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  <front>
    <journal-meta />
    <article-meta>
      <title-group>
        <article-title>3D Modeling and optimization of Organic Solar Cells</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Salvatore Sarcia´</string-name>
          <email>salvatoresarci@gmail.com</email>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Giuseppe Di Lorenzo</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Riccardo Zammataro</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>Department of Electrical, Electronics and Computer Engineering University of Catania</institution>
          ,
          <country country="IT">Italy</country>
        </aff>
      </contrib-group>
      <fpage>44</fpage>
      <lpage>48</lpage>
      <abstract>
        <p>- In this paper a new design process for Organic Solar Cells ( O S C s ) are proposed and developed using t h e c o m m e r c i a l modeling software for technical design and a simulation tool Comsol vers. 5.3. Comsol was used to determine the electromagnetic fields on O S C s e l e m e n t interfaces and to optimize aluminum and active layers. A more efficient geometry was founded in order to maximize the light trapping and increase the photovoltaic market. The first experimental results on the new OSCs are reported.</p>
      </abstract>
      <kwd-group>
        <kwd>Industrial lime</kwd>
        <kwd>treatment</kwd>
        <kwd>pollution</kwd>
        <kwd>energy recovery</kwd>
        <kwd>environment</kwd>
        <kwd>distillation</kwd>
      </kwd-group>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>I. INTRODUCTION</title>
      <p>
        The third-generation solar cells can be made of low-cost
and sustainable materials such as polymers however with less
efficiency than the standard silicon cells mainly limited by the
ability of the active layer to absorb light and convert it into
electricity. A good solution could be investigate new light
trapping techniques and the impact of geometry in new model
and architecture design [
        <xref ref-type="bibr" rid="ref1">1</xref>
        ]. In organic solar cells (OSCs) the
geometrical parameters influence significantly the efficiency
and performance. The variation in the length of the devices is
not negligible affecting the recombination of charge carriers in
the organic solar cells. Many authors have demonstrated as the
geometry of organic solar cells influences the electrical
enhancements, the absorption and scattering efficiency of the
particles [
        <xref ref-type="bibr" rid="ref2 ref4 ref5">2-8</xref>
        ]. The authors in describe the effect of
geometrical parameters, particularly shape, on optical
absorption enhancement for thin film solar cells based on
crystalline silicon (c- Si) and gallium arsenide (GaAs) using a
rigorous coupled wave analysis (RCWA) method. The light
trapping schemes for organic thin film solar cells include
geometric engineering of the structure of the solar cell at the
micro and nanoscale, plasmonic structures, and more as
reported in [
        <xref ref-type="bibr" rid="ref5">4</xref>
        ].
      </p>
      <p>For specific types of geometrically shaped solar panels a
simpler method was derived and applied, however with the
limitations to broaden the applicability of the model to a wider
range of geometric shapes.</p>
      <p>Deepak K. Gupta et al present an efficient manner to
maximize the power output with the application of topology
optimization (TO) to optimize the front metallization patterns
for free-form solar cells that are cells of unconventional shapes
(e.g. hexagonal, leaf-shaped, circular, motorbike fairings etc)
with flexible shape added to the aesthetics of the surround- ings</p>
    </sec>
    <sec id="sec-2">
      <title>Copyright held by the author(s).</title>
      <p>and an important factors of metallization design [8]. In order to
provide more absorbtion of solar radition graphene
nanostructures are incorporates from 0.5 to 5 µm in the device
design or reduced graphene oxide as anode buffer layer is used.
Graphene has a high optical transmittance, an excellent
electron/hole transport properties, superior mechanical stiffness
and flexibility. The Graphene can be used as transparent
electrode to retard charge recombination in OPVs .To reduce or
retard the carrier recombination we could form a direct channel
between anode and cathode creating an alternating of graphene
and ITO patterns. Other authors have investigate the
electromagnetic field induced on solar devices in order to
evaluate the interactions of the optical model at several
frequencies and the magnetic field using as tool COMSOL to
calculate the electric field effects starting from an organic
sample. In this work we have presented different
threedimensional models of multilayer bulk hetero- junction organic
nanoscale solar cells. The 3D simulations of electromagnetic
fields applied to OSCs presented in this work clearly reveal
that the physical mechanisms depend on this particular contact
design [9]. Using a cross-platform finite element analysis,
solver and Multiphysics simulation software, we have analyzed
specific geometrical patterns that could be optimal for
capturing and holding light in thin-cell organic solar cells.</p>
    </sec>
    <sec id="sec-3">
      <title>II. GEOMETRIC MODEL</title>
      <p>
        A solar organic cell is schematized in Fig. 1. In order to
investigate the shape in OSCs we proposed new design with
different geometry types that could lead to more efficient
organic solar cells. Five main parts are assembled in the
electronic device such as a rigid glass support, an anode, an
intermediate layer, a photo-active layer and cathode layer [8].
The glass support has the peculiarity to be transparent for light.
Furthermore, Indium Tin Oxide (ITO)is used as anode or
positive electrode with a work function greater than metal [
        <xref ref-type="bibr" rid="ref4">3</xref>
        ].
The intermediate layer consists of conductive polymer
PEDOT: PSS (Poly (3,4 ethylenedioxythiophene) poly
(styrenesulfonate)) layer deposited directly on anode with the
Spin-coater 2.The active material is deposited on PEDOT:PSS
layer mainly composed of poly (3-hexylthiophene) (P3HT) and
the fullerene (6,6)- phenyl-C61 butyric acid methyl ester
(PCBM) responsible for light absorption, charge carrier
production, and carrier separation. Aluminum is evaporated
used exclusively as cathode.
      </p>
      <p>
        The parametric modeling of the OSCs was performed in a
similar way to that described by Calì et al. [
        <xref ref-type="bibr" rid="ref12">10,11</xref>
        ].
      </p>
      <p>The parametric 3D design software of Solidworks has been
an useful tool to model mechanical and electronic device.</p>
      <p>
        In our case we have considered the device manufactured
(Fig.4) in the laboratories in the University of Ben Gurion [
        <xref ref-type="bibr" rid="ref1">1</xref>
        ],
[5]. The thickness of ITO is 70 nm on 0.7 mm thick glass
substrate (12 × 12 mm), 30 nm of PEDOT: PSS, 200nm the
P3HT:PCBM and 90 nm aluminum cathode. In each sample
are inserted four OSCs with different lengths 7.5, 6.5, 5.5 and
4.5 mm. Rendering and 3D visualization problems are avoid
increasing the thickness of deposited materials and decreasing
the size glass thickness as in Fig. 3. On the basis of OSCs
structure, different alternative shapes are proposed for
aluminum cathode taking in account the increasing of charge
density. The electrons and holes inside the metal react to the
electromagnetic excitation inducing surface charges. The local
surface charge density increases drastically in geometrical
singularity such as tip apex. We have investigated the effects of
different geometry characterized of several tip apexes to
response to electromagnetic excitations. In general, the charge
density is concentrated in the region with largest value of
curvature and thus smaller radius of curvature. Two charged
spherical conductors of radius R1 and R2 with R2 &gt; R1
connected by a conducting wire. The potentials V1 e V2 have
to be the same, the charge on each sphere is in proportion to
their radii:
      </p>
      <p>V1 = V2 =
=
(1)</p>
      <p>This means that the surface charge density of the smaller
sphere is larger, i.e. that the charge is more crowded per unit
area on the smaller sphere.In particular the ratio between the
charge density Q on the surface of the sphere and the radius R
is constant and with the same potential. For smaller surface
namely largest curvature, lower surface charge density
distribution is observed than larger surface.</p>
      <p>The surface charge densities are calculated:
(3)
(4)
(5)</p>
      <p>The surface charge density is lower on second sphere. Thus
the curvatures and apertures of the tip apex strongly influence
the density charges. The effects of different apertures,
curvature and sharpness of tip are analyzed to enhance the efficiency
and electromagnetic field in OSCs. To model the cell with the
rectangular cathode a 2D sketch was created on the upper face
of the active layer and using the ”rectangle of the corner”
function, it was possible to draw the cathodes. Through the
“basic extrusion” function, it was possible to realize the final
form. To create the Arabic cell, a 2D sketch was created on the
upper face of the active layer 5. Using the ”spline” function,
it was possible to draw the curved profile of the cathode.</p>
      <p>The rectangular part was created using the ”rectangle of the
corner” function. Extruding the sketch the shape of an Arabic
shape was created. The nine-pointed star shape was also
created by a 2D sketch on the upper face of the active layer12.
First a circumference with a radius equal to 2245 µm was
drawn using the ”circle” function, then another circle with a
radius of 300 µm and a geometric center on the first
circumference was drawn. First of all using the ”circular
repetition” function and then the ”shorten entities” function, it
was possible to obtain the definitive profile The pentagonal
shape was configured by means a 2D sketch on the upper face
of active layer 6. Using the ”polygon” function a hexagon has
(6)
been created inscribed in a circumference having a diameter
equal to 1376 µm, with the ”tangent arc” function it was
possible to realize the curved shape of the sides as shown in
Fig. 7.</p>
    </sec>
    <sec id="sec-4">
      <title>III. SIMULATION MODEL</title>
      <p>The types of geometric models proposed of the samples
processed in SolidWorks have been imported in COMSOL and
then the physical parameters has been set useful for the
simulation of electromagnetic field. We have considered the
Maxwell equations with particular referring to the electric field
E and the magnetic flux density B as reported below:
∇ · E = 0
∇ × E =
∇ · B = 0
(7)
(8)
(9)</p>
      <p>
        The material properties are described using relative
permeability ε and the relative permittivity µ. In this application RF
module is used for Multiphysics simulation models for
wavelengths of the visible spectrum from 400 nm to 700 nm. In
order to guarantee the simulation phenomena, optical values
and electric properties of different materials are used as
reported in [
        <xref ref-type="bibr" rid="ref2">2</xref>
        ]. Each sample was exposed to an incident light
beam. Considering the discretization by Finite Element Method
in order to obtain reliable simulation results, was used “Free
mesh” able to automatically thicken free elements on the edges
of the organic cell. On the basis of the light incident on device,
the electromagnetic field is applied in perpendicular direction
on glass substrate chosen as active port for port boundary
conditions. The outgoing signal is determined on surface of the
aluminum cathode whereby to calculate the electric field, the
magnetic field and power electric flow. From obtained results,
power electric flow for cathode of 5.5 mm has less electric
value considering rectangular shape aluminum than pentagonal
shape as reported in Fig. 9.The maximum peak of electric field
along the direction of the organic cell is obtained for length of
5.5 mm and has a value of 2.91*10−4 Vm-1.
      </p>
    </sec>
    <sec id="sec-5">
      <title>IV. CONCLUSIONS</title>
      <p>In this paper the ultrathin organic solar cells costitued by
GLASS/ITO/PEDOT: PSS/ PF3HT:PCBM/ Al layers with
different geometry of aluminum cathode are investigated. In
particular different geometrical models of OSCs are proposed
using the 3D design software SolidWorks and processed in
COMSOL to simulate the physical phenomena of
electromagnetic fields.</p>
      <p>The proposed shape of Aluminum cathode are rectangular,
pentagonal and nine-pointed stars and are simulated using the
RF Module of Comsol Multiphysics. The optimal results of
electric field are obtained for cathode of 5.5 mm with
pentagonal shape. Thus we have demonstrated that the shape of
cathode influences the performances of solar cells.</p>
      <p>Fig. 11. Electric Field Aluminum pentagonal Shape</p>
      <p>Fig. 12. Electric Field Aluminum rectangular Shape</p>
      <p>In our case based on charge density distribution it is
observed that for lower curvature of Aluminum cathode the
electric field increases also for lenght dimensions of 5.5 nm.</p>
    </sec>
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