energies
Article
Design and Analysis of Nano-Structured Gratings for
Conversion Efficiency Improvement in GaAs
Solar Cells
Narottam Das 1,2, * and Syed Islam 2
1
2
*
School of Mechanical and Electrical Engineering, University of Southern Queensland,
Toowoomba, QLD 4350, Australia
Department of Electrical and Computer Engineering, Curtin University, Perth, WA 6845, Australia;
[email protected]
Correspondence: [email protected]; Tel.: +61-746-311-195
Academic Editor: Andrés G. Muñoz
Received: 9 June 2016; Accepted: 18 August 2016; Published: 29 August 2016
Abstract: This paper presents the design and analysis of nano-structured gratings to improve the
conversion efficiency in GaAs solar cells by reducing the light reflection losses. A finite-difference
time domain (FDTD) simulation tool is used to design and simulate the light reflection losses of
the subwavelength grating (SWG) structure in GaAs solar cells. The SWG structures perform as
an excellent alternative antireflective (AR) coating due to their capacity to reduce the reflection losses
in GaAs solar cells. It allows the gradual change in the refractive index that confirms an excellent AR
and the light trapping properties, when compared with the planar thin film structures. The nano-rod
structure performs as a single layer AR coating, whereas the triangular (i.e., conical or perfect
cone) and parabolic (i.e., trapezoidal/truncated cone) shaped nano-grating structures perform as
a multilayer AR coating. The simulation results confirm that the reflection loss of triangular-shaped
nano-grating structures having a 300-nm grating height and a 830-nm period is about 2%, which
is about 28% less than the flat type substrates. It also found that the intermediate (i.e., trapezoidal
and parabolic)-shaped structures, the light reflection loss is lower than the rectangular shaped
nano-grating structure, but higher than the triangular shaped nano-grating structure. This analysis
confirmed that the triangular shaped nano-gratings are an excellent alternative AR coating for
conversion efficiency improvement in GaAs solar cells.
Keywords: FDTD simulation; nano-structures; light reflection loss; solar cells; subwavelength grating
(SWG); triangular or conical shaped nano-grating
1. Introduction
In recent years, subwavelength grating (SWG) structures have been identified as promising
candidates for realizing high conversion efficiency in photovoltaics or solar cells due to their small
amount of reflection losses. If the period or pitch of a single grating structure is less than the wavelength
of the incident light then it behaves like a homogeneous medium with an effective refractive index [1].
Therefore, the SWG structures can provide gradual changes of the refractive index that confirm
an excellent antireflective (AR) and light-trapping properties into the substrate compared to a planaror flat-type thin film substrates [1,2]. This type of nano-grating or nano-rod structure performs as
a single layer AR coating, whereas the triangular (such as, conical or perfect cone) and parabolic
shaped nano-grating structures are performing as a multilayer broadband AR coating [3–8]. There are
some other reports found in the literature related to improving the optical gain in solar cell systems,
including surface plasmon resonance-based multilayer structures and also a new design of GaAs solar
cells [9–12].
Energies 2016, 9, 690; doi:10.3390/en9090690
www.mdpi.com/journal/energies
Energies 2016, 9, 690
2 of 13
There are several types of losses in solar cell that always reduces its conversion efficiency.
Among them, the reflection loss is one of the most important factor that decreases the conversion
efficiency of solar cells significantly. The thin-film AR coating can minimize the reflection losses only
for certain ranges of wavelengths and the formation of coating on film can be a complex process, as well
as having several drawbacks, such as, adhesion and thermal mismatch, etc., and the instability under
thermal cycling [2–4,8]. Therefore, the SWG structure (i.e., triangular or conical shaped) has a gradual
change in refractive index that lead to a lesser reflection losses over a wide range of wavelengths and
the angle of incidences [2,8,13–17].
In this paper, a finite-difference time domain (FDTD) simulation tool is used to simulate the
reflection losses for different types of nano-grating structures or shapes [9–11,16–22]. We have
considered the following nano-grating profiles: (i) rectangular-; (ii) trapezoidal (i.e., truncated cone or
hatch top)-; and (iii) triangular (i.e., conical or perfect cone)-shaped, which is used for the simulation.
From the simulation results, an optimum nano-grating height and pitch or period for the SWG
structures were optimized. The reflection loss for a rectangular-shaped SWG structure is >30%, but
for a triangular (i.e., conical or perfect cone)-shaped SWG structure, the refractive index changes
gradually in several steps; finally, the reflection loss is about 2%. However, the intermediate structures
(such as, trapezoidal- or truncated cone- and parabolic-shaped), the reflection loss is lower than the
rectangular-shaped SWG structure, but higher than the triangular (i.e., conical or perfect cone)-shaped
SWG structures. This reduction of reflection losses confirms the improvement of conversion efficiency
in solar cells. The optimized SWG structures confirm that the reflection loss is about 2%, which is
about 28% less than that of a flat type substrate or a rectangular shaped nano-grating structure.
This paper is organized as follows: the introduction is in Section 1, Section 2 consists of
an antireflective coating, moth’s-eye principle, and the SWG structure. Geometric shape design of
nano-gratings is discussed in Section 3. The design of nano-grating structures is discussed in Section 4.
A nano-structures simulation by using FDTD simulation tool is in Section 5. Section 6 presents the
simulation results and discussion. Finally, the conclusion is presented in Section 7.
2. Background of Coating and SWG Structure
2.1. Antireflection Coating
The application of the AR coating is suitable for the reduction of reflection losses in solar cells.
The conversion efficiency of a solar cell can be increased by using an AR coating, because the AR
coating can reduce the reflection losses of light only for certain wavelengths (such as, IR (infrared),
visible, an UV (ultraviolet), give good performance). A minimum reflectance can be achieved when
the refractive index equates to the square root of the refractive indices of two media [2]. The strength
of the light reflection depends on the refractive indices of both the media and angle of the surface to
the beam of light.
Figure 1 shows the comparison of light reflection and transmission on a glass substrate with and
without a thin film coating [17]. Here, the incident light is travelling from air to a plain or common
glass substrate (upper portion in Figure 1). The intensity of the incident light is I, reflected light is
R.I, and transmitted light is T.I. However, when a thin film coating is added on top of the plain glass
substrate then the light reflection is reduced. Here, I is the incident light on the coating, R01 is the
reflected light at the interface of air and thin film coating, and transmitted light is T01 I. Hence, the
incident light at the coating and glass interface is T01 I, transmitted light is T1s T01 I and reflected light is
R1s T01 I (as shown in Figure 1).
Energies 2016, 9, 690
3 of 13
Energies 2016, 9, 690 3 of 13 FigureFigure 1. Comparison of light reflection losses on a plain glass substrate (upper portion: sky blue) by 1. Comparison of light reflection losses on a plain glass substrate (upper portion: sky blue) by
using a thin film on the plain glass substrate (lower portion: light green). using a thin film on the plain glass substrate (lower portion: light green).
Now, the percentage of light reflection can be calculated by using the following Fresnel equation: Now, the percentage of light reflection can be calculated
by using the following Fresnel equation:
2
n n 
R  0 s 2 nn0 −
 nnss
R=  0
(1) n0 + n s
(1)
where, R is the reflection co‐efficient or reflectance, n0 is the refractive index of the first media (here, s is refractive index of the second media (here, it is glass substrate). where,it is air), and n
R is the reflection
co-efficient or reflectance, n0 is the refractive index of the first media (here, it
In this situation, if the visible light is travelling from the first media (i.e., air, where n
0 = 1.0) to is air), and ns is refractive index of the second media (here, it is glass substrate).
the second media (i.e., a plain or common glass substrate, where ns = 1.5), the light reflection R is 4%. In this situation, if the visible light is travelling from the first media (i.e., air, where n0 = 1.0) to
However, when a thin film coating is added on the plain or common glass substrate then it (i.e., thin the second
media (i.e., a plain or common glass substrate, where ns = 1.5), the light reflection R is 4%.
film coating and the glass together) reduced the reflection losses. The new optimum or equivalent However,
when
a thin1film
is added
on the plain or common glass substrate then it (i.e., thin
refractive index, n
= coating
= √1.0
1.5 = 1.225. The reflection loss of each interface is about 1%. film coating
and the glass together) reduced the reflection losses. The new optimum or equivalent
i.e., the total reflection is about 2%. It was calculated that an intermediate coating between the air and √
√
refractive
index,
n1 = n0can ns =reduce 1.0 ×
1.5
= 1.225.losses The reflection
loss of
is aboutthe 1%. i.e.,
plain glass substrate the reflection by half (which is each
about interface
50%). However, formation of an AR coating film can be a complex process and there are several drawbacks, such as the total
reflection is about 2%. It was calculated that an intermediate coating between the air and plain
adhesion, thermal mismatch, and instability under thermal cycling [2–4,8]. glass substrate
can reduce the reflection losses by half (which is about 50%). However, the formation
of an AR coating film can be a complex process and there are several drawbacks, such as adhesion,
2.2. Moth’s‐Eye Principle thermal mismatch, and instability under thermal cycling [2–4,8].
The versatile visual systems of animals are interesting examples for imagination of nature’s design. The complex optical concepts evolved as a result of adaptation of different species to their 2.2. Moth’s-Eye
Principle
environment. To identify the innovative applications for modern optics from broad biological The
versatile visual systems of animals are interesting examples for imagination of nature’s design.
repertoire requires two necessary steps. These are: (i) to understand how a system works; and (ii) The complex
optical concepts evolved as a result of adaptation of different species to their environment.
appropriate process technology to reproduce the nature’s design on non‐living matters. To identifyA real example of this concept is the AR surface that found on the eyes of certain butterfly species the innovative applications for modern optics from broad biological repertoire requires
in the nature. The compound eyes of these insects are equipped with a periodic array of the SWG two necessary
steps. These are: (i) to understand how a system works; and (ii) appropriate process
structured bumps. This structure is simply referred to as “moth eye” structure after the moth’s were, technology to reproduce the nature’s design on non-living matters.
it was observed for the first time, thereby it reduces the light reflection losses, while the transmission A real example of this concept is the AR surface that found on the eyes of certain butterfly species
of the chitin‐lens is increased. The evolutionary benefit for the moth is improved vision in a dim in the environment while chances to be seen by a predator are lowered. nature. The compound eyes of these insects are equipped with a periodic array of the SWG
structured The idea of SWG structures has been adopted from moths’ eyes principle [8,17]. The surface of bumps. This structure is simply referred to as “moth eye” structure after the moth’s were, it
was observed
for the first time, thereby it reduces the light reflection losses, while the transmission
a moth’s eyes is covered with nano‐structured film that absorbs most of the lights instead of reflecting of the back as shown in Figure 2. The nano‐structured film consists of a hexagonal pattern bump about 200 chitin-lens is increased. The evolutionary benefit for the moth is improved vision in a dim
nm high, which performs as an AR, because the bumps are smaller than the wavelength of the visible environment
while chances to be seen by a predator are lowered.
light. The refractive index between the air and the surface changes gradually, and this gradual change The
idea of SWG structures has been adopted from moths’ eyes principle [8,17]. The surface of
of refractive index decreases the light reflection. This approach is suitable for solar cells model to a moth’s
eyes is covered with nano-structured film that absorbs most of the lights instead of reflecting
reduce the reflection losses and increase the conversion efficiency [2,8,13,15,17]. back as shown in Figure 2. The nano-structured film consists of a hexagonal pattern bump about
200 nm high, which performs as an AR, because the bumps are smaller than the wavelength of the
visible light. The refractive index between the air and the surface changes gradually, and this gradual
change of refractive index decreases the light reflection. This approach is suitable for solar cells model
to reduce the reflection losses and increase the conversion efficiency [2,8,13,15,17].
Energies 2016, 9, 690
Energies 2016, 9, 690 4 of 13
4 of 13 Energies 2016, 9, 690 4 of 13 Figure 2. The structure of moth‐eyes which is covered by the nano‐structured film [8,17]. Figure 2. The structure of moth-eyes which is covered by the nano-structured film [8,17].
2.3. Subwavelength Grating (SWG) Structure Figure 2. The structure of moth‐eyes which is covered by the nano‐structured film [8,17]. 2.3. Subwavelength Grating (SWG) Structure
The subwavelength features have a gradual change in refractive index which acts as a multilayer 2.3. Subwavelength Grating (SWG) Structure The
subwavelength
features
have a gradual change
refractive
index
which
as a multilayer
AR coating leading to a reduced light reflection losses in
over broadband ranges of acts
wavelength and ARangle of incidence. The AR coating is an optical coating that is applied to the surface of lenses or any coating
leading to a reduced light reflection losses over broadband ranges of wavelength and
The subwavelength features have a gradual change in refractive index which acts as a multilayer AR coating leading to a coating
reduced light reflection losses that
over is
broadband ranges of wavelength and angle
of incidence.
The AR
is an optical coating
applied to
the surface
of lenses
or any
other optical devices to reduce the light reflections. This coating assists the light capturing capacity angle of incidence. The AR coating is an optical coating that is applied to the surface of lenses or any other
optical
devices
to
reduce
the
light
reflections.
This
coating
assists
the
light
capturing
capacity
or improves the efficiency of optical devices, such as lenses or solar cells. Hence, an optimum light other optical devices to reduce the light reflections. This coating assists the light capturing capacity or reflection can be obtained when the refractive index equates to the square root of the refractive indices improves
the efficiency of optical devices, such as lenses or solar cells. Hence, an optimum light
or improves the efficiency of optical devices, such as lenses or solar cells. Hence, an optimum light reflection
can be obtained when the refractive index equates to the square root of the refractive indices
of two medium [2]. The multilayer AR coatings can reduce the light reflection losses and increases reflection can be obtained when the refractive index equates to the square root of the refractive indices the conversion efficiency of solar cells. of two
medium [2]. The multilayer AR coatings can reduce the light reflection losses and increases the
of two medium [2]. The multilayer AR coatings can reduce the light reflection losses and increases Figure 3 shows the nano‐grating structures of rectangular and triangular shaped profiles and conversion
efficiency of solar cells.
the conversion efficiency of solar cells. the plot of SWG structure height versus the effective refractive (n) for shaped
silicon profiles
(Si) substrate Figure
3 shows
the nano-grating
structures
of rectangular
andindex triangular
and the
Figure 3 shows the nano‐grating structures of rectangular and triangular shaped profiles and [16,17]. It shows that for a rectangular‐shaped SWG structure, the refractive index changes very plot of
SWG
height versus
the effective
refractive
indexindex (n) for
(Si) (Si) substrate
[16,17].
the plot structure
of SWG structure height versus the effective refractive (n) silicon
for silicon substrate rapidly from air (n = 1.0) to the nano‐structured grating zone (approximately 2.5 at TM mode) [1]. It shows
thatIt for
a rectangular-shaped
SWG structure,
refractive
changes
rapidly
[16,17]. shows that for a rectangular‐shaped SWG the
structure, the index
refractive index very
changes very from
airThe light reflection loss of a SWG structure can be calculated easily using Fresnel’s equation (which (n rapidly from air (n = 1.0) to the nano‐structured grating zone (approximately 2.5 at TM mode) [1]. = 1.0) to the nano-structured grating zone (approximately 2.5 at TM mode) [1]. The light reflection
is very similar to the Equation (1)): loss
ofThe light reflection loss of a SWG structure can be calculated easily using Fresnel’s equation (which a SWG structure can be calculated easily using Fresnel’s equation (which is very similar to the
is very similar to the Equation (1)): 2
Equation
(1)):
 n2  n1 22
(2) R   n2 − nn1  (2)
R =  nn2 
(2) R n22 + nn111   n2  n1 
where,
n1 is1 is the refractive index of first medium and n
the refractive index of first medium and n22 is the refractive index of second medium. is the refractive index of second medium.
where, n
where, n1 is the refractive index of first medium and n2 is the refractive index of second medium. Figure 3. Nano‐structured grating of rectangular (or flat type)‐ and triangular (or conical)‐shaped profile, Figure 3. Nano‐structured grating of rectangular (or flat type)‐ and triangular (or conical)‐shaped profile, Figure
3. Nano-structured grating of rectangular (or flat type)- and triangular (or conical)-shaped
and the plot of SWG height versus the effective refractive index (n) for a silicon (Si) substrate [16,17]. and the plot of SWG height versus the effective refractive index (n) for a silicon (Si) substrate [16,17]. profile, and the plot of SWG height versus the effective refractive index (n) for a silicon (Si) substrate [16,17].
Energies 2016, 9, 690
5 of 13
Energies 2016, 9, 690 5 of 13 From
Figure 3, the total light reflection from the nano-grating structure can be calculated using
From Figure 3, the total light reflection from the nano‐grating structure can be calculated using thethe following equation: following equation:
Rtotal = R1 + R2
(3)
Rtotal  R1  R2 (3) where, R1 is the light reflection at the interface of the air and the grating structure, and R2 is the light
where, R1 is the light reflection at the interface of the air and the grating structure, and R2 is the light reflection
at the interface of the grating structure and the substrate.
reflection at the interface of the grating structure and the substrate. If the grating structure has a shorter pitch or period than the wavelength of the incident light,
If the grating structure has a shorter pitch or period than the wavelength of the incident light, it it acts as a homogeneous medium with an effective refractive index [1]. According to Figure 3, the
acts as a homogeneous medium with an effective refractive index [1]. According to Figure 3, the calculated light reflection loss is more than 20.2% for a rectangular-shaped grating structure [1]. For the
calculated light reflection loss is more than 20.2% for a rectangular‐shaped grating structure [1]. For triangular- or conical-shaped SWG structures, the refractive index changes gradually in several steps,
the triangular‐ or conical‐shaped SWG structures, the refractive index changes gradually in several hence
the reflection becomes less than 8% [1]. In the parabolic structure, the reflection loss is lower than
steps, hence the reflection becomes less than 8% [1]. In the parabolic structure, the reflection loss is thelower rectangular-shaped
grating structure
but higher
thanbut that
the triangular-shaped
grating structure
than the rectangular‐shaped grating structure higher than that the triangular‐shaped (about
5%) [14].
grating structure (about 5%) [14]. 3. 3. Geometric Shape Design of Nano‐Gratings Geometric Shape Design of Nano-Gratings
This
section briefly discussed the geometric shape design of nano-grating structure on the GaAs
This section briefly discussed the geometric shape design of nano‐grating structure on the GaAs substrates.
The SWG structures are namely; (i) rectangular-shaped SWG (as shown in Figure 4c);
substrates. The SWG structures are namely; (i) rectangular‐shaped SWG (as shown in Figure 4c); (ii) (ii)trapezoidal‐shaped SWG with different aspect ratios (i.e., 0.1, 0.2, 0.5, 0.8, and 0.9) as shown in Figure trapezoidal-shaped SWG with different aspect ratios (i.e., 0.1, 0.2, 0.5, 0.8, and 0.9) as shown in
Figure
4b; and (iii) triangular-shaped SWG (as shown in Figure 4a).
4b; and (iii) triangular‐shaped SWG (as shown in Figure 4a). (a) (b) (c) Figure 4. Geometric shape design of nano‐grating structures those are used in the simulations. Figure 4. Geometric shape design of nano-grating structures those are used in the simulations.
(a) triangular‐shaped SWG; (b) trapezoidal‐shaped SWG; and (c) rectangular‐shaped SWG. (a) triangular-shaped SWG; (b) trapezoidal-shaped SWG; and (c) rectangular-shaped SWG.
The term aspect ratio (AspR) is defined as the ratio between the top length over the base length The term aspect ratio (AspR) is defined as the ratio between the top length over the base length
of a trapezoid, triangle, and/or rectangle [5,6,14,16,17]. It is clear from Figure 5 that the AspR can be of awritten as follows: trapezoid, triangle, and/or rectangle [5,6,14,16,17]. It is clear from Figure 5 that the AspR can be
written as follows:
a
AspR= a (4) (4)
AspR
bb
where,
“a”“a” is is thethe top
length
and
of the the geometric geometricshapes shapes(such (suchas, as,
triangle,
where, top length and “b”
“b” isis the
the base
base length
length of triangle, trapezoid,
and
rectangle).
For
a
rectangular-shaped
nano-grating
profile,
the
AspR
is
‘1’
(i.e.,
the top
trapezoid, and rectangle). For a rectangular‐shaped nano‐grating profile, the AspR is ‘1’ (i.e., the top andand base length of the rectangle is equal) and for the triangular‐shaped nano‐grating profile, the AspR base length of the rectangle is equal) and for the triangular-shaped nano-grating profile, the AspR
is ‘0’
(i.e., the top length of the triangle is ‘0’ compared to the base length of the triangle). However,
is ‘0’ (i.e., the top length of the triangle is ‘0’ compared to the base length of the triangle). However, forfor a trapezoidal‐shaped nano‐grating the AspR is 0 < (a/b) < 1, i.e., it lies between ‘0’ to ‘1’ (such as, a trapezoidal-shaped nano-grating the AspR is 0 < (a/b) < 1, i.e., it lies between ‘0’ to ‘1’ (such as,
0.1–0.9.). These nano‐grating shapes play an important role for the light trapping inside the substrate 0.1–0.9.).
These nano-grating shapes play an important role for the light trapping inside the substrate
thatthat affect on the conversion efficiency of solar cells. Therefore, the design of nano‐grating structures affect on the conversion efficiency of solar cells. Therefore, the design of nano-grating structures is
is essential to reduce the light reflection losses and improve the conversion efficiency in GaAs solar essential
to reduce the light reflection losses and improve the conversion efficiency in GaAs solar cells.
cells. In the next section, the design of nano‐grating structures is discussed briefly. In the next section, the design of nano-grating structures is discussed briefly.
4. 4. Design of Nano‐Grating Structures Design of Nano-Grating Structures
This section discussed about the
the nano-gratings
nano‐gratings shape
shape design This
section
discussed
about
design and andmodeling modelingof ofnano‐gratings nano-gratings
structures (i.e., SWG structures). The light reflection is strongly dependent on the nano‐grating structures (i.e., SWG structures). The light reflection is strongly dependent on the nano-grating
structures; therefore, an appropriate design of nano‐grating structure is important and essential to structures;
therefore, an appropriate design of nano-grating structure is important and essential to
Energies 2016, 9, 690
6 of 13
Energies 2016, 9, 690 6 of 13 model for reduction of reflection losses of light. For this reason, the nano-grating shapes are designed
model for reduction of reflection losses of light. For this reason, the nano‐grating shapes are designed and
optimized to reduce the light reflection losses from the surface of the GaAs solar cells or panels.
and optimized to reduce the light reflection losses from the surface of the GaAs solar cells or panels. The modeled nano-structured gratings are: (i) rectangular-shaped nano-grating profile (as shown
The modeled nano‐structured gratings are: (i) rectangular‐shaped nano‐grating profile (as shown in in Figure 5a); (ii) trapezoidal-shaped nano-grating profile with different aspect ratios of 0.1–0.9 (as
Figure 5a); (ii) trapezoidal‐shaped nano‐grating profile with different aspect ratios of 0.1–0.9 (as shown in Figure 5b); and (iii) triangular-shaped nano-grating profile (as shown in Figure 5c). Here,
shown in Figure 5b); and (iii) triangular‐shaped nano‐grating profile (as shown in Figure 5c). Here, we discussed all these nano-grating shapes as shown in Figure 5a–c. For the rectangular-shaped
we discussed all these nano‐grating shapes as shown in Figure 5a–c. For the rectangular‐shaped nano-grating
profile, the aspect ratio is ‘1’ (i.e., the top and base length of the trapezoid is equal),
nano‐grating profile, the aspect ratio is ‘1’ (i.e., the top and base length of the trapezoid is equal), for fortrapezoidal‐shaped nano‐grating profile, the aspect ratio varies from ‘0.1–0.9’ (i.e., it depends on the trapezoidal-shaped nano-grating profile, the aspect ratio varies from ‘0.1–0.9’ (i.e., it depends
ontop length of the trapezoid), and for the triangular‐shaped nano‐grating profile, the aspect ratio is ‘0’ the top length of the trapezoid), and for the triangular-shaped nano-grating profile, the aspect
ratio
is ‘0’
top length
the trapezoid
is zero
compared
to the
length
of the
trapezoid).
(i.e., the (i.e.,
top the
length of the of
trapezoid is zero compared to the base base
length of the trapezoid). These
shapes
are
used for the
analyzed the the results resultsfor forlight lightreflection reflection
the
SWG
These shapes are used for the simulation
simulation and
and analyzed of of
the SWG structures
[5,6,14,16,17].
structures [5,6,14,16,17]. (a)
(b)
(c)
Figure 5. Nano‐grating profiles for the simulation of light reflection in GaAs solar cells: (a) Figure 5. Nano-grating profiles for the simulation of light reflection in GaAs solar cells: (a) rectangular-shaped
rectangular‐shaped nano‐grating profile; (b) trapezoidal‐shaped nano‐grating profile; and (c) nano-grating profile; (b) trapezoidal-shaped nano-grating profile; and (c) triangular- or conical-shaped
triangular‐ or conical‐shaped nano‐grating profile. Here, the nano‐gratings and substrate are gallium nano-grating profile. Here, the nano-gratings and substrate are gallium arsenide (GaAs).
arsenide (GaAs). 5. 5. Nano‐Structures Simulation by FDTD Nano-Structures Simulation by FDTD
The
Optiwave FDTD (OptiFDTD) simulation tool is a very powerful, highly-integrated software
The Optiwave FDTD (OptiFDTD) simulation tool is a very powerful, highly‐integrated software that
allows computer aided design and advanced simulation of passive photonic components.
that allows computer aided design and advanced simulation of passive photonic components. The
FDTD method is an intuitive way to solve the partial differential equations numerically [19].
The FDTD method is an intuitive way to solve the partial differential equations numerically [19]. It is
a simple method utilizes the central difference approximation to discretize the two Maxwell’s
It is a simple method utilizes the central difference approximation to discretize the two Maxwell’s Energies
2016, 9, 690
Energies 2016, 9, 690 77 of 13 of 13
curl equations, namely, Faraday’s and Ampere’s laws, both in time and spatial domains, and then it curl equations, namely, Faraday’s and Ampere’s laws, both in time and spatial domains, and then it
solves the resulting equations numerically to derive the electric and magnetic field distributions at solves the resulting equations numerically to derive the electric and magnetic field distributions at
each time step using an explicit leapfrog scheme. The FDTD solution, thus derived, is second‐order each time step using an explicit leapfrog scheme. The FDTD solution, thus derived, is second-order
accurate, and is stable if the time step satisfies the Courant condition. One of the most important accurate, and is stable if the time step satisfies the Courant condition. One of the most important
attributes of the FDTD algorithm is that it is appropriately parallel in nature, i.e., parallel processing attributes of the FDTD algorithm is that it is appropriately parallel in nature, i.e., parallel processing in
in both the time and spatial domains, because it only requires exchange of information at the both the time and spatial domains, because it only requires exchange of information at the interfaces
interfaces of the sub‐domains in the parallel processing scheme, which consequently makes it faster of the sub-domains in the parallel processing scheme, which consequently makes it faster and more
and more efficient [20]. efficient [20].
The OptiFDTD software package is based on the FDTD algorithm was originally proposed by The OptiFDTD software package is based on the FDTD algorithm was originally proposed by
K. S. Yee in 1966 [21,22]. It introduced a modeling technique with second order central differences to K. S. Yee in 1966 [21,22]. It introduced a modeling technique with second order central differences
solve the Maxwell equations applying a finite difference approach (or mathematics). The FDTD to solve the Maxwell equations applying a finite difference approach (or mathematics). The FDTD
algorithm can directly calculate the value of E (electric field intensity) and H (magnetic field intensity) algorithm can directly calculate the value of E (electric field intensity) and H (magnetic field intensity)
at different points of the computational domain. Since then, it has been used for several applications at different points of the computational domain. Since then, it has been used for several applications
and many extensions of the basic algorithm have been developed [22–28]. and many extensions of the basic algorithm have been developed [22–28].
In the two‐dimensional (2D) FDTD simulation for TM wave (Ex, Hy, Ez—nonzero components, In the two-dimensional (2D) FDTD simulation for TM wave (Ex , Hy , Ez —nonzero components,
propagation along with Z, transverse field variations along with X) in lossless media, Maxwellʹs propagation along with Z, transverse field variations along with X) in lossless media, Maxwell's
equations take the following form: equations take the following form:
Hy
1  Ex Ez  Ex 1 H
y
∂Ex
∂E
 z, , ∂Ex = 1 ∂Hy ,,
−
µ
z ∂z x ∂x
∂t
t μ0 0 ∂z
z

0
∂Hy  
− µ10
t∂t = μ

E
1 Hy
z
1 ∂Hy
∂Ez
=
∂t t ε ε∂xx
(5) (5)
The
location of the TM fields in the computational domain (mesh) follows the same philosophy
The location of the TM fields in the computational domain (mesh) follows the same philosophy as
shown
in the following Figure 6.
as shown in the following Figure 6. Figure 6. Basic numerical simulation of a 2D computational domain of FDTD software for nano‐
Figure 6. Basic numerical simulation of a 2D computational domain of FDTD software for nano-grating
grating structures. The detail location of TM fields in the computational domain. structures. The detail location of TM fields in the computational domain.
Figure 6 shows the basic numerical representation of a 2D computational domain of OptiFDTD Figure
shows the basic
numerical
representation
a 2D
computational
domain E
ofx OptiFDTD
software for 6 nano‐grating structures simulation. Now, of
the electric field components and Ez are software
for
nano-grating
structures
simulation.
Now,
the
electric
field
components
E
and
x
associated with the cell edges, while the magnetic field Hy is located at the center of the cell. Ez are
associated with the cell edges, while the magnetic field Hy is located at the center of the cell.
6. Simulation Results and Discussion 6. Simulation Results and Discussion
In this section, we discussed the simulation results of SWG structures. The simulation results In this section, we discussed the simulation results of SWG structures. The simulation results
obtained by using the OptiFDTD software package, which is based on the FDTD method that was obtained by using the OptiFDTD software package, which is based on the FDTD method that was
developed by Optiwave Inc. (Ottawa, ON, Canada) [22]. This FDTD software gives numerical developed by Optiwave Inc. (Ottawa, ON, Canada) [22]. This FDTD software gives numerical solutions
solutions by using Maxwell’s equation. by using Maxwell’s equation.
The FDTD simulation tool is used to calculate the light reflection losses of SWG structures (here, GaAs solar cells) for conversion efficiency improvement. The nano‐grating pitch or period and height of the SWG structures were varied to realize the minimum reflection losses in GaAs solar cells. Figure Energies 2016, 9, 690
8 of 13
The FDTD simulation tool is used to calculate the light reflection losses of SWG structures (here,
8 of 13 GaAs solar cells) for conversion efficiency improvement. The nano-grating pitch or period and height
of the SWG structures were varied to realize the minimum reflection losses in GaAs solar cells. Figure 7
7 shows the light reflection losses spectra for several nano‐grating heights (such as, the heights are shows the
light
reflection
losses
spectra
severalpitches nano-grating
heights
(such
as, the
arefor varied
varied from 100 nm to 400 nm) with for
different or periods. The pitches or heights
periods this from
100
nm
to
400
nm)
with
different
pitches
or
periods.
The
pitches
or
periods
for
this
simulation
simulation are: (Figure 7a) 200 nm, (7b) 300 nm, (7c) 350 nm, (7d) 400 nm, and (7e) 830 nm. For this are: (Figure 7a) 200 nm, (7b) 300 nm, (7c) 350 nm, (7d) 400 nm, and (7e) 830 nm. For this simulation,
simulation, the incident light wavelength was kept constant at 830 nm. The simulated results show the incident
light
wavelength
was kept constant
830
nm.reflection The simulated
results
thatto with
that with the increase of nano‐grating heights, at
the light reduces and show
reached the the
increase
of
nano-grating
heights,
the
light
reflection
reduces
and
reached
to
the
saturation
of
saturation of light reflection at 300 nm. In this case, the nano‐grating height about 300 nm has the light
reflection
at
300
nm.
In
this
case,
the
nano-grating
height
about
300
nm
has
the
minimum
light
minimum light reflection losses for GaAs solar cells. This is due to the saturation of the nano‐grating’s reflection losses for GaAs solar cells. This is due to the saturation of the nano-grating’s height for this
height for this specific design. Hence, this results confirm that when the nano‐grating height is about specific design. Hence, this results confirm that when the nano-grating height is about 300 nm the light
300 nm the light reflection loss is minimum. It has also been observed that the light reflection for 300 reflection
lossnm is minimum.
It has
also is been
observed
that nano‐grating the light reflection
for
300
nm reflection and 350 nm
nm and 350 nano‐grating height very close. This height for light is nano-grating
height
is
very
close.
This
nano-grating
height
for
light
reflection
is
minimum
and
it
is
minimum and it is saturated, which is the similar tendency as reported in [3]. When the nano‐grating saturated, which is the similar tendency as reported in [3]. When the nano-grating height increases
height increases further, such as the nano‐grating height is 400 nm, the light reflection again increases further,
such
as the nano-grating
height
is 400from nm, the
reflection
againreflection increasesversus as shown
in
as shown in Figure 7. It has again confirmed the light
Figure 8. The light nano‐
Figure 7. It has again confirmed from the Figure 8. The light reflection versus nano-grating height is
grating height is plotted in Figure 8 using the data of Figure 7e when the nano‐grating pitch or period plotted
in Figure 8 using the data of Figure 7e when the nano-grating pitch or period is 830 nm.
is 830 nm. Energies 2016, 9, 690 0.35
Grating
Height
0.30
100nm
Light Reflection
150nm
200nm
0.25
250nm
300nm
0.20
350nm
400nm
0.15
0.10
0.65
0.70
0.75
0.80
0.85
0.90
0.95
1.00
Wavelength (μm)
(a)
0.35
Grating
Height
Light Rflection
0.30
100nm
150nm
200nm
0.25
250nm
300nm
0.20
350nm
400nm
0.15
0.10
0.65
0.70
0.75
0.80
0.85
0.90
Wavelength (μm)
(b)
Figure 7. Cont.
0.95
1.00
Energies 2016, 9, 690
9 of 13
Energies 2016, 9, 690 9 of 13 0.35
Grating
Height
Light Reflection
0.30
100nm
150nm
0.25
200nm
250nm
0.20
300nm
350nm
400nm
0.15
0.10
0.65
0.70
0.75
0.80
0.85
0.90
0.95
1.00
Wavelength (μm)
(c)
0.35
Grating
Height
Light Reflection
0.30
100nm
150nm
0.25
200nm
250nm
0.20
300nm
350nm
400nm
0.15
0.10
0.65
0.70
0.75
0.80
0.85
0.90
0.95
1.00
Wavelength (μm)
(d)
0.35
Grating
Height
0.30
Light Reflection
100 nm
0.25
150 nm
200 nm
0.20
250 nm
0.15
300 nm
0.10
350 nm
400 nm
0.05
0.00
0.65
0.70
0.75 0.80 0.85 0.90
Wavelength (m)
(e)
0.95
1.00
Figure 7. Light reflection spectra for several triangular‐ or conical‐shaped nano‐grating heights with Figure 7. Light reflection spectra for several triangular- or conical-shaped nano-grating heights
different pitch or period. The periods are: (a) triangular‐ or conical‐shaped nano‐grating with pitch with different pitch or period. The periods are: (a) triangular- or conical-shaped nano-grating with
200 nm; (b) triangular‐ or conical‐shaped nano‐grating with pitch 300 nm; (c) triangular‐ or conical‐
pitch 200 nm; (b) triangular- or conical-shaped nano-grating with pitch 300 nm; (c) triangular- or
shaped nano‐grating with a pitch 350 nm; (d) triangular‐ or conical‐shaped nano‐grating with pitch conical-shaped nano-grating with a pitch 350 nm; (d) triangular- or conical-shaped nano-grating with
400 nm; and (e) triangular‐ or conical‐shaped nano‐grating with pitch 830 nm. The incident light pitch 400 nm; and (e) triangular- or conical-shaped nano-grating with pitch 830 nm. The incident light
wavelength is kept constant at 830 nm. wavelength is kept constant at 830 nm.
Energies 2016, 9, 690
Energies 2016, 9, 690 10 of 13
10 of 13 30
Energies 2016, 9, 690 10 of 13 Grating Pitch (or Period) 830 nm
30
20
25
Light Reflection (%)
Light Reflection (%)
25
Grating Pitch (or Period) 830 nm
15
20
10
15
5
10
0
5
50
0
100
150 200 250 300 350
Grating Height (nm)
400
450
50 100 150 200 250 300 350 400 450
Figure 8. Light reflection versus nao‐grating height characteristics when the grating pitch or period Figure
8. Light reflection versus nao-grating
heightHeight
characteristics
when the grating pitch or period is
Grating
(nm)
is kept constant at 830 nm. kept constant at 830 nm.
Figure 8. Light reflection versus nao‐grating height characteristics when the grating pitch or period is kept constant at 830 nm. Figure 8 shows the simulated minimum light reflection versus the nano‐grating height Figure 8 shows the simulated minimum light reflection versus the nano-grating height
characteristics for a triangular (i.e., conical or perfect cone)‐shaped nano‐grating structure of GaAs characteristics
forshows a triangular
(i.e., conical
or perfect
cone)-shaped
nano-grating
structure height of GaAs
Figure 8 the simulated minimum light reflection versus the nano‐grating having a constant period at 830 nm. The minimum light reflection about 2% was observed at 300 nm having
a constant period at 830 nm. The minimum light reflection about 2% was observed at 300 nm
characteristics for a triangular (i.e., conical or perfect cone)‐shaped nano‐grating structure of GaAs nano‐grating height. However, when the nano‐grating heights further increased to 350 nm and 400 nano-grating
height. However, when the nano-grating heights further increased to 350 nm and 400 nm,
having a constant period at 830 nm. The minimum light reflection about 2% was observed at 300 nm nm, then the light reflection increased further to higher order direction, such as about 4%. Therefore, nano‐grating height. However, when the nano‐grating heights further increased to 350 nm and 400 then
the light reflection increased further to higher order direction, such as about 4%. Therefore, this
this results indicated that the nano‐grating height about 300 nm has the minimum reflection losses nm, then the light reflection increased further to higher order direction, such as about 4%. Therefore, results
indicated that the nano-grating height about 300 nm has the minimum reflection losses for
for GaAs solar cells. This simulated results confirmed that the nano‐grating height about 300 nm is this results indicated that the nano‐grating height about 300 nm has the minimum reflection losses GaAs
solar cells. This simulated results confirmed that the nano-grating height about 300 nm is the
the optimum nano‐grating height for minimum light reflection losses of GaAs solar cells. Hence, most for GaAs solar cells. This simulated results confirmed that the nano‐grating height about 300 nm is optimum
nano-grating height for minimum light reflection losses of GaAs solar cells. Hence, most of
of the incident light passes through the GaAs substrate without reflecting back to the air (i.e., reduced thethe optimum nano‐grating height for minimum light reflection losses of GaAs solar cells. Hence, most incident light passes through the GaAs substrate without reflecting back to the air (i.e., reduced the
the light reflection losses) and it increases the conversion efficiency of GaAs solar cells significantly. of the incident light passes through the GaAs substrate without reflecting back to the air (i.e., reduced light
reflection losses) and it increases the conversion efficiency of GaAs solar cells significantly.
For minimum light reflection, we have considered different aspect ratio’s for the nano‐grating the light reflection losses) and it increases the conversion efficiency of GaAs solar cells significantly. For minimum light reflection, we have considered different aspect ratio’s for the nano-grating
period or pitches of 830‐nm to obtain the minimum light reflection for GaAs solar cells structure. The For minimum light reflection, we have considered different aspect ratio’s for the nano‐grating period or pitches of 830-nm to obtain the minimum light reflection for GaAs solar cells structure.
parameter “aspect ratio” controls the shape of the nano‐grating structure. Figure 9 shows the period or pitches of 830‐nm to obtain the minimum light reflection for GaAs solar cells structure. The The parameter “aspect ratio” controls the shape of the nano-grating structure. Figure 9 shows the
minimum light reflection for the nano‐grating (or period) of 830 nm. For case, the parameter “aspect ratio” loss controls the shape of the pitch nano‐grating structure. Figure 9 this shows the minimum light reflection loss for the nano-grating pitch (or period) of 830 nm. For this case, the
minimum light reflection is approximately 1%–2% with the nano‐grating height of 300–400 nm, when minimum light reflection loss for the nano‐grating pitch (or period) of 830 nm. For this case, the minimum light reflection is approximately 1%–2% with the nano-grating height of 300–400 nm, when
minimum light reflection is approximately 1%–2% with the nano‐grating height of 300–400 nm, when the aspect ratio is ‘0’. However, the light reflection is increased to 1%–4% (with the aspect ratio of 0.5) thethe aspect ratio is ‘0’. However, the light reflection is increased to 1%–4% (with the aspect ratio of 0.5) aspect ratio is ‘0’. However, the light reflection is increased to 1%–4% (with the aspect ratio of 0.5)
and the nano‐grating height of 250–450 nm; and reaches to 13%–17% with the aspect ratio of 0.8 and and
the nano-grating height of 250–450 nm; and reaches to 13%–17% with the aspect ratio of 0.8 and
and the nano‐grating height of 250–450 nm; and reaches to 13%–17% with the aspect ratio of 0.8 and the nano‐grating height of 200–450 nm. thethe nano‐grating height of 200–450 nm. nano-grating height of 200–450 nm.
Figure 9. 9. Minimum light height characteristics characteristics with the grating Figure Minimum light reflection reflection versus versus the the nano‐grating nano‐grating height with the grating Figure 9. Minimum light reflection versus the nano-grating height characteristics with the grating
period or pitch of 830 nm. Here, the aspect ratio is considered “0” as triangular‐shaped nano‐grating, period or pitch of 830 nm. Here, the aspect ratio is considered “0” as triangular‐shaped nano‐grating, period or pitch of 830 nm. Here, the aspect ratio is considered “0” as triangular-shaped nano-grating,
“0.5” and “0.8” as the trapezoidal‐shaped nano‐grating. “0.5” and “0.8” as the trapezoidal‐shaped nano‐grating. “0.5” and “0.8” as the trapezoidal-shaped nano-grating.
Figure 10 shows the minimum light reflection versus the aspect ratio characteristics for different Figure 10 shows the minimum light reflection versus the aspect ratio characteristics for different nano‐grating heights. For this study, the nano‐grating height is varied from 50 nm to 500 nm. For this nano‐grating heights. For this study, the nano‐grating height is varied from 50 nm to 500 nm. For this Energies 2016, 9, 690
11 of 13
Figure 10 shows the minimum light reflection versus the aspect ratio characteristics for different
Energies 2016, 9, 690 11 of 13 nano-grating heights. For this study, the nano-grating height is varied from 50 nm to 500 nm. For this
case,
the nano-grating period is kept constant at 830 nm. Here, the aspect ratio is varied from ‘0’ to ‘1’.
case, the nano‐grating period is kept constant at 830 nm. Here, the aspect ratio is varied from ‘0’ to As
discussed
earlier, when the aspect ratio is ‘0’ then the shape of the nano-grating is triangular and
‘1’. As discussed earlier, when the aspect ratio is ‘0’ then the shape of the nano‐grating is triangular when
the
aspect
ratio is >0 but <1, then the shape of the nano-grating is trapezoidal. However, when
and when the aspect ratio is >0 but <1, then the shape of the nano‐grating is trapezoidal. However, the
aspect ratio is ‘1’ then the shape of the nano-grating is rectangular. The simulated results show the
when the aspect ratio is ‘1’ then the shape of the nano‐grating is rectangular. The simulated results light
reflection for 50 nm grating height is >26%, which is like a flat type (about 30% light reflection)
show the light reflection for 50 nm grating height is >26%, which is like a flat type (about 30% light substrates.
From the plot, it shows clearly that when the nano-grating height increasing from 50 nm to
reflection) substrates. From the plot, it shows clearly that when the nano‐grating height increasing 250–350
nm,
then the light reflection is decreasing sharply and drops to about 2%. However, if further
from 50 nm to 250–350 nm, then the light reflection is decreasing sharply and drops to about 2%. increasing
the
nano-grating height, the reflection loss is increasing rapidly and reached toward to the
However, if further increasing the nano‐grating height, the reflection loss is increasing rapidly and flat
type of substrates, like a 50 nm nano-grating height.
reached toward to the flat type of substrates, like a 50 nm nano‐grating height. Figure 10. Minimum light reflection versus the aspect ratios for different nano‐grating heights with Figure
10. Minimum light reflection versus the aspect ratios for different nano-grating heights with the
the grating period or pitch of 830‐nm. Here, the nano‐grating height is varied from 50 nm to 500 nm. grating period or pitch of 830-nm. Here, the nano-grating height is varied from 50 nm to 500 nm.
7. Conclusions 7. Conclusions
In conclusion, this paper reported the design and analysis of nano‐structured gratings that can In conclusion, this paper reported the design and analysis of nano-structured gratings that can
improve the conversion efficiency in GaAs solar cells. The light reflection is about 2% with an improve the conversion efficiency in GaAs solar cells. The light reflection is about 2% with an optimized
optimized nano‐grating height of about 300 nm and the period of about 830 nm, which is about 28% nano-grating height of about 300 nm and the period of about 830 nm, which is about 28% lower than
lower than that of flat type substrates. The light reflection is calculated by the FDTD simulation tool. that of flat type substrates. The light reflection is calculated by the FDTD simulation tool. The simulated
The simulated results confirm that the light reflection of a rectangular‐shaped nano‐grating structure results confirm that the light reflection of a rectangular-shaped nano-grating structure is about 30%,
is about 30%, however, the light reflection becomes about 2% for a triangular (i.e., conical or perfect however, the light reflection becomes about 2% for a triangular (i.e., conical or perfect cone)-shaped
cone)‐shaped nano‐grating structure, because the refractive index changes gradually in several steps nano-grating structure, because the refractive index changes gradually in several steps and reduces
and reduces the light reflection losses from the surface of the substrates or panels. From the the light reflection losses from the surface of the substrates or panels. From the simulations, it also
simulations, it also noticed that the intermediate structures (i.e., trapezoidal‐ and parabolic‐shaped), noticed that the intermediate structures (i.e., trapezoidal- and parabolic-shaped), the light reflection
the light reflection loss is lower than the rectangular shaped nano‐grating structure but higher than loss is lower than the rectangular shaped nano-grating structure but higher than the triangular-shaped
the triangular‐shaped nano‐grating structure. The simulated results confirm that the reduction of nano-grating structure. The simulated results confirm that the reduction of light reflection losses will
light reflection losses will increase the conversion efficiency significantly in GaAs solar cells can be increase the conversion efficiency significantly in GaAs solar cells can be correlated to a practical
correlated to a practical example of higher conversion efficiency achieved in thin layer dielectric‐
example of higher conversion efficiency achieved in thin layer dielectric-coated graphene/GaAs
coated graphene/GaAs solar cells [12]. Therefore, it has confirmed that the triangular (i.e., conical or solar cells [12]. Therefore, it has confirmed that the triangular (i.e., conical or perfect cone)-shaped
perfect cone)‐shaped nano‐grating structures are an excellent alternative antireflective (AR) coating nano-grating structures are an excellent alternative antireflective (AR) coating for the reduction of light
for the reduction of light reflection losses and improve the conversion efficiency in GaAs solar cells reflection losses and improve the conversion efficiency in GaAs solar cells for a sustainable future.
for a sustainable future. Acknowledgments: This research is supported by the Centre for Smart Grid and Sustainable Power Systems,
Acknowledgments: This research is supported by the Centre for Smart Grid and Sustainable Power Systems, the
Faculty of Science and Engineering, Curtin University, Perth, WA, Australia and School of Mechanical
and
Electricalof Engineering,
of Health,
Engineering,
and
Sciences,
University
of Southern
Queensland,
the Faculty Science and Faculty
Engineering, Curtin University, Perth, Australia and School of Mechanical and Toowoomba,
QLD,
Australia.
Electrical Engineering, Faculty of Health, Engineering, and Sciences, University of Southern Queensland, Toowoomba, Australia. Author Contributions: Narottam Das and Syed Islam conceived, designed and performed the simulations, analyzed the data/results and wrote the paper. Energies 2016, 9, 690
12 of 13
Author Contributions: Narottam Das and Syed Islam conceived, designed and performed the simulations,
analyzed the data/results and wrote the paper.
Conflicts of Interest: The authors declare no conflict of interest.
References
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
Song, Y.M.; Lee, Y.T. Simulation of antireflective subwavelength grating structure for optical device
applications. In Proceedings of the 9th International Conference on Numerical Simulations of Optoelectronic
Devices 2009 (NUSOD’09), Gwangju, Korea, 14–17 September 2009; pp. 103–104.
Schmid, J.H.; Cheben, P.; Janz, S.; Lapointe, J.; Post, E.; Delage, A.; Densmore, A.; Lamontagne, B.;
Waldron, P.; Xu, D.-X. Subwavelength grating structures in planar waveguide facets for modified reflectivity.
In Proceedings of the SPIE—The International Society for Optical Engineering, Ottawa, ON, Canada,
4 June 2007; Volume 6796.
Sikder, U.; Zaman, M.A. Optimization of multilayer antireflection coating for photovoltaic applications.
Opt. Laser Technol. 2016, 79, 88–94. [CrossRef]
Bouhafs, D.; Moussi, A.; Chikouche, A.; Ruiz, J. Design and simulation of antireflection coating systems
for optoelectronic devices: Application to silicon solar cells. Sol. Energy Mater. Sol. Cells 1998, 52, 79–93.
[CrossRef]
Das, N.K.; Tan, C.L.; Lysak, V.V.; Alameh, K.; Lee, Y.T. Light absorption enhancement in metal-semiconductor-metal
photodetectors using plasmonic nanostructure gratings. In Proceedings of the 6th International
Symposium on High capacity Optical Networks and Enabling Technologies, HONET’09, Alexandria, Egypt,
28–30 December 2009; pp. 86–90.
Das, N.; Karar, A.; Vasiliev, M.; Tan, C.L.; Alameh, K.; Lee, Y.T. Analysis of nano-grating assisted
light absorption enhancement in metal-semiconductor-metal photodetectors patterned using focused ion
beam lithography. Opt. Commun. 2011, 284, 1694–1700. [CrossRef]
Ko, H.D. Surface Plasmon Coupled Sensor and Nanolens. Ph.D. Thesis, Texas A&M University,
College Station, TX, USA, 2009.
Lee, Y.T. High-efficiency GaInP/LCM-GaInP/GaAs triple-junction solar cells with antireflective subwavelength
structures. In Proceedings of the Pioneering Symposium (PC-02), Gwangu, Korea, October 2009.
Udagedara, I.B.; Rukhlenko, I.D.; Premaratne, M. Surface plasmon-polariton propagation in piecewise
linear chains of composite nanospheres: The role of optical gain and chain layout. Opt. Express 2011, 19,
19973–19986. [CrossRef] [PubMed]
Rukhlenko, I.D.; Pannipitiya, A.; Premaratne, M. Dispersion relation for surface plasmon polaritons in
metal/nonlinear-dielectric/metal slot waveguides. Opt. Lett. 2011, 36, 3374–3376. [CrossRef] [PubMed]
Zhu, W.; Rukhlenko, I.D.; Premaratne, M. Graphene metamaterial for optical reflection modulation.
Appl. Phys. Lett. 2013, 102, 241914. [CrossRef]
Li, X.; Zhang, S.; Wang, P.; Zhong, H.; Wu, Z.; Chen, H.; Li, E.; Liu, C.; Lin, S. High performance solar cells
based on graphene/GaAs hetero-structures. Nano Energy 2015, 16, 310. [CrossRef]
Thelen, A. Design of Optical Interference Coatings; McGraw-Hill: New York, NY, USA, 1989.
Sahoo, K.C.; Li, Y.; Chang, E.Y. Shape effect of silicon nitride subwavelength structure on reflectance for
silicon solar cells. IEEE Trans. Electron. Device 2010, 57, 2427–2433. [CrossRef]
Song, Y.M.; Jang, S.J.; Yu, J.S.; Lee, Y.T. Bioinspired parabola subwavelength structures for improved
broadband antireflection. Small 2010, 6, 984–987. [CrossRef] [PubMed]
Moushumy, N.; Das, N.K.; Alameh, K.; Lee, Y.T. Design and development of silver nanoparticles to reduce
the reflection loss of solar cell. In Proceedings of the 8th International Conference on High-capacity Optical
Networks and Emerging Technologies (HONET’11), Riyadh, Saudi Arabia, 19–21 December 2011; pp. 38–41.
Das, N.K.; Islam, S.M. Optimization of nano-grating structure to reduce the reflection losses in GaAs
solar cells. In Proceedings of the Australasian Universities Power Engineering Conference 2012 (AUPEC 2012),
Denpasar-Bali, Indonesia, 26–29 September 2012.
Bondeson, A.; Rylander, T.; Ingelstrom, P. Computational Electromagnetics, 1st ed.; Springer: New York, NY,
USA, 2005.
Jin, J.M. Theory and Computation of Electromagnetic Fields; John Wiley & Sons: Hoboken, NJ, USA, 2010.
Energies 2016, 9, 690
20.
21.
22.
23.
24.
25.
26.
27.
28.
13 of 13
Yu, W. Electromagnetic Simulation Techniques Based on the FDTD Method; John Wiley & Sons: Hoboken, NJ,
USA, 2009.
Yee, K.S. Numerical solution of initial boundary value problems involving Maxwell’s equations in
isotropic media. IEEE Trans. Antennas Propag. 1966, 14, 302–307.
Optiwave Support Team. Finite Difference Time Domain Photonics Simulation Software; OptiFDTD Technical
background and Tutorials, Version 8; Optiwave System Inc.: Ottawa, ON, Canada, 2008.
Rakić, A.D.; Djurišić, A.B.; Elazar, J.M.; Majewski, M.L. Optical properties of metallic films for vertical-cavity
optoelectronic devices. Appl. Opt. 1998, 37, 5271–5283. [CrossRef] [PubMed]
Markovic, M.I.; Rakic, A.D. Determination of reflection coefficients of laser light of wavelength from the
surface of aluminum using the Lorentz-Drude model. Appl. Opt. 1990, 29, 3479–3483. [CrossRef] [PubMed]
Markovic, M.I.; Rakic, A.D. Determination of optical properties of aluminum including electron reradiation
in the Lorentz-Drude Model. Opt. Laser Technol. 1990, 22, 394–398. [CrossRef]
Dhakal, D. Analysis of the Sub-Wavelength Grating in OptiFDTD Simulator. Master’s Thesis, Jacobs University,
Bremen, Germany, 2009.
Ferry, V.E.; Sweatlock, L.A.; Pacifici, D.; Atwater, H.A. Plasmonic nanostructure design for efficient light
coupling into solar cells. Nano Lett. 2008, 8, 4391–4397. [CrossRef] [PubMed]
Kabir, M.I.; Ibrahim, Z.; Sopian, K.; Amin, N. Effect of structural variations in amorphous silicon based
single and multi-junction solar cells from numerical analysis. Sol. Energy Mater. Sol. Cells 2010, 95, 1542–1545.
[CrossRef]
© 2016 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access
article distributed under the terms and conditions of the Creative Commons Attribution
(CC-BY) license (http://creativecommons.org/licenses/by/4.0/).