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Double-layer anti-reflection coating containing a
nanoporous anodic aluminum oxide layer for
GaAs solar cells
Tianshu Yang,1 Xiaodong Wang,1,2 Wen Liu,1 Yanpeng Shi,1 and Fuhua Yang1,2,*
1
Engineering Research Center for Semiconductor Integrated Technology, Institute of Semiconductors, Chinese
Academy of Sciences, Beijing 100083, China
2
xdwang@semi.ac.cn
*
fhyang@semi.ac.cn
Abstract: Multilayer anti-reflection (AR) coatings can be used to improve
the efficiency of Gallium Arsenide (GaAs) solar cells. We propose an
alternate method to obtain optical thin films with specified refractive
indices, which is using a self-assembled nanoporous anodic aluminum
oxide (AAO) template as an optical thin film whose effective refractive
index can be tuned by pore-widening. Different kinds of double-layer AR
coatings each containing an AAO layer were designed and investigated by
finite difference time domain (FDTD) method. We demonstrate that a λ /4n
– λ /4n AR coating consisting of a TiO2 layer and an AAO layer whose
effective refractive index is 1.32 realizes a 96.8% light absorption
efficiency of the GaAs solar cell under AM1.5 solar spectrum (400 nm-860
nm). We also have concluded some design principles of the double-layer
AR coating containing an AAO layer for GaAs solar cells.
©2013 Optical Society of America
OCIS codes: (310.1210) Antireflection coatings; (310.4165) Multilayer design; (310.6628)
Subwavelength structures, nanostructures.
References and links
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Received 31 May 2013; revised 13 Jul 2013; accepted 15 Jul 2013; published 22 Jul 2013
29 July 2013 | Vol. 21, No. 15 | DOI:10.1364/OE.21.018207 | OPTICS EXPRESS 18207
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layers for nanostructuring on silicon substrate,” Appl. Phys. Lett. 91(5), 053117 (2007).
1. Introduction
Compared with Silicon, Gallium Arsenide (GaAs) is a major material applied in concentrator
solar cells and space solar cells for its higher photoelectric conversion efficiency and antiradiation ability. The light transmitted into GaAs can be absorbed quickly as GaAs is a direct
band gap semiconductor. In other words, the active layer of a GaAs solar cell as thin as
several microns is enough to make full use of the transmitted light [1]. The major loss of light
is the reflection of the bare cell surface. To reduce the surface reflection and improve the
solar cell efficiency, single-layer and multilayer anti-reflection (AR) coatings are widely
studied [2–6]. Compared with the single-layer AR coating, the multilayer AR coating has
better AR effect for reducing reflection in broader band of the solar spectrum [7]. However,
the variety of materials which can be used as AR coatings is not wide. A designed thin film
with a specified refractive index always has no perfect match in real materials, which is a
main problem in multilayer AR coatings application.
Producing nano-porous material is a main way to realize optical thin films with specified
refractive indices. Oblique-angle deposition is a vapour-deposition technique widely used to
grow nanostructured thin-film materials, and it has good control over the refractive index
profile [8–10]. An optical thin film with an ultra-low refractive index of n = 1.05 was realized
by this technique and a graded-index coating consisting of TiO2 and SiO2 nanorod layers was
successfully demonstrated to reduce reflection over a broad range of wavelengths [11]. But
this technique needs precise control over the process conditions, which raises the difficulty in
practical application. We propose an alternate method that is using a self-assembled
nanoporous anodic aluminum oxide (AAO) template as an optical thin film. AAO is an Al2O3
thin film with self-organized hexagonal arrays of uniform parallel nanopores. AAO has been
widely used as a template for fabricating a periodic nano-structure [12–15], however using
AAO as an AR structure is rarely reported. The component of AAO is Al2O3 which has little
absorption of visible light. The interpore distance of AAO can be made as small as 50 nm
[13] which is far less than visible light wavelengths. In this case, the AAO thin film behaves
approximately as a homogenous layer with an effective refractive index [16] which can be
#191494 - $15.00 USD
(C) 2013 OSA
Received 31 May 2013; revised 13 Jul 2013; accepted 15 Jul 2013; published 22 Jul 2013
29 July 2013 | Vol. 21, No. 15 | DOI:10.1364/OE.21.018207 | OPTICS EXPRESS 18208
customized by tuning the fill factor of pores in pore-widening process. In this paper, we
designed different kinds of double-layer AR coatings for GaAs solar cells using AAO and
TiO2. The effective refractive index of AAO was optimized by finite difference time domain
(FDTD) method in order to realize a maximum light absorption efficiency (LAE) of the GaAs
solar cell.
2. Simulation model and numerical method
Fig. 1. Schematic diagram of the simulation model: perspective view (a), top view (b), and side
view (c).
Numerical simulations were performed using the FDTD solutions package from Lumerical
software [17]. The simulation model of a GaAs solar cell is shown in Fig. 1. The bare GaAs
solar cell consists of a GaAs substrate and an Al0.8Ga0.2As window layer of 15 nm thick (as
used in Refs [18,19].). The GaAs substrate is set infinitely thick by placing the bottom edge
of the simulation region into the GaAs layer and using perfectly matched layers (PML)
boundary conditions. Ideally, PML boundaries will absorb all incident light with zero
reflection. In this case, the GaAs substrate is assumed to absorb all light passing through its
top surface. Above the bare GaAs solar cell is a double-layer AR coating. Layer2 is TiO2 and
layer1 is AAO. The period (the distance between two centers of adjacent pores) of AAO is
fixed at 50 nm, which is far less than visible light wavelengths. In this case the AAO thin film
can be regarded as a homogenous layer with an effective refractive index. To obtain AAO
thin films with different effective refractive indices, the diameter of a pore is a variable which
can be tuned from 20 nm to 50 nm. Correspondingly the fill factor of pores can be tuned from
0.145 to 0.906. The thickness of each layer (h1 and h2) of the AR coating has been designed
and the design principles are explained in Sec. 3. A plane-wave light source is used to
illuminate the structure at normal incidence. The wavelengths range of the source is from 400
nm to 860 nm, which lies in the intrinsic absorption spectrum of GaAs. After running the
simulation, the reflectance curve and the LAE of the GaAs solar cell under AM1.5 solar
spectrum (400 nm-860 nm) were calculated.
#191494 - $15.00 USD
(C) 2013 OSA
Received 31 May 2013; revised 13 Jul 2013; accepted 15 Jul 2013; published 22 Jul 2013
29 July 2013 | Vol. 21, No. 15 | DOI:10.1364/OE.21.018207 | OPTICS EXPRESS 18209
3. Design principles of layer thicknesses of the double-layer AR coating
3.1 Effective refractive indices calculation of the AAO thin films with different fill factors of
pores
Fig. 2. Schematic diagram of an AAO thin film: perspective view (a), top view (b), and side
view (c).
The effective refractive indices of the AAO thin films with different fill factors of pores
should be calculated before designing the layer thicknesses of the AR coating. One estimation
method is to assume that the effective refractive index is simply given by the weighted
average
neff = f ⋅ n0 + (1 − f ) ⋅ n1
(1)
of the refractive indices of the two materials [20]. For the AAO thin film in Fig. 2, n0 is the
refractive index of air, n1 is the refractive index of Al2O3, and f is the fill factor of pores.
Derived from Eq. (1), the effective refractive index of the AAO thin film in Fig. 2 is 1.66.
Brauer et al. performed rigorous calculations which showed that Eq. (1) was only a rough
approximation and presented a relatively complex estimation method [21]. In their method,
the effective refractive index is 1.64 for the same AAO thin film above. We compared the
degree of approximation of these two estimation methods by FDTD method and confirmed
the second was more accurate.
#191494 - $15.00 USD
(C) 2013 OSA
Received 31 May 2013; revised 13 Jul 2013; accepted 15 Jul 2013; published 22 Jul 2013
29 July 2013 | Vol. 21, No. 15 | DOI:10.1364/OE.21.018207 | OPTICS EXPRESS 18210
Fig. 3. Reflectance curves of the AAO thin film above and two dielectric thin films with
refractive indices derived from method1 and method2 respectively.
We used the same plane-wave light source to illuminate three thin films with the same
thickness at normal incidence in simulations by FDTD method respectively, and three
reflectance curves were calculated. Results are shown in Fig. 3. The black solid line is the
reflectance curve of the AAO thin film in Fig. 2. The blue dot line and the red dash line are
the reflectance curves of two imaginary dielectric thin films with refractive indices of 1.66
and 1.64, respectively. Considering the reflectance difference only results from the refractive
index difference in this case (the thickness is the same and the absorption of light is ignored),
the refractive index of 1.64 derived from the second estimation method is more approaching
the effective refractive index of the AAO thin film. Therefore we calculated the effective
refractive indices of the AAO thin films with different fill factors of pores using the second
method.
Fig. 4. Fill factors of pores and effective refractive indices of the AAO thin films with different
pore diameters.
The results are shown in Fig. 4. As the pore diameter changing from 20 nm to 50 nm, the
fill factor of pores changes from 0.145 to 0.906 and the effective refractive index of the AAO
thin film changes from 1.64 to 1.10.
#191494 - $15.00 USD
(C) 2013 OSA
Received 31 May 2013; revised 13 Jul 2013; accepted 15 Jul 2013; published 22 Jul 2013
29 July 2013 | Vol. 21, No. 15 | DOI:10.1364/OE.21.018207 | OPTICS EXPRESS 18211
3.2 Center wavelength selection method and thickness design of the double-layer AR coating
The center wavelength was selected by optimizing the thickness of a TiO2 single-layer AR
coating on the GaAs substrate without a window layer. A single-layer AR coating of λ / 4n
thick gives minimum reflectance at the center wavelength λ . After performing an
optimization simulation by FDTD method, we found the best TiO2 thickness was 60 nm
which corresponded to the center wavelength of 560nm. Under this circumstance the GaAs
solar cell had a maximum LAE under AM1.5 solar spectrum (400 nm-860 nm), as shown in
Fig. 5.
Fig. 5. LAEs of the GaAs solar cells with TiO2 single-layer AR coatings of different
thicknesses.
LAE represents the photon number ratio of the light absorbed by the GaAs substrate to the
light incident on the GaAs solar cell surface under AM1.5 solar spectrum (400 nm-860 nm),
which is defined as
LAE =
860 nm
λ
400 nm
hc

AE (λ ) I AM 1.5 (λ )d λ
860 nm
λ
400 nm
hc

.
(2)
I AM 1.5 (λ )d λ
Here, h is Plank’s constant, c is the speed of light in the free space and I AM 1.5 is AM 1.5
solar spectrum. AE (λ ) is defined by
AE (λ ) =
Pabs (λ )
Pin (λ )
(3)
where Pabs (λ ) and Pin (λ ) are the powers of the light absorbed by the GaAs substrate and the
light incident on the GaAs solar cell surface at a wavelength λ , respectively.
Therefore, we chose 560nm as the center wavelength for the thickness design of the
double-layer AR coating. For double-layer AR coatings, two schemes are widely used to
design the thickness of each layer [22]. One is to make each layer λ / 4n thick. Here, λ is
the center wavelength, and n is the refractive index of each layer. This kind of double-layer
AR coating is called a λ / 4n − λ / 4n AR coating or a v-shaped AR coating, because if the
refractive indices of two layers satisfy
#191494 - $15.00 USD
(C) 2013 OSA
Received 31 May 2013; revised 13 Jul 2013; accepted 15 Jul 2013; published 22 Jul 2013
29 July 2013 | Vol. 21, No. 15 | DOI:10.1364/OE.21.018207 | OPTICS EXPRESS 18212
n2 = n1 ng / n0 ,
(4)
where n0 , n1 , n2 and ng are the refractive indices of air, layer1, layer2 and the substrate
respectively, the reflectance at λ will be reduced to zero and the reflectance curve looks like
a “v”. The other scheme is to make layer2 λ / 2n thick and layer1 λ / 4n thick, respectively.
This kind of double-layer AR coating is called a λ / 4n − λ / 2n AR coating or a w-shaped
AR coating because if the refractive indices of two layers match well the reflectance will be
reduced in a broad band around λ and the reflectance curve looks like a “w”. In our work,
we used TiO2 for layer2 and AAO for layer1 to design these two kinds of AR coatings. The
effective refractive index of AAO was optimized to make the refractive indices of two layers
more matching and to realize a maximum LAE of the GaAs solar cell.
4. Results and discussions
Fig. 6. Results of AAO-TiO2 λ / 4n − λ / 4n AR coatings. (a) Reflectance curves of the
GaAs solar cells with AAO-TiO2 double-layer AR coatings (colored solid lines with symbols,
different colors stand for the AAO layers with different pore diameters) compared with a bare
one (black solid line) and one with a TiO2 single-layer AR coating (red dash line). (b) LAEs of
the GaAs solar cells with AAO-TiO2 double-layer AR coatings compared with one with a TiO2
single-layer AR coating.
At first, we calculated the reflectance curves of the bare GaAs solar cell in Fig. 1 (which
consists of a GaAs substrate and a thin window layer) and the same cell covered with a 60 nm
TiO2 single-layer AR coating, respectively. LAE of the GaAs solar cell with the single-layer
AR coating was also calculated, which is 90.2%. As shown in Fig. 6(a), the single-layer AR
coating achieves a minimum reflectance at about 620 nm, which has a red shift from the
center wavelength because of the existence of the thin window layer. Secondly, we calculated
the reflectance curves and LAEs of GaAs solar cells with AAO-TiO2 λ / 4n − λ / 4n AR
coatings. When the pore diameter of the AAO layer is 50 nm, the reflectance curve is quite
close to the one of the GaAs solar cell with the TiO2 single-layer AR coating. This is because
the fill factor of pores of the AAO layer approximately equals to 1 in this case, which makes
the AAO layer almost not exist. The effective refractive index of the AAO layer is 1.22 when
the pore diameter is 45nm, which basically satisfies Eq. (4) (the refractive index of GaAs is
substituted for ng in Eq. (4)). In this case the reflectance is reduced to zero at about 640 nm,
which also has a red shift from the center wavelength because of the existence of the thin
window layer. As seen in Fig. 6(b), the results of the AAO-TiO2 double-layer AR coatings are
all better than the TiO2 single-layer AR coating. Especially, when the pore diameter of the
AAO layer is 40 nm, corresponding to the effective refractive index of 1.32, LAE of the
GaAs solar cell reaches a maximum value of 96.8%, which has a 6.6% increase to the TiO2
#191494 - $15.00 USD
(C) 2013 OSA
Received 31 May 2013; revised 13 Jul 2013; accepted 15 Jul 2013; published 22 Jul 2013
29 July 2013 | Vol. 21, No. 15 | DOI:10.1364/OE.21.018207 | OPTICS EXPRESS 18213
single-layer AR coating. In this case the reflectance is reduced in a broad band and has a
minimum total value, as shown in Fig. 6(a).
In this optimized double-layer AR coating the thicknesses of TiO2 and AAO are 60 nm
and 106 nm, respectively. This thickness of AAO is achievable in experiments. Ultrathin
AAO template around 50 nm thick has been realized to fabricate nanodot arrays [23].
Growing a TiO2 layer of a specified thickness is a more ordinary technology. So this
optimized AAO-TiO2 double-layer AR coating for GaAs solar cells can be realized in
experiments.
Fig. 7. Results of AAO-TiO2 λ / 4n − λ / 2n AR coatings. (a) Reflectance curves of the
GaAs solar cells with AAO-TiO2 double-layer AR coatings (colored solid lines with symbols,
different colors stand for the AAO layers with different pore diameters) compared with a bare
one (black solid line) and one with a TiO2 single-layer AR coating (red dash line). (b) LAEs of
the GaAs solar cells with AAO-TiO2 double-layer AR coatings compared with one with a TiO2
single-layer AR coating.
Thirdly, we calculated the reflectance curves and LAEs of GaAs solar cells with AAOTiO2 λ / 4n − λ / 2n AR coatings. We can find that most of the AAO-TiO2 double-layer AR
coatings basically realize a broad band reduction of reflectance, especially in the short
wavelengths range from 400 nm to 450 nm, as shown in Fig. 7(a). But around the center
wavelength the reduction result is much poorer than the TiO2 single-layer AR coating.
Therefore LAEs of the GaAs solar cells with the double-layer AR coatings are lower, as
shown in Fig. 7(b).
In addition to the work above, we have also tried using SiO2 for layer2 and AAO for
layer1 to design λ / 4n − λ / 4n and λ / 4n − λ / 2n AR coatings. Both results of the two kinds
of AR coatings are poorer than the SiO2 single-layer AR coating. Especially, for the AAOSiO2 λ / 4n − λ / 4n AR coating, the refractive index of SiO2 is so low that the matching
refractive index of layer1 derived from Eq. (4) is out of the effective refractive indices range
of AAO. That is the reason why however the pore diameter of AAO changes, the doublelayer AR coating always works poorly.
From all the results above, we can basically conclude some design principles of the
double-layer AR coating containing an AAO layer for GaAs solar cells. For the
λ / 4n − λ / 2n AR coating, we need to find a more proper material for layer2 to achieve a
better result. For the λ / 4n − λ / 4n AR coating, the material of layer2 must be chosen
properly to make sure the refractive index of layer1 derived from Eq. (4) is within the tuning
range of AAO effective refractive indices. The reflectance will be reduced to zero around the
center wavelength when the refractive indices of the two layers satisfy Eq. (4). However, it
doesn’t mean that LAE of the GaAs solar cell will have a maximum value at the same time.
We need to optimize the effective refractive index of AAO around this value to obtain the
highest LAE of the GaAs solar cell.
#191494 - $15.00 USD
(C) 2013 OSA
Received 31 May 2013; revised 13 Jul 2013; accepted 15 Jul 2013; published 22 Jul 2013
29 July 2013 | Vol. 21, No. 15 | DOI:10.1364/OE.21.018207 | OPTICS EXPRESS 18214
5. Conclusion
As the effective refractive index of AAO can be tuned within a certain range, we used AAO
templates as optical thin films to design λ / 4n − λ / 4n and λ / 4n − λ / 2n double-layer AR
coatings for GaAs solar cells by FDTD method. TiO2 was used for the bottom layer and AAO
for the top layer in the AR coatings. The effective refractive index of AAO was optimized by
tuning the fill factor of pores to realize a maximum LAE of the GaAs solar cell. The results of
the double-layer AR coatings have been analyzed and compared with the conventional TiO2
single-layer AR coating. We demonstrate that a λ / 4n − λ / 4n double-layer AR coating
consisting of a TiO2 layer and an AAO layer whose effective refractive index is 1.32 realizes
a 96.8% LAE of the GaAs solar cell under AM1.5 solar spectrum (400 nm-860 nm), which
has a 6.6% increase to the TiO2 single-layer AR coating. We also have concluded some
design principles of the double-layer AR coating containing an AAO layer for GaAs solar
cells.
Acknowledgments
The authors greatly acknowledge the support from the National Basic Research Program of
China (973 Program) under grant number 2012CB934204 and the National Natural Science
Foundation of China under grant numbers 61076077, 61274066.
#191494 - $15.00 USD
(C) 2013 OSA
Received 31 May 2013; revised 13 Jul 2013; accepted 15 Jul 2013; published 22 Jul 2013
29 July 2013 | Vol. 21, No. 15 | DOI:10.1364/OE.21.018207 | OPTICS EXPRESS 18215