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Current Applied Physics 15 (2015) 833e838

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Current Applied Physics

journal homepage: www.elsevier .com/locate/cap

Design of near-unity transmittance dielectric/Ag/ITO electrodes forGaN-based light-emitting diodes

Han-Kyeol Lee a, Jin-Young Na a, Yoon-Jong Moon a, Tae-Yeon Seong b, Sun-Kyung Kim a, *

a Department of Applied Physics, Kyung Hee University, Gyeonggi-do 446-701, Republic of Koreab Department of Materials Science and Engineering, Korea University, Seoul 136-713, Republic of Korea

a r t i c l e i n f o

Article history:Received 7 March 2015Received in revised form21 April 2015Accepted 24 April 2015Available online 6 May 2015

Keywords:Interference coatingsThin filmsMetal opticsTransparent conducting electrode

* Corresponding author.E-mail address: sunkim@khu.ac.kr (S.-K. Kim).

http://dx.doi.org/10.1016/j.cap.2015.04.0441567-1739/© 2015 Elsevier B.V. All rights reserved.

a b s t r a c t

We designed a near-unity transmittance dielectric/Ag/ITO electrode for high-efficiency GaN-based light-emitting diodes by using the scattering matrix method. The transmittance of an ultrathin metal layer,sandwiched between a dielectric layer and an ITO layer, was investigated as a function of the thicknessand the optical constant of each constituent layer. Three different metals (Ag, Au, and Al) were examinedas the metal layer. The analytical simulation indicated that the transmittance of a dielectric/metal/ITOmultilayer film is maximized with an approximately 10-nm-thick Ag layer. Additionally, the trans-mittance also tends to increase as the refractive index of the upper dielectric layer increases. By tailoringthe thickness of the dielectric layer and the ITO layer, the dielectric/Ag/ITO structure yielded a trans-mittance of 0.97, which surpasses the maximum transmittance (0.91) of a single ITO film. Furthermore,this extraordinary transmittance was present for other visible wavelengths of light, including violet andgreen colors. A complex phasor diagram model confirmed that the transmittance of the dielectric/metal/ITO multilayer film is influenced by the interference of reflected partial waves. These numerical findingsunderpin a rational design principle for metal-based multilayer films that are utilized as transparentelectrodes for the development of efficient light-emitting diodes and solar cell devices.

© 2015 Elsevier B.V. All rights reserved.

1. Introduction

Dielectric/metal/dielectric multilayer films are considered anefficient and facile transparent electrode scheme for the develop-ment of a variety of optoelectronic applications, including solar celldevices [1,2], light-emitting diodes [3,4], and general color-selective light absorbers [5e7], due to their superior optical(transmission > 90% [8]) and electrical properties (sheetresistance < 10 U/sq [8]). In addition, a dielectric/metal/dielectricmultilayer film that is composed of relatively thin (<a few tens ofnm) metal and dielectric layers is suitable for use in flexible opto-electronic devices [9,10]. Conversely, a thick (over ~100 nm)transparent conducting oxide precludes inclusion within flexibledevices due to its brittleness [8]. For upper and/or lower dielectricsin a multilayer film, various oxide compounds, such as ITO [11e13],ZnO [12,14], Al-doped ZnO [15], and In-doped ZnO [16], have beenexamined thus far. For example, Mohamed et al. reported ZnO/Ag/ZnO electrodeswith a sheet resistance of <6.3U/sq and amaximum

transmittance of 0.93 at l ¼ 550 nm [14]. Girtan et al. studied ITO/Ag/ITO electrodes placed on a low refractive index substrate (e.g.,glass and PET) that yielded a resistivity of 3 � 10e5 U cm and atransmittance of up to 97% at l ¼ 550 nm [11]. Although metal-based multilayer electrodes have been shown to exhibit decentoptical, electrical and mechanical performances, the design prin-ciples related to their transmission properties are not yetcompletely understood.

In this paper, we studied the optical properties of dielectric/Ag/ITOmultilayer films placed on a semi-infinite GaN layer where lightis generated in the GaN medium. Using the scattering matrixmethod [17,18], the transmittance of dielectric/Ag/ITO multilayerfilms was investigated as a function of the thickness and the opticalconstant of each constituent layer. A complex phasor diagrammodel was introduced to illustrate the trends in transmittance [7].By applying rational design principles, the optimum Ag-basedmultilayer film that yielded the greatest transmittance was deter-mined. These numerical findings help to provide a generic route fordesigning efficient transparent electrodes for the development ofhigh-efficiency light-emitting diodes.

H.-K. Lee et al. / Current Applied Physics 15 (2015) 833e838834

2. Simulation model

Fig. 1(A) shows the schematic of a dielectric/metal/ITO multi-layer film placed on a GaN (refractive index n¼ 2.5) layer. A normalplanewave of l¼ 450 nmwas generated in the GaNmedium. Usingthe scattering matrix method, the transmittance was calculatedwith respect to the thickness of the dielectric layer (d) and thethickness of the metal layer (t). For simplicity, the thickness of theITO layer was set to be equal to that of the dielectric layer. Thecomplex scattering matrix can be induced by applying electric andmagnetic boundary conditions as in [18]:

Mj ¼

264 cos dj

iPjsin dj

iPj sin dj cos dj

375; (1)

where

Pj ¼�nj þ ikj

�cos qj;incident ; (2)

dj ¼2pPjdj

l: (3)

Here, qj, incident is the incident angle upon a j-th optical mediumand dj is the phase shift experienced by the optical medium with athickness of dj. For a dielectric/metal/ITO multilayer film, the scat-tering matrix is expressed as:

M ¼ MITOMmetalMdielectric ¼�m11 m12m21 m22

�: (4)

Finally, the transmittance (T) is given by:

Fig. 1. Transmission properties of dielectric/Ag/ITO multilayer films. (A) Schematic of adielectric/metal/ITO multilayer film placed on a GaN medium. (B) Calculated trans-mittance (l ¼ 450 nm) of dielectric/Ag/ITO multilayer films as a function of thedielectric thickness for different Ag thicknesses. The refractive index of the dielectriclayer was 2.0. (C) Angular TE transmittance of the dielectric/Ag/ITO multilayer film anda single ITO film that exhibited the maximum transmittance in (B). For the multilayerfilm, the thickness of the Ag layer was 12 nm.

T ¼ nairnGaN

1

ðm11 þm22Þ2 þ ðm12 þm21Þ2

!2

: (5)

For this calculation, we chose a Ag material as the middle metallayer and set its optical constants at l ¼ 450 nm as (n, k) ¼ (0.04,2.65) [19]. For the ITO layer, the optical constants (n, k) were (2.06,0.014) [20]. The refractive index of the upper dielectric layer was2.0, which corresponds to that of Si3N4. The calculated trans-mittance reveals three key aspects related to the optical propertiesof a dielectric/metal/ITO multilayer film [Fig. 1(B)]. First, thetransmittance is sinusoidally modulated with d due to the inter-ference between reflected waves. Second, the overall transmittanceis degraded with increasing t. However, it is noteworthy that themaximum transmittance of the multilayer film within a range oft ¼ 4e10 nm is kept nearly constant despite different Ag thick-nesses. The maximum transmittance was nearly constant at theoptimum Ag thicknesses because for dielectric/metal/dielectricmultilayer films, their partial reflected waves can be interfereddestructively at the conditions, which will be discussed in Fig. 2.Increasing Ag thickness up to 10 nm yields the maximum trans-mittance and enables the fabrication of a dielectric/Ag/ITO elec-trode [21,22]. For example, Dhar et al. reported that the depositedAg film was changed from islands to a continuous film at a criticalthickness (tc) of 9.5 nm [22]. Hence, the optical and electricalproperties of the Ag film were stabilized when its thickness waslarger than tc. More importantly, the maximum transmittance of0.97 surpasses that of a single ITO film (0.91) [black line, Fig. 1(B)].Third, the maximum transmittance peaks of the multilayer filmoccur at the same thicknesses (d ~ 30 and 140 nm), which aremarginally affected by t. The transmittance has local maxima atevery destructive condition for the partial reflected waves. Themodulation period (Dd) of 110 nm is determined by the quarterwavelength antireflecting coating condition of dielectric materials[17]. Note that the maximum transmittance decreases withincreasing d because of the material absorption of the ITO layer.

Light-emitting diodes generate omnidirectional light from theirmultiple quantumwells. Therefore, one must investigate the angle-dependent optical properties of the transparent electrode [23]. Theangular transmittance with transverse-electric (TE) polarized lightfor a multilayer film (t ¼ 12 nm) with was compared with a singleITO film [Fig. 1(C)]. For normally incident light, the maximumtransmittance of the multilayer film with t ¼ 12 nmwas nearly thesame as that of a single ITO film [Fig. 1(B)]. Interestingly, thetransmittance of the multilayer film remains almost constantwithin a critical angle (~24�) as compared with the ITO film. Thedifference in the transmittance between the two films is moresignificant at a steeper incident angle. The broadband angulartransmittance from the dielectric/ITO/Ag stems from the multipleinterferences between reflectedwaves that occur at each of the fourdifferent interfaces: GaN/ITO, ITO/Ag, Ag/dielectric, and dielectric/air [24]. Taken together, a dielectric/metal/ITO multilayer film witha substantial (t > 8 nm) Ag layer provides near-unity transmittanceand an ultralow sheet resistance, whichmakes it a strong candidatefor next-generation transparent electrodes.

3. Theory

To better understand the transmission behavior of a dielectric/metal/ITO multilayer film, we represented phasors for the reflectedpartial waves in the complex plane, accounting for Fresnel re-flections and transmission coefficients [17]. Fig. 2(A) represents thefour lowest orders of optical paths: (l, m) ¼ (0, 0), (2, 0), (4, 0), and(2, 2), where l (m) is the number of lights passing through the ITO

Fig. 2. Complex phasor representations. (A) Schematic illustrating the available optical paths belonging to the four lowest orders of groups (0, 0), (2, 0), (4, 0), and (2, 2). For the (2,0) group, the optical paths with relatively large magnitudes in the phasor are represented. The optical paths assigned to f and f0 , g and g0 , and i and i0 are degenerate sets. (B) Arepresentative group phasor (dashed arrow) and its partial phasors (solid arrow) for the (0, 0), (2, 0), and (2, 2) groups. (C, D) Complex phasor representations for the maximum (C)and minimum (D) transmittance conditions in Fig. 1(B). The thickness of the Ag layer was 12 nm.

H.-K. Lee et al. / Current Applied Physics 15 (2015) 833e838 835

(dielectric) layer. Optical paths passing through the Ag layer morethan four times were not accounted for because of their largeextinction coefficient [19]. For each group, a representative phasor(dashed arrow) was constructed by adding the partial phasors(solid arrows) that correspond to each different optical path[Fig. 2(B)]. For example, for the (2, 0) group, the representativephasor was the vector sum of the partial phasors assigned to opticalpaths b, c, and d.

We examined two different cases in the complex phasor dia-gram: (t, d) ¼ (12, 30) and (12, 100) nm, which yielded themaximum [Fig. 2(C)] and minimum [Fig. 2(D)] transmittance inFig. 1(B), respectively. All of the reflected partial waves in the samegroup undergo the same phase shift, as caused by the same thick-nesses of the ITO and dielectric layers; thus, the correspondingpartial phasors and their representative phasor are rotated equallyin the complex plane. For example, the rotation angle (fl, m) for agroup (l, m) is expressed by:

fl;m ¼ l� 2pnITOdITOl

þm� 2pndielectricddielectricl

: (6)

For simpler analysis, group (4, 0) and other higher order groupswere not included in the phasor diagram because their phasorswere negligibly small. For the maximum transmittance case[Fig. 2(C)], each phasor is added destructively such that the totalphasor spirals the origin in the complex plane [7]. Conversely, forthe minimum transmittance case [Fig. 2(D)], each phasor is addedin phase such that the total phasor significantly deviates from theorigin [7]. Hence, one can conclude that the modulated trans-mittance that results from changes in the dielectric thickness is adirect consequence of the interference between reflected partialwaves.

4. Results and discussion

The transmittance of a dielectric/metal/ITO multilayer film is

dictated by the destructive or constructive interference of reflectedlight. This can be modulated by changing either the optical con-stants or thickness of each layer. We first investigated the trans-mittance of a dielectric/Ag/ITO multilayer film as a function of d fora variety of dielectric refractive indices (n) [Fig. 3(A)]. For thesesimulations, the wavelength of incident light was 450 nm. First, thethickness of the Ag layer was set to be 8 nm because the maximumtransmittance occurred at the condition as shown in Fig. 1(B) [left,Fig. 3(A)]. The calculated results clearly show that the maximumtransmittance occurs at a smaller dielectric thickness withincreasing n (e.g., for t ¼ 12 nm, d ¼ 54 nmwith n ¼ 1.5, d ¼ 32 nmwith n ¼ 2.0, and d ¼ 22 nm with n ¼ 2.4) because an optical pathlength is proportional to the refractive index of the dielectric ma-terial. Also, the modulation period in transmittance decreases withincreasing the refractive index of the dielectric material. For anupper dielectric layer with n ¼ 2.4, the transmittance reaches aminimum at d ¼ 50 � 60 nm, which meets the first constructiveinterference condition for the partial reflected waves. These find-ings can be understood as a general trend of interference. Moreimportantly, transmission increases gradually until n is equal toapproximately 2.0. An upper dielectric layer with a high refractiveindex produces a large reflection coefficient at the interface be-tween the dielectric and air, which is beneficial to the completedestructive interference condition for reflected light. The effect ofhigh refractive index becomes more apparent for the multilayerfilms with t ¼ 12 nm; the maximum transmittance increasesslightly more even when n is larger than 2.0 [right, Fig. 3(A)].Dielectric materials with n � 2.0 (e.g., Si3N4, TiO2, or ZrO2) can bereadily prepared by conventional deposition techniques. Further-more, the optical absorption of the dielectric material can beignored in these types of thin layers (d ~ 25 nm), which is anotheradvantage of Ag-based multilayer films.

Next, we examined three different metals with distinct opticalconstants (n, k): Au (1.38, 1.92) [19], Ag (0.04, 2.65) [19], and Al(0.62, 5.30) [20] at l ¼ 450 nm [Fig. 3(B)]. For all of the metals, the

Fig. 3. Dependence of optical constants on transmittance. (A) Calculated transmittance of dielectric/Ag/ITO multilayer films with a Ag layer of 8 nm (left) and 12 nm (right) as afunction of the dielectric thickness for various refractive indices of the dielectric layer. (B) Calculated transmittance of dielectric/metal/ITO multilayer films as a function of thedielectric thickness for Au, Ag, and Al metal layers. The refractive index of the dielectric layer was 2.0.

H.-K. Lee et al. / Current Applied Physics 15 (2015) 833e838836

thickness was fixed at 8 nm. The calculated results show that themultilayer film with a Ag layer provides the greatest transmissionas compared with the other metal layers. The large extinction co-efficient of Al gives rise to significant optical absorption as lightpasses the metal layer. Alternatively, for Au, the real part of theoptical constants (i.e., the refractive index) is relatively large, whichdiminishes the reflection coefficients for the ITO/Au and Au/dielectric interfaces. A metal suitable for use in a high-transmittance multilayer film must have a small refractive index(n) and a moderate extinction coefficient (k). The optical constantsof Ag meet these criteria. Notably, the transmittance peaks appearat the same d for the three different metals. The reason for this isthat the refractive index of metals is typically small compared tothat of dielectric materials, which marginally rotates phasors in thecomplex plane. Using the same explanation, the maximum trans-mittance is observed at the same d for different Ag thicknesses, asshown in Fig. 1(B).

GaN-based light-emitting diodes emit violet, blue, and greencolors because their band gaps can be tuned by modulating the In[25] or Al [26] composition. To examine the performance of adielectric/Ag/ITO multilayer film for other wavelengths, we con-ducted the same simulations for l ¼ 400 nm [left, Fig. 4], 550 nm[middle, Fig. 4], and 280 nm [right, Fig. 4]. The optical constants (n,k) of Ag were (0.05, 2.10) at l ¼ 400 nm, (0.55, 3.60) at l ¼ 550 nm,and (1.41, 1.29) at l ¼ 280 nm [19]. The absolute transmittance atthe different wavelengths depends on the details of the opticalconstants; however, the overall trend with respect to the dielectricthickness is the same. In general, for the visible spectrum, thetransmittance of a dielectric/Ag/ITO multilayer film tends todecrease at longer wavelengths because of the increased extinctioncoefficient (k). Such high-transmittance of the dielectric/Ag/ITO

Fig. 4. Transmittance for other visible wavelengths of light. Calculated transmittance of diethicknesses. The wavelength of the incident light was (left) 400 nm, (middle) 550 nm, and

structure over visible spectrum is consistent with previous works[3,8]. For example, Lee et al. demonstrated that the transmittance ofITO (15 nm)/Ag (7 nm)/ITO (15 nm) multilayer films is superior tothat of a single ITO film (60 nm) for l ¼ 350e600 nm [3]. Themaximum transmittance of the ITO/Ag/ITO structure was ~90% atl ¼ 400 nm, ~92% at l ¼ 450 nm, and ~89% at l ¼ 550 nm, whichcould be more augmented by adjusting the thickness of the ITOlayer. In addition, we examined the dielectric/Ag/ITO multilayerfilms for a deep ultraviolet wavelength (l ¼ 280 nm) because thewavelength region is of great interest due to the development ofwater purifiers and sterizers [27]. The transmittance result showedthat the dielectric/Ag/ITO structurewas superior to a single ITO filmonly when t was smaller than 8 nm [right, Fig. 4]. The refractiveindex (n) of Ag increases abruptly at l < 350 nm (e.g., n ¼ 1.41 atl ¼ 280 nm [20]), which diminishes the reflection coefficients atthe interfaces of multilayer films, as discussed in the example of Au[Fig. 3(B)]. Therefore, the optical effect of the dielectric/Ag/ITOmultilayer films is less significant at deep ultraviolet wavelengths.

We have investigated dielectric/Ag/ITO multilayer films wherethe thickness of the dielectric layer (d1) is the same as that of theITO layer (d2). However, from Eq. (6), the rotation angle will have anadditional degree of freedom if d1 is dissimilar from d2, as shown inFig. 5(A). Therefore, we calculated the transmittance while varyingd1 and d2 simultaneously; this is depicted as a surface plot exhib-iting the transmittance [left, Fig. 5(B)]. For these simulations, thethickness of the Ag layer was fixed at 12 nm where the maximumtransmittance of themultilayer filmwas nearly the same as that of asingle ITO film [Fig. 1(B)]. The refractive index of the dielectric layerwas 2.0. The surface plot shows that the transmittance is modu-lated with changes to both d1 and d2; however, the modulation isless significant when d2 is changed. As discussed in Fig. 2, the

lectric/Ag/ITO multilayer films as a function of the dielectric thickness for different Ag(right) 280 nm. The refractive index of the dielectric layer was 2.0.

Fig. 5. Transmittance of asymmetric dielectric/Ag/ITO multilayer films. (A) Schematic of an asymmetric dielectric/Ag/ITO multilayer film placed on a GaN medium. In this structure,the thickness of the dielectric layer can differ from that of the ITO layer. (B) Left: Surface plot representing the transmittance of dielectric/Ag/ITO multilayer films with respect to thethicknesses of the dielectric and ITO layers. Right: transmittance of dielectric/Ag/ITO multilayer films as a function of the ITO thickness along the dashed horizontal line (d1 ¼ 34 nm)of the surface plot.

H.-K. Lee et al. / Current Applied Physics 15 (2015) 833e838 837

phasors from groups (2, 0) and (2, 2) are the most dominant fordetermining the transmittance; these are rotated equally, evenwith different ITO thicknesses, for a fixed dielectric thickness. Asmall modulation in the transmittance along the horizontal lineresults from the effects of higher-order of groups. More impor-tantly, by tailoring the thicknesses of the dielectric and ITO layers,the transmittance was enhanced further. For example, atd1 ¼ 34 nm, the transmittance increases with decreasing d2 [right,black line in Fig. 5(B)]. The first (second) maximum transmittancewas 0.97 (0.94) at d2 ¼ 0 nm (d2 ¼ 90 nm), which is far greater thanthe maximum transmittance (0.91) of the symmetric case inFig. 2(B). The trend in transmittance with respect to d2 is the sameeven if the ITO layer has no material absorption [right, red line inFig. 5(B)], which suggests that the transmittance could be higherwith its smaller material absorption. Additionally, the fact that theoptimum multilayer film requires a minimal ITO layer will helpreduce the overall fabrication costs.

5. Summary and conclusions

We studied the transmission features of dielectric/metal/ITOmultilayer films placed on a GaN medium using the scatteringmatrix method. Simulation results indicated that the multilayerfilm consisting of a thick (~10 nm) Ag layer exhibits a transmittanceof 0.94, which is larger than themaximum transmittance of a singleITO film (0.91). The transmittance of the multilayer film can befurther enhanced (up to 0.97) by individually tailoring the thick-nesses of the dielectric and ITO layers. Such extraordinary trans-mittance from dielectric/Ag/ITO multilayer films was not limited tothe blue wavelength of light, but also exhibited a similar effect forviolet and green wavelengths. The modulation of transmittancewith respect to the structural parameters was completely investi-gated using a phasor diagram model; the maximum and minimumtransmittances were a direct consequence of the destructive andconstructive interference of reflected light. Designing dielectric/metal/ITO multilayer films for light-emitting diode and solar cellapplications represents a unique strategy for realizing more effi-cient transparent electrodes with improved optical and electricalperformances.

Acknowledgments

This research was supported by the Basic Science ResearchProgram through the National Research Foundation of Korea (NRF)

funded by the Ministry of Science, ICT & Future Planning (NRF-2013R1A1A1059423). H.-K. Lee and J.-Y. Na contributed equally tothis work.

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