Hassan Arafa 2017 SRL

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Photonic band gap materials and monolayer solar cell
Article in Surface Review and Letters · September 2017
DOI: 10.1142/S0218625X18501032
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Arafa H Aly
Hassan Sayed
Beni Suef University
Beni Suef University
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Surface Review and Letters, Vol. 25, No. 8 (2018) 1850103 (6 pages)
c World Scienti¯c Publishing Company
°
DOI: 10.1142/S0218625X18501032
Surf. Rev. Lett. Downloaded from www.worldscientific.com
by THE UNIVERSITY OF NEW SOUTH WALES on 09/17/17. For personal use only.
PHOTONIC BAND GAP MATERIALS
AND MONOLAYER SOLAR CELL
ARAFA H. ALY* and HASSAN SAYED
Physics Department, Faculty of Sciences,
Beni-Suef University, Egypt
*[email protected]
Received 5 May 2017
Revised 7 July 2017
Accepted 24 August 2017
Published 15 September 2017
In this paper, we demonstrate theoretically an e±cient way to improve the optical properties of the
PIN silicon solar cell. We design an anti-re°ecting coating (ARC) from one-dimensional ternary
photonic crystals (PCs). Also, we design a back-re°ector that composed of one-dimensional binary
PC. By adding ARC layers, we have observed that the absorption is increased from 0.5 to 0.75.
Moreover, by adding back re°ector layers, we found that the absorption values rise to reach over
0.95 in the range of the photonic band gap (PBG) of the back re°ector. Thus, using PCs in each
ARC and back re°ector has a signi¯cant enhancement of the absorption of the cell. Our design could
have a distinct e®ect on the conversion e±ciency of the cell. We use transfer matrix method to
optimize the PBG of the back re°ector. Finally, the numerical and simulated results of the cell are
investigated by COMSOL Multiphysics that based on the ¯nite element method (FEM).
Keywords: Photonic crystals; solar cell; anti-re°ection coating; COMSOL.
1. Introduction
Energy crisis encourages the consumers to search for
development more stable and possibly less expensive
new sources of energy. Renewable energy is the solution for energy crisis all over the world. Thus, renewable energy received considerable attention due
to its novel properties rather than the conventional
source of energy (fossil fuels). The most popular type
of renewable energy among all types is the solar energy, and many researchers devoted the attention
toward the solar cell. Wherein, solar cell converts
electromagnetic radiation into electrical energy, and
this process occurs particularly in some semiconductor materials which are called photovoltaic (PV)
e®ect.1 PIN solar cell structure is a layer of intrinsic
*Corresponding
semiconductor immersed between two layers of
p-doped and n-doped semiconductor materials. PIN
is characterized by the built-in electric ¯eld which is
the same as in the p-n junction. However, PIN solar
cell di®ers in the electric ¯eld and depletion region,
which extend over a wide range. However, the generated electron hole pairs within each P-region and
N-region will be recombined before being collected.
So that, the only generation which causes photocurrent is within the depletion region. Therefore, the
wide range of depletion region is considered as an
advantage in materials which have short minority
carrier di®usion lengths because the light-generated
carriers have less probability of recombination
before being collected.2
author.
1850103-1
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A. H. Aly & H. Sayed
Recently, silicon is widely spread in the PV industry due to the low cost, high e±ciency and easy to
fabricate. Above all, PIN silicon solar cell provides
some limitations in e±ciency due to the indirect band
gap of silicon beside the transmitted photons from the
active area of the cell without any generation, in
addition to energy losses by re°ection on the top
surface of the cell. Wherein the polished silicon solar
cell su®ers from signi¯cant losses by re°ection which
reached to 35% at wavelength ¼ 600 nm for normal
incidence.3 This large portion of re°ected light is due
to the high refractive index of silicon that leads to a
high dielectric contrast between the air and silicon.
Therefore, many researchers directed the attention
toward the usage of the anti-re°ecting coating (ARC)
and back re°ector to reduce the re°ectivity of the cell
and to reduce the leakage of the transmitted photons
from the cell, respectively.4
Recently, photonic crystals (PCs) or photonic
band gap (PBG) could be of potential use as ARC
and back re°ector due to their unique properties. PCs
are inhomogeneous arti¯cial structures with periodic
modulation of dielectric constants in one, two and
three dimensions.5–7 PCs have a distinct e®ect on the
propagation of the incident electromagnetic waves.8
Thus, PCs received considerable attention duo to
their unique properties, especially on the improvement of solar cell e±ciency. Thus, we use onedimensional PCs in each ARC and back re°ector due
to its low cost and variety of applications.9–11
In this paper, we demonstrate the e®ect of 1D
ternary PCs (i.e. three material layers constituting a
period of lattice) as a planner ARC on the characteristics of the PIN solar cell. Moreover, the e®ect of 1D
binary PCs (i.e. two material layers constituting a period of lattice) as a back re°ector to the cell is studied.
The e®ect on the optical properties such as absorption
through the cell and the optical generation of electron
hole pairs is considered here. Our simulation procedures have investigated by transfer matrix method
(TMM) for the back re°ector and COMSOL Multiphysics that essentially based on the ¯nite element
method (FEM) for the overall PIN silicon solar cell.
2. Modeling and Motivation
PV simulation by COMSOL Multiphysics requires
semiconductor and wave optics modules. Also, it
necessitates to solve the Poisson (Eq. (1)) and continuity (Eqs. (2) and (3))12 equations to determine
the electrostatic potential , electron concentration n
(cm 3 ) and hole concentration p (cm 3 ) as functions
of space:
r ð"s rÞ ¼ ;
ð1Þ
@n 1
r Jn þ Un ¼ 0;
@t q
ð2Þ
@p 1
r Jh þ Uh ¼ 0;
@t q
ð3Þ
where "s and are the semiconductor permittivity
and the space charge density given by Eq. (4), q is the
charge of the electron, (Jn ; Jh ) are current densities
(A/cm2) and Un ; Uh are the net number of electrons
and holes recombined in the unit of time and volume
[1/(S cm 3 Þ]:
¼ qðn p þ NA ND Þ;
ð4Þ
Un ¼ Rn Gn ;
ð5Þ
Uh ¼ R h G h ;
ð6Þ
where Rn ; Gn are the generation and the recombination rate of electrons. Rh , Gh are generation and
recombination rate of holes. The current densities, Jn
and Jh , with drift and di®usion components, are given
by Eqs. (7) and (8). Then the total current density is
given by Eq. (9):
Jn ¼ qnn r þ qDn rn;
ð7Þ
Jh ¼ qph r þ qDh rp;
ð8Þ
J ¼ Jn þ Jh ;
ð9Þ
where n ; h are the temperature-dependent electron
and hole mobilities [m2/(VS)] given by Eqs. (10)
and (11). Dn and Dh are the di®usion coe±cients of
electrons and holes with D ¼ kT/q the di®usion
coe±cient.13 k is the Boltzmann constant and T is the
temperature:
e ¼ 7:7 10 4 ;
T 1:8
h ¼ 850
:
300
ð10Þ
ð11Þ
In wave optics module to determine photogeneration
rates, G ¼ Gn ¼ Gp, we calculate the optical electric
¯eld by solving Maxwell's equations in the frequency
domain:
1850103-2
r ðr EÞ k 20 "r E ¼ 0
ð12Þ
PBG Materials and Monolayer Solar Cell
where ki is the wave number and given by:
ki ¼
!ni cos i
:
c
ð16Þ
Di is the dynamical matrix and given by Eqs. (17)
and (18), for the electric component (TE) and the
magnetic component (TM), respectively.
"
#
1
1
Dq ¼
;
ð17Þ
nq cos q nq cos q
"
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Dq ¼
(a)
(b)
(c)
Fig. 1. (Color online) Monolayer solar cell simulated in
COMSOL (a) without anti-re°ection coating, (b) with antire°ection coating consisting of layer of (Si3N4) embedded
between two layers of Sio2 and (c) with the same ARC as in
(b) and one-dimensional PCs as aback re°ector.
cos q cos q
nq
nq
#
;
ð18Þ
where i ¼ A with nA ¼ 1 for air. The transmittance T
is determined by the following relationship:
1 2
2
;
T ¼ jtj ¼ ð19Þ
M11 where t is the transmission coe±cient.
3. Result and Discussion
"r ¼ ðnr ikÞ 2
ð13Þ
where k0 is the wave vector and ð"r Þ is the complex
permittivity that can be described in terms of the real
part (nr ) and the imaginary part (k).14
Our structure is composed of p-region, intrinsic
region and n-region of thicknesses 15, 200 and 27 nm,
respectively. Those decomposed in silicon wafer are
shown in Fig. 1(a). Our model in the presence of ARC
is shown in Fig. 1(b). Moreover, our model with ARC
and back re°ector is shown in Fig. 1(c).
In this work, we use the TMM to analyze onedimensional binary PCs as a back re°ector to the PIN
silicon solar cell. The transmittance spectrum can be
calculated by TMM.15 According to TMM, the total
transfer matrix given by Eq. (12).
!
M11 M12
1
1 N
¼ D 1
A ðD1 P1 D 1 D2 P2 D 2 Þ DA ;
M21 M22
ð14Þ
where Pi is the propagation matrix in layer i since
i ¼ 1, 2 and A, which is given by:
"
#
expðjki di Þ
0
Pi ¼
;
ð15Þ
0
expðjki di Þ
In the following, we present the numerical and simulation results of our work. The planner ARC was
designed from 1D ternary PCs, which composed of a
layer of silicon nitride (Si3N4) immersed between the
two layers of silicon dioxide (SiO2). The optimum
thicknesses are 98, 48 and 8 nm for the ¯rst SiO2
layer, the Si3N4 layer and the second SiO2 layer, respectively, structure for one period. These ARCs are
optimized in our previous work.16 Our results are
presented in two stages. The ¯rst one is optimized by
our back re°ector by TMM. The distinct e®ect of the
ARC and back re°ector on the optical properties of
the PIN solar cell is discussed, to investigate the
enhancements on the optical generation of the cell
through the second stage.
3.1. The back re°ector
For normal incidence of light, the output transmission spectra for our back re°ector which composed of
1D binary PBG structure are investigated via a different number of periods, as shown in Fig. 2. The
values of various parameters for this 1D binary PBG
structure were chosen as the Sio2 layer is characterized by the refractive index of 1.4617 and thickness
d1 ¼ 40 nm. The c Sio2 :H layer is speci¯ed with
1850103-3
A. H. Aly & H. Sayed
1
0.9
wavelength longer than 730 nm, due to its energy gap
being 1.7 eV19 which corresponding to 730 nm. So
that, any photon with the wavelength longer than
730 nm will be transmitted from the cell without
any generation. Thus, we use the number of periods,
N ¼ 10 to act as a back re°ector to the PIN silicon
solar cell with ARC.
N=3
N=5
N=10
0.8
Transmission
0.7
0.6
0.5
0.4
0.3
3.2. The optical properties
0.2
0.1
350
400
450
500
550
600
Wavelength [nm]
650
700
750
800
Fig. 2. (Color online) The transmission spectrum of 1D
binary PCs of Sio2 and c-SiOx:H, the thicknesses of the
materials are denoted by 40 and 85 nm, respectively, with
di®erent numbers of periods as shown.
the refractive index of 2.818 and thickness d2 ¼ 85 nm.
The transmission spectrum is calculated by TMM as
discussed previously. We optimized the back re°ector
with the last parameters to localize the PBG in the
range of 550–700 nm, because the transmitted photons from the PIN silicon solar cell with ARC
as shown in Fig. 3 are beginning approximately at
550 nm. So that, we are concerned about the
range of wavelengths from 550 nm to 730 nm, because
the active area of the cell which composed of amorphous silicon does not absorb any photons with the
0.8
0.7
We will simulate the absorption of the PIN silicon
solar cell by FEM as described in Eq. (20)20:
AðÞ ¼
jEactive area ðÞj 2
:
jEtotal ðÞj 2
ð20Þ
Equation (20) relates the electric ¯eld which is
absorbed in the active area of the cell (Eactive area ðÞÞ
as a function of wavelength with the total incident
electric ¯eld (Etotal ðÞÞ.
Therefore, in Fig. 4, we investigate the e®ect of the
ARC and the back re°ector on the values of the
absorbed light through the cell. Without ARC, the
absorption value is not exceeding 0.5. In the presence
of the ARC, we obtained a signi¯cant enhancement in
the absorption values, which increased to reach over
0.75. The de¯nite increase in the absorption values is
due to the decrements on re°ection at the interface
that allows to a signi¯cant portion of the incident
light to reach the active area of the cell, which, in
turn, increases the absorption of the considered
structure. Moreover, by adding the back re°ector
layer, we observed that the absorption values increase
0.6
1.0
0.5
0.9
0.4
0.8
0.3
0.7
0.2
0.6
Absorption
Transmission
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0
300
0.1
0.0
300
400
500
600
700
0.5
0.4
0.3
800
Wavelenght [nm]
0.2
Fig. 3. (Color online) The transmission spectrum of the
PIN silicon solar cell with ARC. These ARCs consist of 1D
ternary PCs that composed of a layer of silicon nitride
(Si3N4) immersed between the two layers of silicon dioxide
(SiO2). The optimum thicknesses are 98, 48 and 8 nm for
the ¯rst SiO2 layer, the Si3N4 layer and the second SiO2
layer, respectively.
0.1
0.0
300
base cell
with ARC
with ARC & back reflector
400
500
600
700
800
Wavelenght [nm]
Fig. 4. (Color online) Absorption curve for the hydrogenated amorphous silicon (a-Si: H) solar cell in the range
(300–800 nm), for the three cases as shown.
1850103-4
PBG Materials and Monolayer Solar Cell
×1025
×1025
8
Optical generation [m4 kg2/(S6 A2)]
5
Generation rate [1/(m3s)]
4
Air region
PIN
3
400 [nm]
500 [nm]
600 [nm]
700 [nm]
800 [nm]
2
1
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200
400
6
5
4
3
2
600
base cell
with ARC
with ARC & back reflecor
1
0
300
0
0
7
400
Arc lenght [nm]
Fig. 5. (Color online) Generation rate versus arc length of
the PIN silicon solar cell at di®erent wavelength values.
to reach over 0.95 in the range of the PBG of the
back re°ector. Thus, using PCs in each ARC and
back re°ector has a signi¯cant enhancement on the
absorption of the cell.
Then, we calculate the generation term due to the
incident electromagnetic waves on the cell without
any modi¯cation, as shown in Fig. 5. The generation
rate is equal to zero in the air region and decreases
exponentially inside the active area of the cell, due to
the absorption of the incident electromagnetic wave
as shown in Fig. 5. Moreover, the generation rate
depends on the wavelength of the incident light corresponding to the energy gap of the cell. Also, we
observed high generation rate at the wavelength of
500 nm. Thus, we demonstrate in Fig. 6 the relation
between the optical generation rate and incident
wavelength in the three cases, without any modi¯cation, with ARC only and the cell with ARC and
back re°ector. Here, the optical generation rate
(Goptical ) of electrons is calculated as a function of
wavelength using Eq. (21). The optical generation
rate is directly proportional to the intensity of the
electric ¯eld in the active layer, and the imaginary
part of the permittivity (" 00 ) as in Ref. 21:
Gopt ðÞ ¼
" 00 jEj 2
:
2}
500
600
700
800
Wavelenght [nm]
ð21Þ
Figure 6 indicates the presence of the ARC which has
a signi¯cant e®ect on the generation rate due to the
decrements of the re°ection part in the incident light.
Also, the presence of each ARC and back re°ector has
Fig. 6. (Color online) Relation between optical generation
rate and the incident wavelength for the following cases.
Black color for PIN silicon solar cell without any modi¯cation. Red is the cell with ARC only and green for the cell
with ARC and back re°ector.
a signi¯cant enhancement on the generation rate in
the active area due to the decrements of energy losses
by re°ection and transmission of the incident electromagnetic waves. By the way, the absorbed electric
¯eld increased in the active area of the cell, which
causes high generation rate. This e®ect could obtain a
good indication of high current density and also high
cell e±ciency.
4. Conclusion
PCs are a suitable candidate to overcome the limitation of PIN silicon solar cell e±ciency. Thus, we
investigate the optical properties of the PIN solar cell
in the presence of a planner ARC and back re°ector.
The ARC is designed from one-dimensional ternary
PCs that contains only one period. Also, the back
re°ector is composed of 1D binary PCs for 10 periods.
By adding ARC, we have observed that the absorption is increased from 0.5 to 0.75. Moreover, by adding the back re°ector layer, we found that the
absorption values increase to reach over 0.95 in the
range of the PBG of the back re°ector. Thus, using
PCs in each ARC and back re°ector has a signi¯cant
enhancement of the absorption of the cell. Our design
could have a distinct e®ect on the conversion e±ciency of the cell. Finally, the numerical results are
obtained by COMSOL Multiphysics that based on
1850103-5
A. H. Aly & H. Sayed
the FEM use TMM and MATLAB program to optimize the PBG of the back re°ector.
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References
1. J. Johansson, Modelling and optimization of CIGS
solar cell modules, Master's thesis, Avdelningen f€
or
energi och byggnadsdesign Institutionen f€or arkitektur
och byggd milj€o Lunds tekniska h€ogskola Lunds universitet (2008).
2. S. Abdellatif and K. Kirah, Energy Proced. 36 (2013)
488.
3. A. N. Sprafke and R. B. Wehrspohn, Green 2 (2012)
177.
4. K. Han and C. Chang, Nanomater 4 (2014) 87.
5. J. D. Joannopoulos, S. G. Johnson, J. N. Winn and
R. D. Meade, Photonic Crystals: Molding the Flow of
Light (Princeton University Press, Princeton, NJ,
1995).
6. A. H. Aly, W. Sabra and H. A. Elsayed, Int. J. Mod.
Phys. B 31 (2017) 1750123.
7. A. H. Aly, H. A. Elsayed and S. A. El-Naggar, J. Mod.
Opt. 64 (2017) 74.
8. S. John, Phys. Rev. Lett. 58 (1987) 2486.
9. A. H. Aly and H. A. ElSayed, J. Mod. Opt. 64 (2017)
871.
10. E. Yablonovitch, Phys. Rev. Lett. 58 (1987) 2059.
11. A. H. Aly and M. F. Eissa, Surf. Rev. Lett. 24 (2017)
1750106.
12. R. J. Elliot and A. F. Gibson, An Introduction to Solid
State Physics and its Application (William Clowes &
Sons Ltd, London, 1974).
13. M. J. Tajik, Analytical and numerical modeling of
organic photovoltaic devices, MSc thesis, McMaster
University Hamilton, Ontario, Canada (2010).
14. C. Kittel, Introduction to Solid State Physics (Wiley,
1986).
15. R. C. Thompson, J. Mod. Opt. 37 (1990) 147.
16. A. H. Aly and H. Sayed, Opt. Appl.
17. A. Banerjee, Prog. Electromagn. Res. Lett. 11 (2009)
129.
18. A. Ho®mann, U. W. Paetzold, C. Zhang, T.
Merdzhanova, A. Lambertz, C. Ulbrich, K. Bittkau
and U. Rau, Opt. Expr. 22 (2014) A1270.
19. C. Feser, J. Lacombe, K. V. Maydell and C. Agert,
Prog. Photovolt. Res. Appl. 20 (2012).
20. O. A. M. Abdelraouf and N. K. Allam, Opt. Mater.
54 (2016) 84.
21. M. G. Deceglie, V. E. Ferry, A. P. Alivisatos and
H. A. Atwater, Nano Lett. 12 (2012) 2894.
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