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
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PHOTONIC BAND GAP MATERIALS
AND MONOLAYER SOLAR CELL
ARAFA H. ALY
*
and HASSAN SAYED
Physics Department, Faculty of Sciences,
Beni-Suef University, Egypt
*
[e-mail]
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 so-
lution for energy crisis all over the world. Thus, re-
newable 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 en-
ergy, 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 semiconduc-
tor materials which are called photovoltaic (PV)
e®ect.
1
PIN solar cell structure is a layer of intrinsic
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 gen-
erated electron hole pairs within each P-region and
N-region will be recombined before being collected.
So that, the only generation which causes photo-
current 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
*
Corresponding author.
Surface Review and Letters, Vol. 25, No. 8 (2018) 1850103 (6 pages)
°
cWorld Scienti¯c Publishing Company
DOI: 10.1142/S0218625X18501032
1850103-1
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Recently, silicon is widely spread in the PV in-
dustry 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 ¼600 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 improve-
ment of solar cell e±ciency. Thus, we use one-
dimensional 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 character-
istics of the PIN solar cell. Moreover, the e®ect of 1D
binary PCs (i.e. two material layers constituting a pe-
riod 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 proce-
dures have investigated by transfer matrix method
(TMM) for the back re°ector and COMSOL Multi-
physics 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 con-
tinuity (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"srÞ¼; ð1Þ
@n
@t1 qrJnþUn¼0;ð2Þ
@p
@t1 qrJhþUh¼0;ð3Þ
where "sand are the semiconductor permittivity
and the space charge density given by Eq. (4), qis the
charge of the electron, (Jn;Jh) are current densities
(A/cm
2
)andUn;Uhare the net number of electrons
and holes recombined in the unit of time and volume
[1/(S cm3Þ]:
¼qðnpþNANDÞ;ð4Þ
Un¼RnGn;ð5Þ
Uh¼RhGh;ð6Þ
where Rn;Gnare the generation and the recombina-
tion rate of electrons. Rh,Ghare 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):
Jn¼qnnrþqDnrn;ð7Þ
Jh¼qphrþqDhrp;ð8Þ
J¼JnþJh;ð9Þ
where n;
hare the temperature-dependent electron
and hole mobilities [m
2
/(VS)] given by Eqs. (10)
and (11). Dnand Dhare the di®usion coe±cients of
electrons and holes with D¼kT/qthe di®usion
coe±cient.
13
kis the Boltzmann constant and Tis the
temperature:
e¼7:7104;ð10Þ
h¼850 T
300
1:8
:ð11Þ
In wave optics module to determine photogeneration
rates, G¼Gn¼Gp, we calculate the optical electric
¯eld by solving Maxwell's equations in the frequency
domain:
r  ðr  EÞk2
0"rE¼0ð12Þ
A. H. Aly & H. Sayed
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"r¼ðnrikÞ2ð13Þ
where k0is the wave vector and ð"rÞis 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 one-
dimensional 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
M21 M22
!
¼D1
AðD1P1D1
1D2P2D1 2ÞNDA;
ð14Þ
where Piis the propagation matrix in layer isince
i¼1, 2 and A, which is given by:
Pi¼expðjkidiÞ0
0expðjkidiÞ
"#
;ð15Þ
where kiis the wave number and given by:
ki¼!nicos i
c:ð16Þ
Diis the dynamical matrix and given by Eqs. (17)
and (18), for the electric component (TE) and the
magnetic component (TM), respectively.
Dq¼11
nqcos qnqcos q
"#
;ð17Þ
Dq¼cos qcos q
nqnq
"#
;ð18Þ
where i¼Awith nA¼1 for air. The transmittance T
is determined by the following relationship:
T¼jtj2¼1
M11
2
;ð19Þ
where tis the transmission coe±cient.
3. Result and Discussion
In the following, we present the numerical and sim-
ulation results of our work. The planner ARC was
designed from 1D ternary PCs, which composed of a
layer of silicon nitride (Si
3
N
4
) immersed between the
two layers of silicon dioxide (SiO
2
). The optimum
thicknesses are 98, 48 and 8 nm for the ¯rst SiO
2
layer, the Si
3
N
4
layer and the second SiO
2
layer, re-
spectively, 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 transmis-
sion spectra for our back re°ector which composed of
1D binary PBG structure are investigated via a dif-
ferent number of periods, as shown in Fig. 2. The
values of various parameters for this 1D binary PBG
structure were chosen as the Sio
2
layer is character-
ized by the refractive index of 1.46
17
and thickness
d1¼40 nm. The cSio2:H layer is speci¯ed with
(a) (b) (c)
Fig. 1. (Color online) Monolayer solar cell simulated in
COMSOL (a) without anti-re°ection coating, (b) with anti-
re°ection coating consisting of layer of (Si
3
N
4
) embedded
between two layers of Sio
2
and (c) with the same ARC as in
(b) and one-dimensional PCs as aback re°ector.
PBG Materials and Monolayer Solar Cell
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the refractive index of 2.8
18
and thickness d2¼85 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 pho-
tons from the PIN silicon solar cell with ARC
as shown in Fig. 3are 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 amor-
phous silicon does not absorb any photons with the
wavelength longer than 730 nm, due to its energy gap
being 1.7 eV
19
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,
N¼10 to act as a back re°ector to the PIN silicon
solar cell with ARC.
3.2. The optical properties
We will simulate the absorption of the PIN silicon
solar cell by FEM as described in Eq. (20)
20
:
AðÞ¼jEactive areaðÞj2
jEtotalðÞj2:ð20Þ
Equation (20) relates the electric ¯eld which is
absorbed in the active area of the cell (Eactive areaðÞÞ
as a function of wavelength with the total incident
electric ¯eld (EtotalðÞÞ.
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
300 400 500 600 700 800
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Transmission
Wavelenght [nm]
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
(Si
3
N
4
) immersed between the two layers of silicon dioxide
(SiO
2
). The optimum thicknesses are 98, 48 and 8 nm for
the ¯rst SiO
2
layer, the Si
3
N
4
layer and the second SiO
2
layer, respectively.
300 400 500 600 700 800
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Absorption
Wavelenght [nm]
base cell
with ARC
with ARC & back reflector
Fig. 4. (Color online) Absorption curve for the hydroge-
nated amorphous silicon (a-Si: H) solar cell in the range
(300–800 nm), for the three cases as shown.
300 350 400 450 500 550 600 650 700 750 800
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Wavelength [nm]
Transmission
N=3
N=5
N=10
Fig. 2. (Color online) The transmission spectrum of 1D
binary PCs of Sio
2
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.
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