J. Coat. Technol. Res.
DOI 10.1007/s11998-014-9614-7

Hybrid antireflection structure with moth eye and multilayer
coating for organic photovoltaics
Shigeru Kubota, Kensaku Kanomata,Takahiko Suzuki, Bashir Ahmmad, Fumihiko Hirose

 American Coatings Association 2014
Abstract We propose a hybrid antireflection structure (ARS), which integrates moth eye texturing andmultilayer interference coating, to improve efficiency
of organic photovoltaic (OPV) solar cells. We performnearly global optimization of the geometric parameterscharacterizing the hybrid ARS, by using optical simulations based on the finite-difference time-domain
method. The proposed optimization algorithm consistsof two steps: in the first step, only the moth eye
structure is globally optimized and, in the second step,
the whole hybrid structure is optimized efficiently
based on the results of the first step. Thus, the optimal
moth eye structure is additionally obtained as anintermediate result. By applying this optimization
method to an organic thin film solar cell, we show thatthe short-circuit current density (JSC) is increased by
8.90% with the moth eye structure and by 9.89% withthe hybrid ARS. We also study the sensitivity ofphotocurrent to the geometric parameters of hybrid
ARS, and the change in the spatial distribution ofelectric field intensity by the ARS. The results showthat the hybridization of the two types of light trapping
techniques is effective to reduce the inhomogeneity inthe electric field distribution and obtain higher electric
intensity in almost the whole active layer. The designconcept of the hybrid ARS is quite useful for improving light trapping in OPVs and allows for extending theoptions available for broadband antireflection.
Keywords Organic solar cell, Moth eye, Multilayer
antireflection coating, Optimization, Opticalsimulation
S. Kubota (&), K. Kanomata, T. Suzuki,
B. Ahmmad, F. Hirose
Graduate School of Science and Engineering, Yamagata
University, 4-3-16 Jonan, Yonezawa, Yamagata 992-8510,
Japan
e-mail: kubota@yz.yamagata-u.ac.jp

Introduction
Organic photovoltaics (OPVs) have been attracting
considerable attention due to their potential for largearea, flexible, and low-cost solar cells.1–4 The power
conversion efficiency of OPVs has been rapidly
increasing in the past decade,5 although further
improvement will be required for large-scale commercialization. A key factor limiting the efficiency of OPVs
is a low mobility of charge carriers in the organic
semiconductors.6–8 To improve the carrier extraction
from them, the thickness of the active layer, which is
responsible for photocurrent generation, should be as
small as 100 nm. To maximize the light absorption insuch a thin active layer, it is particularly important todevelop an efficient antireflection (AR) coating thatallows for broadband light trapping.
The antireflection structure (ARS) is categorized tomainly two techniques, i.e., the single- or multilayer
coating and surface texturing. Currently, the ARS thatis most widely used is the multilayer interference
structure, in which transparent materials with different
refractive indexes are deposited in one dimension.9
This simple structure can effectively reduce the mismatch in optical admittance to suppress reflection oflight for a certain range of wavelength. To further
improve the performance, recent studies are focusing
on the ARS with moth eye texturing, in which thesurface of a device is covered with two-dimensional
array of cones which have the period and height ofseveral hundred nanometers.10–15 In a recent experimental study that applied moth eye structure to an
OPV based on poly(3-hexylthiophene) (P3HT) and[6,6]-phenyl-C61-butyric acid methyl ester (PCBM)
blend, an increase in the performance by 2.5–3% was
observed for a wide range of incident angles.15
Recent studies also suggest that the antireflective
performance of moth eye structure significantly depends on the geometric feature of cone array.11,14

J. Coat. Technol. Res.

Boden and Bagnall11 performed optical simulations forsilicon moth eye array, and showed that the reflectanceis given by a complicated function of the wavelength aswell as the period and height of moth eye texturing. A
theoretical study by Deinega et al.14 also showed that,for silicon-textured surfaces, the minimum reflectanceis achieved when each cone has sufficiently largeheight, and the period of moth eye array takes anoptimal value within a very narrow range. Thesefindings strongly suggest that the numerical optimization of geometric parameters is essential to bring out
the full potential of moth eye structure. However, theglobal optimization of the textured pattern is quitedifficult, because the optical simulation of threedimensional nanostructure is generally computationally costly due to the necessity of fine division of space
and time.16 In addition, most previous simulation
studies on the surface nanostructure are limited tothe cases of silicon substrate, and therefore, theoptimal configuration of the textured surface for OPVs
is largely unclear.
When the moth eye texturing is applied to OPVs, it
is additionally important that the textured material
should have compatibility with the advantage of OPV
devices, such as large-scale manufacturing. From this
aspect, the use of organic polymers is highly beneficial, because the textured surface made of polymers
can be easily fabricated by nanoimprint lithography(NIL) with polymeric resists.17,18 In a wide range ofapplications, the technology of polymer NIL is used
for a low-cost realization of a large-area nanopatterned surface.19,20 However, the use of polymers forthe front surface of organic solar cells producesanother problem, that is, the discontinuity in therefractive index between the OPV itself and thesurface structure. Since the discontinuous change inthe reflective index inevitably produces reflection, it
may be worth making use of multilayer interferencecoat, in addition to moth eye, to reduce such opticalmismatching.
From these viewpoints, we consider numerical
optimization of a novel hybrid ARS that integrates
the moth eye and multilayer interference structures.
We propose a nearly global optimization algorithm forthe geometric parameters of the hybrid ARS. By the
optical simulations based on the finite-difference timedomain (FDTD) method,16 we demonstrate the effectiveness of the hybrid ARS in improving the shortcircuit current density (JSC) of OPVs. In addition, weinvestigate the sensitivity of JSC to the characteristic
parameters of the ARS, and show that the level of JSC
significantly depends on the period of moth eye array.
Furthermore, we study the changes in the absorption
spectrum and the electric field distribution by ARS,
which underlie the enhancement in performance. The
proposed hybrid ARS, combined with the quasi-global
optimization method, provides a new option available
for improving light trapping in the thin active layer of
OPVs.

Experimental
Optical model
We numerically analyzed the optical properties of
ARS by the FDTD simulations. Figure 1a shows astructure of the OPV cell in the absence of ARS, which
serves as the reference for evaluating performance. In
the OPV device, the thin films of P3HT:PCBM andMoO3 work as the active layer and the hole transporting layer, respectively. These materials are sandwiched
between the transparent forward electrode of theindium-doped tin oxide (ITO) and the bottom electrode of Al. Thus, the layer configuration of the OPV issummarized as ITO (100 nm)/MoO3 (7 nm)/P3HT:PCBM (100 nm)/Al (100 nm). The OPV device
structure with the moth eye coat is illustrated inFig. 1b, where the cones are hexagonally arranged on
the front surface of the device. The base circles of two
adjacent cones in the moth eye array touch each other.
The configuration of moth eye structure is determinedby the period L of the cone array and the height H ofeach cone. We assume that the moth eye structure isfabricated with organic polymer, because a large-scalenanostructure can be readily fabricated by NIL withpolymeric resists,17–20 as mentioned above. Accordingly, in our model, the refractive index of moth eyearray is set to be 1.5, which is a typical value forpolymer materials.21 The device structure of the OPVwith the hybrid ARS, proposed in this study, is given in
Fig. 1c. The hybrid ARS contains the moth eye arrayand the two-layer coat composed of Al2O3 and MgF2
films, in which the Al2O3 layer is deposited adjacent to
the moth eye surface. Both Al2O3 and MgF2 are thematerials typically used for multilayer AR coating(e.g., reference 22). The thicknesses of the Al2O3 andMgF2 films are denoted as d1 and d2, respectively.
Additionally, Fig. 1 implies that the examined
structures have an inverted configuration,23 in which
the bottom Al electrode is in contact with thesubstrate. We consider the inverted structure, throughout this study, for the following two reasons. First, inthe conventional devices, the existence of a very thicksubstrate at the front surface greatly increases thecalculation time for FDTD simulations24 and makes
the numerical optimization extremely difficult (seebelow for the computation time). Second, due to therecent advancements in deposition techniques, several
studies realized the room temperature deposition ofhigh-quality ITO thin films, which allow for the
inverted configuration.25–27 In addition, obviously the
proposed design method for hybrid ARS can beapplied to improve the performance of the conventional OPV devices by using computers with higher
computing power (e.g., supercomputer).
The coordinate system is defined as shown in Fig. 1.
The incident light is assumed to propagate alongz-direction. The absorbing boundary conditions withperfectly matched layer16 are imposed for the upper

J. Coat. Technol. Res.

ITO

MoO3

Al

P3HT:PCBM

Al2O3

MgF2

(a)

z

y

x

y
x

Moth eye

(c)

(b)

z

Two-layer coat
OPV

OPV

OPV withHybrid ARS

OPV with
Moth eyeFig. 1: Structures of a reference OPV cell (a), an OPV cell with only moth eye array (b), and an OPV cell with the proposed
hybrid ARS (c) (Color figure online)

Table 1: Optimal parameters for the moth eye array andhybrid ARS, which are obtained by Steps 1 and 2 in the
proposed algorithm, respectively

L (nm)H (nm)
d1 (nm)d2 (nm)JSC (mA/cm2)

Moth eyeHybrid ARS

592
901
0
0
11.68 [8.90%]

608
797
186
15
11.78 [9.89%]

L and H are the period and height of moth eye array,
respectively, and d1 and d2 are the thicknesses of the Al2O3
and MgF2 films, respectively. The values in square brackets
show the increase rate of JSC compared to the reference celland lower boundaries in z-direction. The FDTD
simulation using the inputs of unpolarized light, suchas sunlight, usually requires the averaging of the results
obtained with the x- and y-polarized light.23 However,in the devices considered in this study (Fig. 1), due to ahigh symmetry of moth eye array, the difference in JSC
by using the x- and y-polarized incident light was muchsmaller than the change obtained by ARS (9–10%;
Table 1). Therefore, we show the results obtained by
the x-polarized incident light throughout this study.
To evaluate JSC, the absorbance in the active layer
was calculated for a range of wavelengths from 300 to
700 nm. To obtain the optical response for this range of
wavelength in a single simulation, the results of FDTD
simulation by a brief input pulse were Fourier transformed.16 If we define Ap(k) to be the absorbance inthe active layer at wavelength k, the number ofphotons absorbed in this layer, corresponding to k, is
described by the following equation23,28:
Np ðkÞ ¼ Ap ðkÞFðkÞ

k
:
hc

ð1Þ

Here F(k) represents the spectrum of solar irradianceunder the AM 1.5 standard,29 h is Planck’s constant,and c is the speed of light in free space. With the unit
charge q, the number of photons is converted into thegenerated photocurrent as follows23,28:
Z kg
qNp ðkÞFNR ðkÞdk;
ð2Þ
JSC ¼
0

where kg is the wavelength corresponding to the band
gap energy of P3HT (653 nm). FNR(k) is thenonrecombination factor, which is simply assumed tobe 1 for all k.30 In addition, the weighted reflectance isobtained by the following equation31:
R kg
Rw ¼

0

RðkÞFðkÞdk
;R kg
0 FðkÞdk

ð3Þ

where R(k) is the reflectance at wavelength k.
The optical data for the materials of MoO3,
P3HT:PCBM (1:1 by weight), Al, Al2O3, and MgF2
were obtained by the measurements of spectroscopic
ellipsometry for the range of wavelength of interest(300–700 nm). The optical data for ITO were takenfrom Hoppe et al.32 These data were fitted by the
Lorentz-Drude model,33 which allows for efficient
FDTD simulations for the dispersive materials.16

J. Coat. Technol. Res.

Optimization Algorithm
Numerical optimization of the parameters characterizing the hybrid ARS was conducted to maximize JSC.
There are four parameters to be optimized, i.e., theperiod L and height H of the moth eye array, and thethicknesses d1 of the Al2O3 film and the thickness d2 ofthe MgF2 film. To efficiently obtain quasi-global
optimal solution, we constructed a new algorithm thatcombines the simple grid search method34,35 with the
Hooke and Jeeves pattern search method.34,36,37
The simple grid search is an algorithm that is mostfrequently used for global optimization.34,35 In thisalgorithm, a uniform grid is defined in the parameter
space. Then, all the points in the grid are evaluated tofind optimal solutions. In a parameter space spannedby N parameters xi (i = 1, …, N), the grid is defined by
selecting points for each coordinate x(s)i = xi,min + (s/ni)(xi,max  xi,min) (i = 1, …, N; s = 0, 1, …, ni). Here[xi,min, xi,max] is the domain of parameter xi, and ni is
the number of subdivisions of the domain. Thus, thetotal number of grid points is given as N
i=1(ni + 1). The
local optimal solutions of the simple grid search are
given, in this study, by the grid points in which JSC islarger than that of any adjacent point in the grid.
The pattern search method proposed by Hooke andJeeves36 consists of iteration of two phases called
exploratory and pattern moves. In the exploratory
move, the search point travels in all the directions in
the local parameter space near the base point xb,
which is a starting point of the exploratory move. Let
us define xn to be a point that gives the best value ofobjective function among the points visited in thecurrent exploratory move. In the pattern move which
follows the exploratory move, the base point is shiftedxn þ
by a relatively long distance such that xb
ðxn  xp Þ; where xp is the point with the best objectivefunction value obtained in the previous iteration.34
The vector xn  xp predicts the best search direction
at the present time. The pattern move aims toaccelerate the search based on the information about
the objective function acquired in the past. The newbase point is used for the exploratory move in thenext round. The pattern search is terminated when
the base point arrives at a local optimum, in which
the exploratory move cannot improve the value ofobjective function.
The objective of the simple grid search is to obtainrough estimation of the global optimal solution,
whereas the objective of the pattern search is to refine
the solution obtained by the grid search. Therefore, thestep size used in the pattern search (DL = 16, DH = 1,
Dd1 = 1, Dd2 = 1) (in nm) is much smaller than thatused in the grid search (DL = 96, DH = 100, Dd1 = 20,
Dd2 = 20) (in nm) for each parameter.
The FDTD simulation of the present model takes
time of the order of 10 min (20–40 min) for eachcase, on our PC equipment (Intel Core i7 2.93 GHz).
This high computational cost makes it extremely
difficult to use common global optimization algorithms,

which require more than thousands of times of function
evaluation (e.g., reference 38). Therefore, to reduce
the total computation time, we divide the optimization
procedure into two steps. In the first step, we conduct
global optimization only for L and H, by maintaining
the values of d1 and d2 at 0, which means the
optimization of moth eye array in absence of twolayer coat. This is because in our device model, thesolar cell performance depends primarily on thecharacteristics of moth eye structure (see ‘‘Results
and discussion’’). In the second step, all the parameters
for hybrid ARS are optimized by using the results ofthe first step as the starting point. By this two-stepprocedure, we can reduce the volume of search spacethat is actually relevant for each step, and canefficiently obtain quasi-global optimal solution which
can be used for practical application.
The proposed optimization algorithm is described asfollows:
Step 1.
Step 1-1.

Optimization of moth eye structure.
Perform the simple grid search with respect
to L and H, by keeping the values of d1 andd2 at 0, and find the optimal solution.
Step 1-2. For the refinement of the solution, executethe pattern search with respect to L and H
with maintaining d1 = d2 = 0. Here, thestarting point for parameter set (L, H) is
given by the solution of Step 1-1. Let us
define (L*, H*) to be the optimal parameterset obtained by the pattern search.
Step 2. Optimization of the whole structure of
hybrid ARS.
Step 2-1. Keep the values of L and H at thoseobtained by Step 1-2 (i.e., L = L* andH = H*), and conduct the simple gridsearch with respect to d1 and d2. Let us
denote the local optimal solutions of theparameter set (d1, d2) as (d*1,i, d*2,i) (for i = 1,…, M), with the number of solutions M.
Step 2-2. Execute the pattern search M times tooptimize all the parameters L, H, d1, and d2,
by using each of the parameter set (L*, H*,
d*1,i, d*2,i) (i = 1, …, M) as the starting point.
Then, as the final solution, select the best of
the M solutions obtained by the patternsearch.
Note that, in Step 1, we can obtain globally optimal
structure of moth eye array as an intermediate result.
The present simulation is performed by repetitively
running the FDTD software, OptiFDTD, from a
MATLAB program. Typically, the four-dimensional
pattern search in Step 2-2 requires around 50–200
times of function evaluation, which corresponds to25–100 h of computation time for the PC with Intel
Core i7 2.93 GHz. We additionally carried out careful
comparisons between the results of the FDTD
method and those of the characteristic matrix method,9 to ensure the stability and accuracy of oursimulations.

J. Coat. Technol. Res.

sponds to JSC = 11.64 mA/cm2 (i.e., 8.56% higher
efficacy than the reference cell). The enhancement of
JSC was correlated negatively with the weighted
reflectance (Fig. 2b), implying that the greater performance relies on the improved light trapping. The
increase ratio of JSC is as small as 2% for L < 400 nm(Figs. 2a and 2b), although this range of L was typicallyused in previous studies.39–41 The results here suggestthat properly selecting the geometric parameters ofmoth eye is very important to fully bring out its
potential to enhance light trapping in OPVs.
In order to refine the solution, we performed thepattern search34,36,37 in Step 1-2, by setting the starting
search point at the solution obtained by Step 1-1. We
found the global optimal solution of moth eye arraygiven as L* = 592 nm and H* = 901 nm. The corresponding value of JSC was 11.68 mA/cm2, which was
8.90% higher than the reference cell (Table 1).
In Step 2, we conducted optimization of all theparameters for hybrid ARS, by making use of theresult of Step 1. The simple grid search was performedin Step 2-1 to optimize the parameters of d1 and d2,

Results and discussion
Optimization of hybrid ARS
We performed optimization of the hybrid ARS (Fig. 1c), according to the two-step algorithm. In Step 1, we
carried out global optimization of the period L andheight H of moth eye array in absence of multilayer
AR coat, i.e., d1 = d2 = 0. Figures 2a and 2b show theparameter-dependent change in the increase rate of
JSC, compared to the JSC value of reference cell(Fig. 1a; JSC = 10.72 mA/cm2), which was obtained by
the simple grid search in Step 1-1. As shown in the
figures, only in a restricted region of parameter space(L = 600 nm and 500 nm < H < 1200 nm), the increase rate of JSC attains >8%, while this value
decreases abruptly in the neighborhood of this region.
This finding indicates that the AR performance is quitesensitive to the geometric parameters of moth eyearray near the optimal parameter region. The optimal
solution obtained by the grid search was L = 576 nm
and H = 900 nm (x-mark in Fig. 2a), which corre-

(a)

(b)

Increase in Jsc (%)

1500

H = 900 nm
Increase in Jsc

6
5
4
3

500

2
1

8

0.12

6

0.09

4

0.06

Rw

H (nm)

1000

Increase in Jsc (%)

8
7

0.15

10

9

Rw

2

0.03

0
0

200

400

600

800

0

–1

0

400

600

800

0
1000

L (nm)L (nm)

(c)

200

(d)

Increase in Jsc (%)
9d2 = 20 nm

10

0.1

Increase in Jsc

6
100
5
4
0

3
0

200

100

d1 (nm)

8

0.08

6

0.06

Rw

d2 (nm)7

Increase in Jsc (%)

8

200

4

Rw

2
0

0.04
0.02

0

100

200

0

d1 (nm)Fig. 2: Results obtained by the simple grid search in Step 1-1 (a, b) and Step 2-1 (c, d) in the proposed optimization
algorithm. (a, c) The increase rate of JSC, compared to that of the reference cell, is plotted as function of the period L andheight H of moth eye array (a) or as function of the thickness of Al2O3 film, d1, and the thickness of MgF2 film, d2 (c). The
x-marks denote the points corresponding to the local maxima of JSC, which are used for the starting points of the patternsearch following the grid search. (b, d) The increase rate of JSC (solid) and the weighted reflectance Rw (dashed) are plotted
as function of L (b) and d1 (d) (H = 900 nm in (b) and d2 = 20 nm in (d))

J. Coat. Technol. Res.
AM1.5

1

HybridNo ARS

0.5

0
300

400

500

AM1.5

(b)

1.5

Photo energy density(×109 W m–2 m–1)

Photo energy density(×109 W m–2 m–1)(a) 1.5

1
Moth eye

0300

600 λg 700

Wavelength (nm)(d)
Hybrid vs No ARS
Moth eye vs No ARS

0.2

0.1
0

–0.1
300

400

500

600 λg 700

Wavelength (nm)

400

500

600 λg 700

Wavelength (nm)0.3
Hybrid vs Moth eye

Photo energy density(×109 W m–2 m–1)

Photo energy density(×109 W m–2 m–1)(c) 0.3

No ARS

0.5

0.2

0.1
0

–0.1
300

400

500

600 λg 700

Wavelength (nm)Fig. 3: Effects of applying the hybrid ARS and moth eye structure, with optimized configuration, on the spectrum ofabsorption energy in the active layer. (a, b) The absorption spectra in the active layer for the cases of using the optimized
hybrid ARS (red) or the optimized moth eye structure (blue) and for the cases of not using ARS (black). The AM1.5 solar
spectrum is shown with the gray dotted lines. (c) Red line: the difference in absorption spectra between the cases of using
the hybrid ARS and not using ARS. Blue line: the difference in absorption spectra between the cases of using the moth eye
and not using ARS. (d) The difference in absorption spectra between the cases of using the hybrid ARS and the moth eyearray (Color figure online)

where L and H were fixed at the values of L* and H*,
respectively. Figure 2c shows the increase rate of JSC,
due to the incorporation of ARS, as a function of d1
and d2. The figure indicates that there are mainly two
subregions of parameter space in which JSC is locallyincreased (i.e., the subregions with white colors surrounding the two x-marks). This is because the change
in JSC shows periodicity with respect to the thickness d1of the Al2O3 film (Fig. 2d), due to an interference
effect of light passing through the thin film.9 The levelof JSC alters gradually everywhere in the parameter
space of d1 and d2. This finding is contrast to the factthat JSC shows abrupt changes in the parameter spaceof L and H (Fig. 2a). As a result of the grid search, we
found three local optimal solutions (i.e., M = 3): (d*1,1,
d*2,1) = (180, 20), (d*1,2, d*2,2) = (20, 20), and (d*1,3,
d*2,3) = (0, 0) (in nm). The points of (d*1,1, d*2,1) and(d*1,2, d*2,2) are shown by the x-marks in Fig. 2c.
In Step 2-2, we conducted the pattern search withrespect to all the four parameters L, H, d1, and d2.
Here, the starting point was set as (L, H, d1, d2) = (L*,H*, d*1,1, d*2,1) or (L*, H*, d*1,2, d*2,2), which we refer to as
the No. 1 or No. 2 parameter set, respectively. The

starting point of (L*, H*, d*1,3, d*2,3) was omitted,
because this parameter set is obviously a local optimal
solution, from the results of Step 1 and Step 2-1. The
solutions obtained with the starting point of the No. 1
and No. 2 parameter set were (L, H, d1, d2) = (608,797, 186, 15) and (576, 847, 19, 27) (in nm), whichcorresponded to the JSC value of 11.78 and11.75 mA/cm2, respectively. These values of JSC are
higher than that of Step 1 (JSC = 11.68 mA/cm2). Fromthe comparison among them, the solution obtained
from the No. 1 parameter set gives the final optimal
solution for the hybrid ARS, which produces 9.89%
increase in JSC (Table 1).
Optical properties of the optimized ARS
In the previous section, we obtained the optimal
structures of both the moth eye array and hybrid
ARS (Table 1). To elucidate the optical properties of
the two types of ARS, we analyzed the wavelengthdependent change in light absorption. We plotted thespectra of absorption energy in the active layer of the

J. Coat. Technol. Res.

OPV with and without the optimized hybrid ARS(Fig. 3a, red and black, respectively) and the difference
between these cases (Fig. 3c, red). The results showthat the absorption energy is increased by applying the
hybrid ARS for a wide range of wavelength k for 300–
700 nm, except for the narrow region of k » 570 nm.
Similarly, as shown in Fig. 3b (blue and black) and
Fig. 3c (blue), the absorption in the active layer is

12

δL

δ d1

δH

δ d2

Increase in Jsc (%)

10

Optimal

8
6
4
2
0
–100

–50

0

50

100

δL, δ H, δ d1, δ d2 (nm)Fig. 4: Increase rate of JSC by the hybrid ARS is shown asfunction of dL (black), dH (green), dd1 (blue), and dd2 (red),which represent the deviations of L, H, d1, and d2 from theoptimal values (Table 1), respectively. The lower limit of dd2
is set to be 215 nm because the optimal value of d2 is
15 nm (Color figure online)(a)enhanced for a wide range of k with the optimized
moth eye structure. In Fig. 3d, we also compared thedifference in the absorption spectra between the casesof applying the hybrid ARS and the moth eye arraywith the optimized parameters. The figure shows thatthe difference between them is particularly large at
longer wavelengths for 600–650 nm. This result suggests that the hybridization of the moth eye andmultilayer coating has a strong impact on the opticalresponse at the longer wavelength near that of theband gap of P3HT (653 nm).
We also studied the sensitivity of the performance ofhybrid ARS to the deviations in the characteristic
parameters. Let us define dX (X = L, H, d1, or d2) tobe the deviation of parameter X from its optimal value
for the hybrid ARS in Table 1. Then, JSC can beobtained by simulation for a given value of dX for theparameter X. In Fig. 4, we plotted the increase ratio of
JSC, compared to the reference cell, as a function of dL,
dH, dd1, and dd2 using the same x-coordinate. Fromdefinition, the value of JSC corresponding to dX = 0
gives the photocurrent density for the optimal solution.
The figure clarifies that the deviation in L has thelargest impact on the AR performance (Fig. 4, black),
and the deviation of dL = ±100 nm decreases theantireflective effect to around 40% of the maximum
level. On the other hand, the deviations in the otherparameters have significantly smaller impact on theperformance. The higher sensitivity of the AR performance to the period of moth eye array was alsosuggested by a recent study.14
To explore the reason for this remarkable effect of
the L values on the performance, we studied how theabsorption spectrum in the active layer depends onthe deviation in L from its optimal value. We plotted
the absorption spectra for the cases with and without

(b)

AM1.5

0.3

1.5

Optimal1

Smaller L
Larger L

0.5

0
300

400

500

600 λg 700

Wavelength (nm)Photo energy density(×109 W m–2 m–1)

Photo energy density(×109 W m–2 m–1)

Optimal vs larger L
0.2 Optimal vs smaller L

0.1

0

–0.1
300

400

500

600 λg 700

Wavelength (nm)Fig. 5: Effects of changing the value of L in the hybrid ARS from its optimized value (608 nm) on the spectrum ofabsorption energy in the active layer. (a) Black line: the absorption spectrum obtained with the optimized hybrid ARS (thesame as Fig. 3a, red line). Red and blue lines: the absorption spectra obtained with the hybrid ARS in which L is larger (red)or smaller (blue) than the optimal value by 96 nm. Gray dotted line: AM1.5 solar spectrum. (b) Red line: difference in theabsorption spectra between the cases using the optimized hybrid ARS and the ARS with the larger L value. Blue line:difference in the absorption spectra between the cases using the optimized hybrid ARS and the ARS with the smaller L
value (Color figure online)

J. Coat. Technol. Res.

(a)Without ARS

P3HT: MoO3
PCBM
ITO

z (nm)

03.10e–2
2.33e–2
1.56e–2
7.81e–3

307 Al6.67e–50x (nm)–532

Moth eye (optimal)

(b)

532

Hybrid (optimal)(c)

L = 592 nm

L = 608 nm
0518

Hybrid (larger L)(d)

P3HT: MoO3
PCBM
ITO

z (nm)
0x (nm)

307 Al307 Alz (nm)

P3HT: MoO3
PCBM
ITO

0
–518

–532

532

Hybrid (smaller L)(e)

L = 704 nm

L = 512 nm

–616

616

P3HT: MoO3
PCBM
ITO

z (nm)
0x (nm)

307 Al307 AlP3HT: MoO3
PCBM
ITO

0

0
z (nm)

0x (nm)–4480x (nm)

448

Fig. 6: Spatial distribution of electric field intensity in the OPV is shown at k = 636 nm for the cases without ARS (a), withthe optimized moth eye structure (b), with the optimized hybrid ARS (c), and with the hybrid ARS using the optimized
parameters except for L (d, e). (d, e) The value of L is larger (d) or smaller (e) by 96 nm than the optimal value (608 nm). (a-e)
The amplitude of the x-component of electric field is shown as function of x and z in the plane of y = 0 (see Fig. 1 for thecoordinate system). The vertical line of x = 0 passes the center of the base circle of a cone in moth eye array, and the region
denoted by horizontal two-headed arrows with length L (2L/2 < x < L/2) shows the region below the base circle. The
distribution of the x-component of electric field is plotted, because the y-component of electric field disappears, due to a
spatial symmetry of our model, and the z-component of electric field in the active layer tends to be much smaller than the
x-component, due to the use of the x-polarized incident light (see ‘‘Experimental’’)the deviation in L (Fig. 5a) and the difference
between these cases (Fig. 5b). Here, we consideredboth the cases where L is larger and smaller than the
optimal value (608 nm) by 96 nm (i.e., DL = ±96nm). The figures show a large change in absorptionenergy for a range of longer wavelength ofk > 570 nm. This range of wavelength nearly agrees
with the L values considered here (608 ± 96 nm),
implying the involvement of the diffraction effectcaused by periodic surface.42

J. Coat. Technol. Res.

The results obtained so far indicate that the opticalresponse at longer wavelengths, a little below the band
gap of P3HT (653 nm), is particularly important todetermine the performance of ARS (Figs. 3d and 5b).
The absorption in the longer wavelength range ishighly associated with the difference in the performance between the hybrid ARS and moth eye array(Fig. 3d), and also is responsible for the strong impact
of L values on the performance of hybrid ARS(Fig. 5b). In order to clarify the light propagation in
OPVs at this wavelength range, we plotted the spatial
distribution of the electric field intensity at k = 636 nm(Fig. 6). In absence of ARS (Fig. 6a), the electric field
intensity changes across the layers, but is homogeneousin the horizontal direction (i.e., in the direction parallelto the layer interfaces), as expected. In contrast, theuse of the optimized moth eye structure made theelectric field inhomogeneous in the horizontal direction (Fig. 6b). As shown in the figure, within the active
layer, the region with strong electric intensity issandwiched by the regions with electric intensity which
is weaker even than the level obtained in the active
layer without ARS (Fig. 6a). Importantly, as shown in
Fig. 6c, the use of the optimized hybrid ARS tended toflatten the electric field intensity and made morehomogeneous distribution, compared to the case ofusing the moth eye only (Fig. 6b). In most of all thearea of the active layer, the electric field obtained by
the hybrid ARS (Fig. 6c) is maintained at a level that issignificantly higher than that obtained without ARS(Fig. 6a). Furthermore, in cases where the period L ofmoth eye array was increased (Fig. 6d; L = 704 nm) or
decreased (Fig. 6e; L = 512 nm) by 96 nm from theoptimal value (608 nm) for the hybrid ARS, thehomogeneity of the electric field was considerably lost
and the subregions with very low electric intensity
emerged. Therefore, the period of moth eye arrayplays an important role in regulating the level ofhomogeneity of the electric field distribution in theactive layer. These results suggest that the excellent
performance of the optimized hybrid ARS is attributable to the intensified electric field with higher homogeneity, which effectively makes use of almost thewhole area of the active layer.
In the optical model of this study (Fig. 1), the moth
eye texture is assumed to be a periodic array of
precisely shaped cones, although this is an idealized
model. From an experimental point of view, it isimportant to elucidate the effects of variations intextured pattern, which arise in fabrication processes,on the performance of solar cells. We evaluated thelevel of decrease in photocurrent due to the deviationsin the geometric parameters of hybrid ARS from theoptimal values (Fig. 4). However, it remains unclear
how the antireflective effect of hybrid ARS can beaffected by other types of variations such as theroundness at the tip and edge of cones or the spatial
gap between adjacent cones.43 It is a future work to
study the effects of such variations in geometriccharacteristics of hybrid ARS on its performance andto design ARS which can improve solar cell efficiency
even in the presence of this effect.

Conclusion
In this study, we considered light trapping of OPVs by
the hybrid ARS that integrates moth eye array andmultilayer interference coating. We proposed a twostep algorithm to find quasi-global optimal configuration of the hybrid ARS. In the first step of ouralgorithm, the moth eye structure was globally optimized in the absence of the multilayer coating. In thesecond step, the whole structure of hybrid ARS was
optimized by using the solutions of the first step as thestarting search point. In each step, the simple gridsearch and the pattern search were used for roughestimation of the optimal solution and for the refinement of the solution, respectively. The increase ratio of
JSC by the optimal moth eye structure and hybrid ARS
were 8.90% and 9.89%, respectively (Table 1).
We also investigated the spectrum of absorptionenergy in the active layer, and showed that the opticalresponse at longer wavelengths, a little lower than thatof the band gap of P3HT (653 nm), is quite important
to determine the difference in AR performance
between the moth eye structure and hybrid ARS(Fig. 3d). We additionally showed that the deviation in
the period of moth eye array from the optimal value
has a strong impact on the performance by decreasing
absorption at the longer wavelength range (Figs. 4 and5b). Furthermore, we studied the spatial distribution ofelectric field intensity at the longer wavelength andshowed that the optimized hybrid ARS contributes tomaintaining the electric field in almost the whole active
layer at higher level (Fig. 6c). These results show theeffectiveness of the hybrid ARS for improving lighttrapping in the thin active layer of OPVs. By adjusting
the materials used in the multilayer interference
coating, the hybrid structure with the same concept
will also be applicable to light trapping of other thinfilm solar cells.
Acknowledgments This study was partially supportedby the A-STEP Program of Japan Science andTechnology Agency and by KAKENHI (26390025)
from the Japanese government.

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