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Study of photon extraction efficiency in InGaNlight-emitting diodes depending on chipstructures and chip-mount schemes

Song Jae LeeChungnam National UniversityElectronics Engineering DepartmentYusung-gu Koong-dong 220Tajeon 305-764, KoreaE-mail: [email protected]

Abstract. The performance of InGaN LEDs in terms of photon extrac-tion efficiency is analyzed by the Monte Carlo photon simulation method.Simulation results show that the sidewall slanting scheme, which workswell for the AlInGaP or InGaN/SiC system, plays a very minimal role inInGaN/sapphire systems. In contrast to InGaN/ SiC systems, a lowerrefractive index sapphire substrate restricts the generated photons toenter the substrate, minimizing the chances for the photons to be de-flected by the slanted sidewalls of the epitaxial semiconductor layers thatare usually very thin. The limited photon transmission to the sapphiresubstrate also degrades the photon extraction efficiency, especially inthe epitaxial side down mount. One approach to exploit the photon ex-traction potential of the epitaxial side down mount may be to texture thesubstrate-epitaxy interface, by possibly growing the epitaxial layers on asapphire substrate that is either appropriately surface textured or pat-terned and etched. In this case, randomized photon deflection off the

textured interface directly increases the number of photons entering thesapphire substrate, from which they easily couple out of the chip, therebyimproving the photon extraction efficiency drastically. 2006 Society ofPhoto-Optical Instrumentation Engineers. DOI: 10.1117/1.2151194

Subject terms: light-emitting diode; photon extraction efficiency; Monte Carloanalysis.

Paper 040641RR received Sep. 9, 2004; revised manuscript received May 21,2005; accepted for publication Jun. 1, 2005; published online Jan. 13, 2006.

1 Introduction

InGaN light-emitting diodes LEDs may be the most im-

portant element in visible LEDs. They have excellent reli-ability and brightness, and also cover a very broad spectralrange, from ultraviolet UV to amber.1 Their blue andgreen lights are combined with red lights from eitherAlInGaP or AlGaAs LEDs to achieve high-quality full-color displays. Furthermore, blue emission from InGaNLEDs has been exploited to excite some phosphors forimplementing white LEDs, which have important applica-tions in backlights for liquid crystal display LCD and,with the light output being enhanced ever more, start toreplace incandescent lamps in general lighting applications.

One of the key issues in achieving enhanced output fromLED chips is how to maximize the photon output couplingefficiency or the photon extraction efficiency. In the case of

rectangular chips, as described in Fig. 1, a significant por-tion of the generated photons are trapped inside the chipcavity, as a result of the continued total internal reflectionsoff the chip wall, significantly degrading the photon extrac-tion efficiency. However, if the LED chip cavity is de-formed either by texturing the surface of the chip or slant-ing the sidewalls, as schematically shown in Fig. 2, thephotons are deflected rather randomly off the chip walls,breaking the chain of the continued total internal reflec-tions. As a consequence, photon extraction efficiency is im-

proved significantly. However, the effectiveness of the chipcavity deformation scheme that has been widely employed

in InGaAlP or AlGaAs LED structures27

depends stronglyon material systems, LED chip structures, and chip-mounting schemeseither epitaxial side up epi-up or ep-itaxial side down epi-down.

Figure 3 shows various InGaN/sapphire LED chipsmounted either epi-up or epi-down on the reflector. In gen-eral, the epi-down mount is preferred over the epi-up mountin terms of heat dissipation. However, in terms of photonextraction efficiency, the advantage of the epi-down mountmay not be very obvious. The sapphire substrate with arelatively low refractive index will function as a total inter-nal reflection barrier for the generated photons to enter thesubstrate, allowing only a small portion of generated pho-tons to be transmitted to the substrate. As a result, the ad-

vantage of the epi-down mount the photons once transmit-ted to the substrate easily couple out, because the substrateis relatively well index-matched to the encapsulant andblocked neither by the reflector conductor or the electrodecannot be fully exploited. Another point in epi-downmounts is that the design of the reflector or heat sink is ingeneral rather complicated. In epi-down mounts, to achieveelectrical isolation between the anode and cathode, the re-flector conductor should be mounted on an insulator layerand partitioned into two parts. The insertion of an insula-tion layer will inevitably degrade heat dissipation. On theother hand, in the epi-up mount, to the LED chip is0091-3286/2006/$22.00 2006 SPIE

Optical Engineering 451, 014601 January 2006

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mounted on a solid conductor block and will not requireany insulting layers. Thus, if we consider only the heatdissipation point of view, the sapphire substrate may beremoved better and mounted in epi-up, as shown in Fig.3d. However, without the sapphire substrate, the effect ofrefractive index matching between LED chip and the en-capsulant becomes poor, degrading the photon extractionefficiency significantly. Figures 3e and 3f show LEDchips in which the substrate-epitaxy interface is textured.The texturing of the substrate-epitaxy interface will deflectincoming photons rather randomly, significantly increasingthe number of photons transmitted to the substrate. As aresult, the photon extraction efficiency will be improved

significantly, especially in the epi-down mount, as shown inFig. 3f. One of the practical approaches to implement thetextured substrate-epitaxy interface may be to grow epitax-ial layers on a substrate that is appropriately patterned andetched.

The most important objective of this study is to providegeneral ideas of how the photon extraction efficiency inInGaN LEDs is affected by particular LED chips or pack-aging structures: surface texturing, sidewall slanting, epi-upor epi-down mount, substrate removal, substrate-epitaxy in-terface texturing, and various combinations of the schemes.Such knowledge may provide valuable insights for devel-oping new LED chip or packaging structures.

2 Important Features of InGaN Light-EmittingDiodes

InGaN LEDs are usually grown either on a sapphire or SiCsubstrate, as schematically shown in Fig. 1, and are quiteunique. In a InGaN system, for instance, the conductivity ofthe p-GaN epitaxial layer is in general at least two orderssmaller than that of the n-GaN layer, mainly due to ex-tremely poor carrier mobility of about 10 cm2/voltsec8 ofthe p-GaN layer. In addition, the p-GaN upper carrier con-finement layer in InGaN LEDs is thin, typically 0.2 m. Asa consequence, the surface resistance of the p-GaN upperconfinement layer alone is extremely high and therefore the

spreading of the current in the lateral direction is very lim-ited, causing severe current crowding in certain regions ofthe active layer.9 Thus, to help the current spread moreuniformly over a wider region of the active layer, thep-GaN upper carrier confinement layer is often depositedon the top with a very thin typically 200 semitranspar-ent p-ohmic metal layer, as illustrated in Fig. 1b. Thefeatures of the thin ohmic metal layer deposited on the topsurface of the chip and the relatively thin upper carrierconfinement layer make the InGaN LED structures quiteunique compared to the well-established high-brightnessAlInGaP LED structure as described in Fig. 1d. The struc-ture in Fig. 1d that has been widely employed either in

Fig. 1 Important LED structures: a InGaN/sapphire, b top view of InGaN/sapphire, c InGaN/SiC,and d AlInGaP.

Lee: Study of photon extraction efficiency in InGaN light-emitting diodes


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AlInGaP or AlGaAs systems utilizes the so-called windowlayer,10 which is thick, typically 50 m, and will help sig-nificantly reduce the photon interaction with the top ohmicelectrode, improving the photon extraction efficiency. It isnoted that ohmic electrodes in general are known to be veryabsorptive, especially either in AlGaAs or AlInGaPsystems.

In InGaN LEDs, however, the upper carrier confinementlayer is usually too thin to work as a window layer, and asignificant portion of generated photons will inevitablyreach either the top electrode or the very thin ohmic metallayer deposited on the top surface. It is noted that even the

photons directed downward can easily arrive at the top sur-face, as a result of reflection off the substrate of relativelylow refractive index. Thus, if the photon absorption in theohmic region underneath the ohmic metal is as severe as inan AlGaAs or AlInGaP system, the photon extraction effi-ciency would be extremely poor. Instead, however, the ac-tual external quantum efficiency achieved in InGaN LEDsis as high as 10 to 30%, comparable to that in the AlInGaPLED structure shown in Fig. 1d. The discrepancy clearlyindicates that the photon absorption in ohmic regions inInGaN systems must be much smaller than either inAlInGaP or AlGaAs systems. It is noted that in general theohmic contact to a wide-bandgap semiconductor such as

GaN has a relatively large contact resistance and may be farfrom truly ohmic. For instance, Ni/Au ohmic metal oftenemployed in InGaN systems shows a fine surface morphol-ogy without any splotchy patterns often observed in alloyedohmic metals for lower-bandgap semiconductors, possiblyindicating that the crystalline state underneath the ohmicmetal may still be rather intact and lead to a very smallphoton absorption compared to other material systems.

3 Fundamentals for Photon Extraction

In terms of photon extraction, InGaN LEDs will have someadvantages over AlInGaP or AlGaAs LEDs due to better

index matching to the encapsulant, most likely the epoxy.For photons to couple out of the chip, the angle of inci-dence to chip wall should be smaller than the critical anglec, given by

c = sin1ne/ns, 1

where ns and ne are the refractive indices for the semicon-ductor crystal and encapsulant, respectively. Otherwise,they will be total internally reflected off the chip wall. As aconsequence, the minimum requirement for photons tocouple out of a chip wall is that they must be emitted insidethe so-called escape cone that has a cone-divergence angle

Fig. 2 Cavity-deformed LED chips: a textured surface, b slanted sidewall, and c partially slantedsidewall.



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of 2c. Especially, in the case of chip cavity of a rectangu-lar shape, once the photons are emitted outside the escapecones, they will repeatedly undergo total internal reflectionsoff the chip walls to be permanently trapped inside thechip. The photons trapped inside the chip will be absorbedeventually, significantly degrading the photon extractionefficiency.

In the case of rectangular chips with perfectly flat chipsurfaces, a photon generated at a given point in the activelayer will have six escape cones, one for each wall of thechip cavity, to escape through to the encapsulant, and therewill be no coupling between neighboring escape cones.Thus, in this case, the ratio of the photons trapped insidethe chip cavity of a rectangular shape, trap can be esti-mated approximately by

trap =4 6cns,ne

4, 2

cns,ne = 21 1 ne/ns21/2 , 3

where c is the solid angle of an escape cone. In Eqs. 2and 3, we have assumed that the various layers compris-ing an LED chip have approximately the same value ofreflective index ofns. In the case of InGaN/sapphire, how-

ever, the refractive index of the substrate is quite differentfrom that of the semiconductor crystal layers, and thus trapshould be estimated by a slightly modified form.11 The trapis about as high as 70% for AlInGaP or AlGaAs systems,while it is about 40 and 50% for InGaN/sapphire andInGaN/SiC structures, respectively.

With such a large fraction of photons trapped inside thechip cavity of a rectangular shape, a significant improve-ment of the photon extraction efficiency can be achievedonly by implementing some measures to free the photons ofthe cavity trap. The most practical approaches are to de-form the chip cavity either microscopically surface textur-ing or macroscopically sidewall slanting, as described in

Fig. 3 Various chip-mounting schemes: a epi-up with substrate, b epi-down with substrate, cepi-up without substrate, d epi-down without substrate, e epi-up with textured substrate, and fepi-down with textured substrate.



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Fig. 2. In deformed cavities, the photons, on reflection offthe chip wall, are directed rather randomly so that theyhave some chances to avoid the total internal reflection inthe next encounters with the chip walls. As a result, virtu-ally no photons are trapped inside the chip cavity, signifi-cantly improving the photon extraction efficiency. How-ever, in InGaN systems with a relatively smaller ratio oftrapped photons, the cavity deformation schemes in general

will not be as effective as in AlGaAs or AlInGaP systems.

4 Some Models Required for Light-EmittingDiode Chip Simulation

For analysis of the LED chips, we have used the MonteCarlo photon simulation method explained in detailelsewhere.7 Monte Carlo analysis is in general very versa-tile and can easily be adapted to take into account variousphenomena occurring inside the chip. Accordingly, thesimulation results are in general quite reliable. In thismethod enough photons, for instance about a half million,are generated one after another such that the cumulativedensity of generation is close to the actual carrier distribu-

tion in the active region. Then, the detailed behavior ofeach photon inside the LED chip cavity is traced by pre-dicting various photon events, such as the reflection ortransmission at various interfaces and absorption in thetraveling medium. In this section, we discuss some modelsthat have been included in the Monte Carlo simulation.

4.1 Modeling for the Textured Surface

Photons incident on the textured surface of a chip will bedeflected in a rather random fashion. In principle, if themicroscopic features of the textured surface can be speci-fied exactly, the trajectory of the photons leaving that sur-face might be determined. However, the detailed micro-scopic features of the textured surface would depend

strongly on various parameters, such as the material systemand the particular texturing process involved, and in gen-eral can hardly be specified accurately. Thus, it would be aformidable job to develop a textured surface model that canbe accurately matched to real cases in practical LEDs. It isnoted, however, that the bottom line property of the tex-tured surface, especially in the LED chip analysis point ofview, may be how the photon directions are randomized offthe surface. Thus, in the modeling of the textured surface,we may focus only on the randomization of the photondirections without necessarily specifying the detailed mi-croscopic features of the surface. The following is a briefsummary of the textured surface model that has been de-scribed in detail in Ref. 7.

In the model, we first assume that the local differentialsurface centered at the photon incidence point is flat andhas an area ofdS, as schematically shown in Fig. 4. Then,the differential local surface area vector dS may be ex-pressed by

dS = dSal , 4

where al is the unit vector normal to dS. Ifal is deviatedfrom ar, the unit vector normal to the nontextured flat ref-erence surface, the photon incidence angle on dS will beshifted from the incidence angle expected when the photonis incident on the nontextured flat reference surface instead.

In this case, an abrupt photon direction shift will occur nomatter if the photon is reflected or transmitted. Since theabrupt shift of the photon direction is proportional to theangle between al and ar, the degree of the photon trajec-tory randomization will be decided by the probability dis-tribution function for the angle . In this study, we assume

the probability distribution function P is given byP = k cosnst, 5

where k is an appropriate proportionality constant and nst,named the surface texturing index, is a positive real numberand is related to the degree of the surface randomness. Withnst increasing, the probability distribution function isskewed more sharply along the nontextured flat referencesurface normal ar and, as a result, the local differentialsurface is more likely to be tilted less from the nontexturedflat reference surface, leading to a smaller shift of the pho-ton direction. In the case ofnst=, P will converge to and the surface becomes perfectly flat, as in the non-

textured reference surface. From this reasoning, we can saythat the surface randomness increases with the number1/nst.

The local differential surface deviation angle has inreality two degrees of freedom and, in the simulation, is tobe assigned by generating two random numbers. Once isdetermined, the photon incidence angle on the differentialsurface dS can be evaluated and will then be used to deter-mine the shifted trajectory of the photons leaving thesurface.

One of the most important advantages of this model isthat the surface randomness or the degree of the photontrajectory shift is adjusted easily by just varying the surfacetexturing index nst. It is noted that, in our model, the sur-

face randomness is assumed to be determined solely by thelocal differential surface deviation angle. In practical tex-tured surfaces, however, the surface randomness may bealso affected by various textured surface parameters, suchas the texturing depth and the size of the microscopic sur-face features.3,4 It has been reported that the degree of thephoton trajectory randomization remains virtually constantif the surface texturing depth is over a certain optimumnumber, especially when the surface features are in theshape of pillars.3 It may be quite obvious that when thepillar-shaped surface features are tall enough, the angle ofphoton incidence on the sidewalls of the pillars should notdepend much on their height. This may indicate that the

Fig. 4 Modeling for textured surface.



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degree of the photon trajectory randomization in the tex-tured surface is determined essentially by the directionangle of the local differential surface on which the photonis incident, as assumed in our modeling of the texturedsurface.

One of the problems in our modeling is how to deter-mine the surface texturing index nst that matches a particu-lar textured surface. In principle, we may estimate nst byfirst measuring the approximate distribution function forthe local differential surface direction angles in the texturedsurface, and then curve fitting the resultant distributionfunction to P given in Eq. 5. However, the surface

texturing index nst may be estimated better by comparingexperimental measurements with simulation results. For in-stance, the factor of improvement of the external quantumefficiency achieved with surface-textured LED chips ismeasured. Then, the value of the surface texturing indexnst, which gives rise to the same improvement factor in thesimulation result of the photon extraction efficiency, isfound. We have found that nst of 10 to 20 is appropriate fortypical surface-textured LED chips.7

4.2 Modeling for the Thin Semitransparent OhmicMetal Layer

One thing that makes analysis of InGaN LEDs especially

difficult is that the true nature of the thin ohmic metal layerdeposited on the top surface may not be simply defined asone of purely metallic, ohmic, or dielectric. For instance,the fact that the thin ohmic metal layer is semitransparent tophotons is not easily explained. However, for proper analy-sis of InGaN LED structures, the photon reflection/transmission coefficient, as well as the photon absorption inthe thin ohmic metal, is required. In this study, a ratherintuitive model for the thin ohmic metal layer, in which thecoefficients for photon reflection or transmission can beeasily adjusted, is described.

In this model, we assume that the thin ohmic metal layeris opened by randomly distributed pin holes, as schemati-

cally described in Fig. 5. The photons incident on the pin-holed spot will then be either reflected or transmitted fol-lowing the regular Fresnel reflection formula, while thephotons incident on the rest of the region will be eitherabsorbed or reflected. Under this assumption, the averagephoton reflectance Rthin and the average photon transmit-tance Tthin of the thin ohmic metal may be expressed, re-spectively, by

Rthin = RFreopen + Rthick1 open , 6

Tthin = open1 RFre, 7where Rthick is the photon reflectivity for the thick ohmicmetal as the ohmic electrode pad, RFre is the Fresnel reflec-tivity in the pin-holed region, and open is the ratio of thearea opened by pin holes to the total area of the thin ohmicmetal surface. In thick ohmic metals, the open will be zeroand all the incident photons that survive the absorption willbe reflected back. Thus, the photon reflectivity for the thickmetal Rthick will be expressed by

Rthick = 1 Athick, 8

where Athick is the fraction of the incident photons absorbedin the thick ohmic metal. Athin will then be expressed by

Athin = 1 openAthick. 9

It is noted that, in this model, the adjustment ofopen willaffect both the reflectance and the transmittance of the thinohmic metal layer and, as a consequence, the adjustment ofopen may have, in reality, a similar effect as varying thethickness of the thin ohmic metal.

4.3 Distributed Photon Generation

In general, the probability for the photons generated tocouple out of the chip will depend somewhat on the posi-tion of the generation in the active layer. Thus, to obtain a

Fig. 5 Modeling for the thin ohmic metal layer based on pin-holed thin metal.



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reasonably accurate photon extraction efficiency, the esti-mation for the density of the photons generated in the ac-tive region should be at least approximate to real cases. Ingeneral, the density of the photons generated in the activeregion will be proportional to the current density. In prin-ciple, the exact solution for the current density distributionwill be obtained by solving Poissons equation with appro-priate boundary conditions. However, it is a formidabletask to solve the equation, especially for LED structures of3-D chip geometry. Thus, in this study, we introduce arather intuitive model that can provide photon distribution

in the active region that may be approximate enough formost cases.9

In this model, as described in Fig. 6, we assume that thedensity of electron-hole pairs at an arbitrary point in theactive layer Gx ,y is given by

Gx,y = kGSPx,ySNx,y , 10

where kG is an appropriate proportionality constant, SP andSN are named the positive carrier spreading function andthe negative carrier spreading function, respectively, and SPand SN are presumed to have the same form as a type ofdiffusion function and are expressed, respectively, by12

SPx,y = exp LPx,y/P, 11

SNx,y = exp LNx,y/N, 12

where Lp and Ln are the shortest lateral distances from thegiven point to the p-electrode and the n-electrode, respec-tively, and P and N are named the positive carrier spread-

ing length and negative carrier spreading length, respec-tively. In general, the degree of lateral spreading of thecarriers in a layer may increase with both the conductanceand thickness of the layer, and thus, P and N may beexpressed by

P = kDl

PltPl , 13

N= kDm

NmtNm , 14

where kD is an appropriate proportionality constant, Pl andtPl are the conductivity and thickness of the lth conductivelayer in the p-side, and Nm and tNm are the conductivityand thickness of the mth conductive layer in the n-side,respectively. An example of various functions defined forthe carrier spreading is shown in Fig. 6.

5 Simulation Results

As mentioned earlier, for the analysis of the LED struc-tures, we have used the Monte Carlo method. Before thesimulation results are considered, a discussion is madeabout some important parameters required in the simula-tion. For the sake of fair comparison between structures of

different material systems, we have assumed, if not speci-fied otherwise, all the LED structures have the same chipsize, 250250 m, and the same substrate thickness of100 m. In general, the average distance traversed by thephotons after being generated will be proportional to thechip size, and consequently the chances for photons to beabsorbed inside the chip will decrease exponentially withthe chip size. Refractive indices n and absorption coeffi-cient , ohmic absorption loss Athick, reflector reflectivity,and carrier spreading length for each material system aresummarized in Table 1. In all the calculations, we haveassumed the LED chips were encapsulated with epoxy ofrefractive index 1.50, and it is also noted that, for a single-point calculation, a half million photons were generated

over the active region.Figure 7 shows the effect of surface texturing on thephoton extraction efficiency for three different material sys-tems. As explained already, the surface randomness, in ourtextured surface model, increases with 1 /nst. Even thoughthe photon extraction efficiency improves in general as sur-face randomness increases, the improvement inInGaN/sapphire systems is rather poor compared toInGaAlP systems. In InGaN/sapphire systems, for instance,when 1/nst changes from 10

3 to 1, the photon extractionefficiency improves by about 38%, while it improves by110% in InGaAlP systems. The improvement inInGaN/SiC systems is in between the two systems. In gen-

Fig. 6 Modeling for the current distribution in the active region.



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eral, the surface texturing scheme is less effective in thesystem with smaller ratios of trapped photons inside thechip cavity of a rectangular shape.

Figure 8 shows the effect of sidewall slanting on thephoton extraction efficiency. The photon extraction effi-ciency increases with the sidewall slanting angle. In thecase of LED chips with slanted sidewalls, even though thephotons were total internally reflected off the walls in thefirst incidence to the wall, they would soon find escapecones in the next encounters with the wall. One of theimportant findings in Fig. 8 is that the improvement of the

photon extraction efficiency in InGaN/sapphire systems isvery small compared to either InGaAlP or InGaN/SiC sys-tems. The reason for that can be attributed to the sapphiresubstrate of low refractive index in the InGaN/sapphire sys-tem. The refractive index of the sapphire substrate is about1.77 and smaller than that of the GaN confinement layer.The substrate will act as a total internal reflection barrierfor the generated photons to enter the substrate, seriously

limiting the number of photons being transmitted to thesubstrate. As a consequence, a significant portion of gener-ated photons will be trapped in the semiconductor layerswith a total thickness of less than typically 5 m, and theywill be rarely deflected by sidewalls so thin. In the case ofphotons that overcome the total internal reflection barrier toenter the substrate, they will easily couple out of the chipno matter if the sidewall is slanted or not, since the sub-strate is relatively well index-matched to the encapsulant.As a result, in InGaN/sapphire LED chips, the sidewallslanting scheme plays a very minimal role in improving thephoton extraction efficiency. However, in InGaN/SiC LEDchips, the refractive index of the SiC substrate is about 2.74and is larger than that of the GaN carrier confinement layer.The generated photons will not meet any total internal re-flection barrier for entering the substrate. As a result, thephotons will be transmitted easily into the substrate to beactively deflected by the slanted sidewall and lead to sig-nificantly improved photon extraction efficiency.

Figure 9 shows the effect of surface texturing in LEDchips, where the sidewalls have been already slanted by40 deg. Both in InGaAlP and InGaN/SiC systems, addi-tional surface texturing contributes virtually nothing to im-proving the photon extraction efficiency, because the effectof the photon trajectory randomization by surface texturingis overwhelmed by that of the sidewall slanting. However,in InGaN/sapphire systems, in which sidewall slantingplays a minimized role, surface texturing still helps to sig-nificantly improve photon extraction efficiency. It is also

Table 1 Important parameters used for simulation of the LEDstructures.

InGaN/sapphire

InGaN/SiC InGaAlP

Active layer n 1/cm

2.7050

2.7050

3.6050

Confinementlayer upper

n 1/cm

2.488

2.488

3.508

Confinementlayer lower

n 1/cm

2.488

2.488

3.508

Substrate n 1/cm

1.771

2.744

NANA

Ohmic loss Athick 0.2 0.2 0.5

Thin ohmic open 0.5 0.5 NA

Reflector reflectivity 0.9 0.9 0.9

Carrier spreading

length

P m

N m

1000

200

1000

500

500

500

Fig. 7 Photon extraction efficiency depending on surface randomness.



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noted that generated photons in InGaN/sapphire systems, inwhich a significant portion of generated photons are to betrapped in relatively thin semiconductor crystal layers, willencounter the textured top surface more frequently to berandomly deflected.

Figure 10 shows the effect of the deformation depth hdefon the photon extraction efficiency in the InGaN/ SiC chipstructure as described in Fig. 3c. In InGaN/SiC systems,as already explained, the generated photons are easilytransmitted into the substrate, and thus the cavity deforma-tion only in a portion of the substrate helps to significantly

improve the photon extraction efficiency. However, in thecase of the surface-textured chips, the effect of the cavity

deformation overlaps with that of the surface texturing, andtherefore the photon extraction efficiency is improvedrather minimally with the deformation depth hdef.

Figure 11 shows how the removal of the substrate affectsthe effectiveness of the sidewall slanting in improving thephoton extraction efficiency. If the substrate is removed inInGaN LEDs, the total thickness of the chip would be typi-cally less than 5 m, and the chances for the photons to bedeflected by the slanted sidewall would be extremely small.As a consequence, in the substrate-removed LED chips, thesidewall slanting would be virtually meaningless.

Figure 12 shows how the photon extraction efficiency isaffected by the way InGaN/sapphire LED chips are

Fig. 8 Photon extraction efficiency depending on the slanting angle of sidewall.

Fig. 9 Photon extraction efficiency in the sidewall-slanted chips depending on surface randomness.



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mounted on the reflector. In the case of the chips mountedepi-down on the reflector, as described in Fig. 4b, intu-itively thinking, the photons transmitted into the sapphiresubstrate, which is blocked by neither the reflector nor elec-trode, may easily couple out of the chip, possibly improv-ing the photon extraction efficiency drastically. Instead,however, the calculated photon extraction efficiency in theepi-down mount is not necessarily better than in the epi-upmount. This rather unexpected result may be understoodonce again by considering the fact that the substrate of asmaller refractive index acts as a total internal reflectionbarrier for the generated photons to enter the substrate. Tohelp to understand this more clearly, we have plotted thephoton extraction efficiency as a function of the refractive

index of the substrate in Fig. 13. In the calculation, we havefixed the refractive indices for the other layers, except thesubstrate. When the refractive index of the substrate issmaller than that of the carrier confinement layer, the num-ber of photons being transmitted to the substrate is seri-ously limited as a result of the total internal reflection offthe substrate. The limited transmission of the generatedphotons to the substrate will degrade the photon extractionefficiency seriously, especially in the epi-down mount, inwhich the epitaxial side of the chip is also blocked by thereflector. Thus, in the regime of lower refractive index sub-strates, the photon extraction efficiency in the epi-downmount is actually lower than in the epi-up mount, in whichsome of the photons could still couple out of the chip

Fig. 10 Photon extraction efficiency depending on the deformation depth in the InGaN/SiC structure.

Fig. 11 Effect of substrate removal and sidewall slanting angle on photon extraction efficiency.



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through the epitaxial top surface. However, as the refractiveindex substrate increases further, the total internal reflectionbarrier resulting from the substrate would become smaller,permitting more photons to enter the substrate, from whichthe photons, without being blocked by the reflector, easilycouple out of the chip. As a result, in the regime of higherrefractive index substrates, the photon extraction efficiencyin the epi-down mount would be higher than in the epi-upmount.

Figure 14 shows the photon extraction efficiency as afunction of the substrate thickness in InGaN/sapphireLEDs. In general, as the substrate thickness decreases, thenumber of photons coupling out of the substrate sidewall

would decrease, seriously degrading the photon extractionefficiency, especially in the epi-up mount, in which thephotons transmitted into the substrate can couple out of thechip only through the substrate sidewall. Thus, as can beseen in the figure, when the thickness of the substrate is lessthan about 50 m, the epi-down mount has a better photonextraction efficiency compared to the epi-up mount.

Even though the advantage of the epi-down mount overthe epi-up mount is not very evident when the substrate isrelatively thick, the epi-down mount will still have greatpotential in terms of photon extraction. For instance, in theepi-down mount, the photons once transmitted into the sap-phire substrate, which is relatively well index-matched to

Fig. 12 Effect of chip-mount schemes and surface randomness on photon extraction efficiency.

Fig. 13 Photon extraction efficiency as a function of the substrate refractive index.



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the encapsulant and blocked neither by the reflector nor theelectrode, easily couple out of the chip. To exploit this po-tential of the epi-down mount, we need some measures thatallow more photons to enter the substrate. One approachshould be to texture the chip surface and randomize thephoton directions, so that the photons overcome the totalinternal reflection barrier due to the sapphire substrate. Ascan be seen in Fig. 14, if the surface is textured, the photonextraction efficiency is improved, especially in the epi-down mount. Similarly, as can be seen in Fig. 13, with the

surface textured, the photon extraction efficiency crossoverbetween the epi-down mount and epi-up mount shifts to alower substrate refractive index.

So far, we have considered only surface texturing thathas been applied only to the external surface of the chip.However, surface texturing may be applied to an internalsurface, for instance, to the substrate-epitaxy interface, bypossibly growing epitaxial layers on a substrate with a tex-tured surface, as illustrated in Figs. 4e and 4f. In thiscase, the photon trajectory randomization off the textured

Fig. 14 Effect of substrate thickness on photon extraction efficiency.

Fig. 15 Effect of the substrate removal, texturing of the substrate-epitaxy interface, chip mountschemes, and surface randomness on photon extraction efficiency.



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substrate-epitaxy interface directly increases the number ofphotons entering the substrate, improving the photon ex-traction efficiency drastically. Figures 15 and 16 comparethe performance of the chips grown on textured substratewith those of the chips grown on flat substrate. As clearlyseen in the figures, the photon extraction efficiency is im-proved drastically in those chips, especially in the epi-downmount. It is noted that one of the practical approaches toachieve the textured substrate-semiconductor interface maybe to grow epitaxial layers on a substrate that is appropri-

ately patterned and etched.

6 Conclusion

The performance of InGaN LEDs in terms of photon ex-traction efficiency, depending on the chip structure and chipmounting schemes on the reflector, is analyzed by theMonte Carlo photon simulation method. One of the impor-tant findings is that the sidewall slanting scheme, whichworks well for either the AlInGaP or InGaN/SiC system,plays a very minimal role in InGaN/sapphire systems. Thesapphire substrate of lower refractive indexes functions as atotal internal reflection barrier for the generated photons toenter the substrate. As a result, a significant portion of gen-

erated photons fail to enter the substrate and be trappedinside the semiconductor layers, the total thickness ofwhich is very tiny compared to the substrate. The photonsthus trapped in thin semiconductor crystal layers will rarelybe deflected by the slanted sidewalls, and therefore the ef-fect of sidewall slanting is hardly expected. On the otherhand, in InGaN/SiC systems, the refractive index of theSiC substrate is about 2.74 and is larger than that of theGaN confinement layer. As a result, generated photonswould enter the SiC substrate easily. As a consequence,photon extraction efficiency is improved significantly, evenwhen the cavity is deformed only in a portion of thesubstrate.

The surface texturing scheme, in contrast to the sidewallslanting scheme, helps improve the photon extraction effi-ciency considerably in InGaN/sapphire systems. The pho-tons trapped in the thin semiconductor crystal layers wouldinteract more frequently with the top surface, to be de-flected off in random fashion. As a consequence, photonextraction efficiency would be improved significantly, evenwhen surface texturing is applied only to the top surface ofthe chip.

Even though the sapphire substrate in InGaN/sapphire

systems plays a negative role in sidewall-slanted LEDchips, it still helps overall to improve photon extractionefficiency. The refractive index of the sapphire substrate isin between the encapsulant epoxy and GaN confinementlayer, and is relatively well index-matched to the encapsu-lant, most likely the epoxy. Thus, the photons transmitted tothe sapphire substrate by overcoming the total internal re-flection barrier would couple out of the chip more easilythan the ones trapped inside the semiconductor layers.Therefore, the photon extraction efficiency is improvedoverall by the sapphire substrate. It is noted, however, thatthe substrate in both InGaN/sapphire and InGaN/SiC sys-tems may be removed better, especially for the purpose of

better heat dissipation. In this case, the photons would in-teract with the ohmic electrodes much more frequently, andthus it may be essential to develop ohmic electrodes thatcan minimize photon absorption therein and compensatethe degraded photon extraction efficiency.

Another important finding in this study is that, inInGaN/sapphire systems, the epi-down mount scheme maynot have considerable advantage over the epi-up mountscheme, at least in terms of photon extraction efficiency.The relatively poor performance of the epi-down mount isattributed to the sapphire substrate of low refractive indexthat severely restricts the generated photons entering thesapphire substrate. It is believed, however, that the epi-

Fig. 16 Effect of texturing of the substrate-epitaxy interface, chip mount schemes, and surface ran-domness on photon extraction efficiency.



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