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  <front>
    <journal-meta />
    <article-meta>
      <title-group>
        <article-title>Numerical investigation of external electromagnetic field induced on Organic Solar Cells model using FEM Analysis</article-title>
      </title-group>
      <contrib-group>
        <aff id="aff0">
          <label>0</label>
          <institution>Grazia Lo Sciuto Department of Electrical, Electronic and Informatics Engineering University of Catania</institution>
          ,
          <country country="IT">Italy</country>
        </aff>
      </contrib-group>
      <fpage>29</fpage>
      <lpage>34</lpage>
      <abstract>
        <p>-Research on photovoltaic energy conversion has recently received great impulse due to the growing demand for low carbon dioxide emission energy sources. In particular, the high manufacturing cost of crystalline silicon and the latest advancements on semiconducting polymer design and synthesis in recent years have directed the attention of the scientific community towards Organic Solar Cells (OSCs). In this paper, the electromagnetic field induced on OSCs has been investigated to evaluate the potential of the optical efficiecy at several frequencies of OSCs. Index Terms-FEM; Organic solar cells; Electromagnetic field</p>
      </abstract>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>I. INTRODUCTION</title>
      <p>
        The electronic devices more efficient and economics able
to work as solar cells can be developed using several types
of material with different structural architectures [
        <xref ref-type="bibr" rid="ref1">1</xref>
        ], [
        <xref ref-type="bibr" rid="ref2">2</xref>
        ]. The
detailed research on the fullerene properties could represent
the keystone for the diffusion of the organic solar cells. The
organic based solar cells are nothing new, but the major
constraint of this innovation lies in his basic constituent, the
fullerene, too expensive for a mass dissemination. To increase
the knowledge of the fullerene has enabled to develop other
low-cost alternatives. It is a mixture of polymers capable of
producing structural and electronic changes in the photovoltaic
cells such as tripling the efficiency. Scientists have embedded
in the active layer of the solar cells, based on carbon, the pure
graphene with surprising results: the conductivity is increased
and the efficiency of photovoltaic cells has grown of the
200% in energy systems. Unlike solar cells based on silicon
or germanium existing in the market, the polymers are less
expensive and more malleable. The polymer solar cells can be
folded like a sheet and carried easily.
      </p>
      <p>In order to be competitive for the production of solar energy
on an industrial scale, this technology must however dissolve
a crucial node. Compared to inorganic semiconductors, the
organic materials have a lower charge transfer coefficient,
namely the electron transfer speeds in the energy system.
Although thinner and flexible, the organic photovoltaic films fail
to capture an equally large portion of the solar spectrum with
a lower amount of energy based on the silicon technologies.</p>
      <p>
        However, the mechanical reliability of full cell packaging
is rarely concerned. As solar cell often appears to be a part
Copyright c 2017 held by the authors.
of structure, stress will inevitably act on the package [
        <xref ref-type="bibr" rid="ref3">3</xref>
        ], [
        <xref ref-type="bibr" rid="ref4">4</xref>
        ],
[
        <xref ref-type="bibr" rid="ref5">5</xref>
        ], [
        <xref ref-type="bibr" rid="ref6">6</xref>
        ].
      </p>
      <p>
        The researchers have tried to solved these problems by
increasing the ability to transport electrons polymer using
polymer mixture, studying the morphology of the organic
photovoltaic and new solutions to increase the charge transfer
coefficient. During the last years the development of
organic photovoltaics (OPV) focuses on inexpensive materials,
promising a simple processing and integration on different
substrates with high performance. In this regard the equivalent
circuit modeling of photovoltaic devices can be useful for
understanding the performance and the optimization of the
design solar cells [
        <xref ref-type="bibr" rid="ref7">7</xref>
        ], developing faster algorithms and
computational techniques without costly experiments, although it
is characterized by a very high level of abstraction. Since
the basic equivalent circuit model is represented by ideal
circuit element such as diode, current source and resistance to
understand and calculate the J V characteristics of inorganic
solar cells.
      </p>
      <p>
        Doo-Hyun Ko et al. [
        <xref ref-type="bibr" rid="ref8">8</xref>
        ] report organic solar cells with
a photonic crystal geometry fabricated using a
materialsagnostic process called PRINT wherein highly ordered arrays
of nanoscale features are readily made in a single processing
step over wide areas ( 4 cm2) that is scalable with the
efficiency improvements of 70% that result not only from
greater absorption, but also from electrical enhancements [
        <xref ref-type="bibr" rid="ref9">9</xref>
        ].
Other authors present the efforts to enhance the stability
of normal-geometry organic solar cells (n-OSCs), which are
generally considered inferior to their inverted-geometry
counterparts in terms of stability. The efficiency of organic solar
cells is primarily limited by the active layer to absorb spectra.
The active layer thickness varied between 95 to 115 nm [
        <xref ref-type="bibr" rid="ref10">10</xref>
        ].
Soo Jin Kim et al analyze the light trapping mechanism for
a cell with a V-shape substrate configuration and demonstrate
significantly improved photon absorption in an 5:3% efficient
PCDTBT:PC70BM bulk heterojunction polymer solar cell.
The measured short circuit current density improves by 29%,
in agreement with model predictions, and the power
conversion efficiency increases to 7:2%.
      </p>
      <p>
        Thomas Rieks et al. [
        <xref ref-type="bibr" rid="ref11">11</xref>
        ] demonstrate a pathway for fully
roll-to-roll (R2R) prepared organic solar cells in a normal
geometry with a R2R sputtered aluminium top electrode,
optimizing the donor: acceptor ratio in the active layer the
efficiency increased to 0:90%. So the normal geometry organic
solar cells using a metal top contact can be produced using
large scale production techniques [
        <xref ref-type="bibr" rid="ref12">12</xref>
        ].
      </p>
      <p>
        Gholamhosain Haidari et al. [
        <xref ref-type="bibr" rid="ref13">13</xref>
        ] report on the simple
fabrication of Ag NP films formed on indium tin oxide
electrodes, coated with PEDOT:PSS and implemented into
PCPDTBT:PC70BM solar cells, applying the finite-difference
time-domain techniques to model the optical properties of
different nanoparticle films and they demonstrate that the
absorption and scattering efficiency of the particles are very
sensitive to particle geometry [
        <xref ref-type="bibr" rid="ref14">14</xref>
        ], [
        <xref ref-type="bibr" rid="ref15">15</xref>
        ]. The author present
an optical simulation of light management in Cu(In,Ga)Se2
thin-film solar cells with reduced absorber layer thickness,
with the goal of absorption enhancement in the absorber
layer [
        <xref ref-type="bibr" rid="ref16">16</xref>
        ]. The optical effects of an extra interfacial layer
of poly (3,4-ethylenedioxythiophene)/(poly(styrenesulfonate)
(PEDOT/PSS) on top of the ITO-electrode of a mono or
multilayer organic photovoltaic device, in which the incident light
of sun is absorbed in the active layer is reported in [
        <xref ref-type="bibr" rid="ref17">17</xref>
        ].
      </p>
      <p>
        From optical and electrical simulations, increasing the
thickness of the organic solar cells device due to the low mobility
of the organic materials, non-geminate recombination rate
enhances and causes the power conversion efficiency reduction
[
        <xref ref-type="bibr" rid="ref18">18</xref>
        ].
      </p>
      <p>
        The optical performance of the P3HT:PCBM solar cell has
been simulated by AMPS-1D to study the J -V characteristics
and electric field with active layer thickness in [
        <xref ref-type="bibr" rid="ref19">19</xref>
        ].
      </p>
      <p>
        The processes controlling the efficiency of hybrid planar
devices comprising two semiconducting donor polymers and
amorphous silicon,charge generation and the distribution of
electric fields in a-Si:H/organic-hybrid solar cells have been
investigated by [
        <xref ref-type="bibr" rid="ref19">19</xref>
        ], applying a transfer matrix formalism to
model the absorption in the hybrid device including
interference in the layer stackby.
      </p>
      <p>By design and simulation of the OSCs devices is possible
to provide a simple model for the performance analysis of
extending the high frequency range. The electromagnetic field
induced on solar devices has been investigated to evaluate
the interactions of the optical model at several frequencies
using as tool COMSOL to calculate the magnetic field effects
starting from a sample with OSCs carried out in
collaboration with Optoelectronic Organic Semiconductor Devices
Laboratory (OOSDL), Department of Electrical and Computer
Engineering Ben-Gurion University of the Negev, Israel.</p>
    </sec>
    <sec id="sec-2">
      <title>II. THE OSC MODEL</title>
      <p>
        A bulk heterojunction solar cell consists of an active organic
part with a donor and an acceptor material, the metal
electrodes and the substrate. The substrate usually glass and
transparent ensures that the light reaches the active material. The
positive and negative electrodes respectively indium tin oxide
and aluminum are responsible for the transport of the charges
from the organic material to the electrical connections. The
absorption of photons from incident light generates excitons
namely bound electron-hole pairs, due to the stronger Coulomb
attraction in an organic materials. To generate electrical
energy it is necessary to separate the charges to contribute to
photocurrent in an organic cell. The exciton with a random
process based on concentration gradients can diffuse at this
donor/acceptor interface to dissociate and convert into free
charge carriers, electrons and holes. To generate electrical
energy it is necessary to separate the charges to contribute
to photocurrent in an organic cell. The photons energy excites
the electron from the HOMO to the LUMO band, where the
HOMO and LUMO are equivalent to the valence band and
conduction band known from classical physics. The exciton
with a random process based on concentration gradients can
diffuse at this donor/acceptor interface to dissociate and
convert into free charge carriers, electrons and holes, when the
interface is within the exciton diffusion length, typically is not
very long some 10 nm depending on the material in organic
semiconductors. However excitons can recombine or decay
back to the ground state, during the diffusion process before
reaching the donor/acceptor interface, leading to absorbed
photons that do not contribute to the current. In this case,
the recombination rate depends on the charge density, as
the probability of two charges meeting increases with higher
carrier density. For an efficient exciton dissociation it has to
be energetically favorable for the electron to be transferred to
the LUMO of the acceptor or for the hole to the HOMO of
the donor material, respectively. Finally, the charges due to
an internal electric field and a gradient in the electrochemical
potential are collected and transported towards the respective
electrodes, electrons and holes can be extracted by cathode and
anode, leading to current’s generation to the external circuit
[
        <xref ref-type="bibr" rid="ref20">20</xref>
        ], [
        <xref ref-type="bibr" rid="ref21">21</xref>
        ], [
        <xref ref-type="bibr" rid="ref22">22</xref>
        ], [
        <xref ref-type="bibr" rid="ref23">23</xref>
        ].
      </p>
    </sec>
    <sec id="sec-3">
      <title>III. MATERIALS AND FABRICATION</title>
      <p>The procedure for fabrication of organic solar cell device
is carried out inside the glovebox at low temperature 22 C
compatible with their sensitivity and degradation very fast
under normal air conditions, performed under a dry nitrogen
atmosphere with an O2 concentration of 1:7 ppm and an
H2O concentration smaller than 0.1 ppm. The fabrication
of polymer solar cells is based on four steps. Before the
first step is the cleaning of IT O coated glass substrate to
eliminate particles, contaminates and imperfections, in
acetone, methanol and isopropanol bath for 15 minutes each one
through an ultrasonic bath (53 kHz at room temperature).
Afterwards the substrate is dipped into distilled water and
put into a vacuum oven; the plasma cleaning need to remove
of remaining oxygen molecules. The glass substrate is sized
12 mm 12 mm 0:7 mm and is coated in the middle with
a rectangular section 6 mm 12 mm and 90 nm 10 nm of
transparent thick ITO layer with resistance of 20 Ohm=m2.
The ITO is the anode with high transparency, conductivity but
it is fragile and susceptible to deterioration. P EDOT : P SS
is a transparent conjugated polymer with thickness layer of
30 nm. Inside the glove box, a solution of photo-active
polymer P3HT and PCBM is prepared. The P3HT:PCBM
layer is deposited onto cleaned substrates by spin coating
the samples at 5000 rpm (revolutions per minute) and an</p>
      <p>Fig. 5. Extinction coefficient of P3HT:PCBM blend
acceleration of 7000 rpm=s for one minute, resulting in a layer
thickness of approximately 200 nm. The acceptor material is
the PCBM and P3HT is the donor material. Devices were
completed by evaporation of aluminum 80 nm in a vacuum,
through a shadow mask used to create the preferred shape of
aluminum cathodes.To connect the thin film to electrical wire
the Silver Conductive Epoxy was deposited on small part of
ITO removed locally and Aluminum layer.</p>
    </sec>
    <sec id="sec-4">
      <title>IV. GEOMETRY</title>
      <p>The model, shown in Figg. 1 and 2, consists of an embedded
structure sample with domain size of 12 12 mm and layers
thicknesses of: 80 nm for metal electrode aluminum, 200 nm
of active layer pcbm, 30 nm of pedot: pss, 90 nm of ITO and
glass substrate with layer of 0:7 mm. The sample contains
F/m
nm
four organic solar cells with different lengths, each of them
has size of 4:50 mm, 5:50 mm, 6:50 mm and 7:50 mm.</p>
    </sec>
    <sec id="sec-5">
      <title>V. METHODOLOGY</title>
      <p>It was presented an OSC simulated model in a large area of
high frequency (1014 3:75 1014 H z). The model is based on
solving solves the Maxwell equation using the finite element
method. The simulation electromagnetic effects in 2D and 3D
were carried out within Comsol Multiphysics. The Maxwells
equations in the time domain are:
5
5
5 D
5 B</p>
      <p>E
H
=
=
=
=</p>
      <p>Under varying assumptions, these equations are solved with
a set of boundary conditions related to material for modeling
perfect electrically conducting surfaces within the RF Module
of COMSOL Multiphysics using the finite element method
to solve for the electromagnetic fields within the modeling
domains.</p>
      <p>The optical properties of the organic thin lm materials such
as poly(3 hexylthiophene) : poly(6; 6 phenylC61
butyricacidmethylester)(P 3H T : P CBM )andP EDOT :
P SS=I T O are described by complex wavelength-dependent
refraction index n. The values of the complex refractive
indexes specified as a function of wavelength and used in the
simulation were taken from the literature for P3HT, PCBM,
ITO and Al. In Figg. 3, 4 and 5 are displayed the plots, as
function of the wavelength, of the optical constants such as
P3HT:PCBM and PEDOT in particular, the refractive index
and the extinction coefficient are related by phisical materials
properties. The refractive index of the environment is equal to
the refractive index of air (n=1). In the table the optical and
electrical values set used for the FEM analysis: The simulation
was carried out at wavelengths in the range of absorption of
the material. Then, parametric analysis of COMSOL was used
with frequency as the changing parameter, ranging from 1014
Hz to 3:75 1014 Hz. The Perfectly matched layers (PMLs)
are used to enclose the model domain. The methodology
is consisted to define the equations to solve, creating the
model geometry, define the material properties, setting up
the boundaries. During the meshing step the model space
has been discretized using finite elements. Solving a set of
linear equations that describe the electric fields. The useful
information are extracted from the computed electric and
magnetic fields.</p>
      <p>Fig. 6. Electic field in 2D, view from above of sample structure with OSCs</p>
    </sec>
    <sec id="sec-6">
      <title>VI. CALCULATION AND RESULTS</title>
      <p>An optical wave is propagated in the system determining
the degradation of electric field amplitude due to interference
by optical properties in each active layer. To better understand
the interaction of the each OSCs, the simulation was repeated
for a range of wavelength from 300 to 800 nm, where the
incident light has an acceptable intensity on the optical models
with different layers. The magnetic field distribution indicates
the absorption of electromagnetic wave externally applied
depending on the refractive index,wavelength and width of
layers. The magnetic field is calculated on sample device
with different OSCs located on top of the glass support. The
structure and the electric field configuration, bidimensional
and tridimensional, are represented in Fig. 6 and in Fig. 7
respectively.</p>
      <p>As shown in Fig. 8, the magnetic field decrease along y
axis illustrating the dependence with the layers and materials
optical properties. Magnetic field results are reported in Fig. 9
for different OSCs, with the same trend. It is necessary to
consider several different factors which affect the absorption of
any organic photovoltaic device defined as number of photons
absorption,exciton dissociaton. Therefore, more excitons are
able to diffuse to the heterojunction and dissociate into free
charges, moving to the electrodes where they are extracted
and establish a photocurrent. An interesting extension to
this work could be to examine and explore the relationship
between efficiency and device thickness considering an ideal
morphology organic solar cell.</p>
    </sec>
    <sec id="sec-7">
      <title>VII. CONCLUSION</title>
      <p>The results obtained by these simulations can promote to
investigate the polymer materials attitudes examining a large
range of frequencies and effects under external electric and
magnetic field. An optical model relative to organic solar
cells sample model is proposed by means the electromagnetic
field simulation at large range of frequency. The simulations
in this work were based upon finite element method with
3D Surface plot of Electic field applied on sample structure with
2D geometry. The simulations were carried out using the RF
module of COMSOL Multiphysics software package</p>
    </sec>
    <sec id="sec-8">
      <title>ACKNOWLEDGMENT</title>
      <p>This work has been supported by the BGU-ENEA joint
lab and the ILSE-Joint Italian-Israeli Laboratory on Solar
and Alternative Energies.In particular, the author would like
to thank the Optoelectronic Organic Semiconductor Devices
Laboratory (OOSDL) , Department of Electrical and Computer
Engineering Ben-Gurion University of the Negev, Israel.</p>
      <p>Magnetic field of the sample containing the OSCs</p>
    </sec>
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