；(b) LEDⅡ

Ⅴ. 结论

本文提出了一种 3 维结构电路仿真模型，对两种不同垂直器件结构且制备不

同电极形状的 Si 衬底 LED 有源区内的电流分布进行了仿真计算，并用实验进行

验证。仿真结果表明，器件结构、芯片采用的电极形状均对两种 Si 衬底 LED 有

源区内的电流分布均匀性有影响。同时，通过研究发现，通孔结构的引入可以降

低 LED 的串联电阻和开启电压，但是，也降低了电流分布的均匀性。然而，通

孔的引入使得电流更容易流向 n 电极，避免了 p 电极的挡光效应。实验测试获得

的器件表面光输出的均匀性同仿真获得的电流扩展均匀性保持了高度一致性。因

此，本文提出的电路模型可以对不同器件结构的 LED 有源区内的电流分布进行

有效地评估，尤其是 Si 衬底 LED。

19

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