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CONTACT GRID OPTIMIZATION
METHODOLOGY FOR
SOLAR CELLS
Paul James Ngana
Nanophotonics Group
Jacobs University Bremen
Campus Ring 7
28759 Bremen
Germany
Type: Guided Research Proposal
Date: May 16, 2007
Supervisor: Prof. Dr. Dietmar Knipp
Abstract
The design of the top grid metal contact becomes increasingly important as the size of individual cells increases. For improved efficiency, better
designs ought to be used.
The aim of this project is to investigate the design of the front contact of
the solar cells, hence to develop a grid pattern which will minimize electrical
and optical losses caused by the design of the front contact.
Furthermore, contemporary solar cells use screen printing technology for
the front contact. However, the screen printing technology has limitations,
since its impossible to print structures below 1µm. Hence our desirable design needs a more advanced technology for the metallization of the front
contact grid. [1]
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Contents
1
Introduction
1.1 Photovoltaic Solar Cells . . . . . . . . . . . . . . . . . . . . . . .
1.1.1 Introduction to How a Solar Cells Works . . . . . . . . .
1.1.2 Efficiency Losses . . . . . . . . . . . . . . . . . . . . . .
4
4
4
6
2
The Solar Sell Front Contact
2.1 The Front Grid Pattern . . . . . . . . . . . . . . . . . . . . . . .
2.2 Influence of Fabrication Process . . . . . . . . . . . . . . . . . .
7
8
10
3
Simulation
3.1 Simulation Tool - OptiFDTD . . . . . . . . . . . . . . . . . . . .
3.2 The Design Parameters . . . . . . . . . . . . . . . . . . . . . . .
3.3 Input Field Parameters . . . . . . . . . . . . . . . . . . . . . . .
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12
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12
4
Results
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5
Conclusion
5.1 Summary . . . . . . . . . . . . .
5.2 Further Investigations . . . . . . .
5.3 Acknowledgement . . . . . . . .
5.4 Matlab Codes for Post-Processing
References
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3
1
Introduction
1.1
Photovoltaic Solar Cells
As the world is becoming more advanced in technology, more energy is being used
to keep up with the changing requirements. At the current rate at which energy
is being used, the world will shortly come to an end of fossil fuels - the world’s
primary energy resource. The world has to look for other alternatives. The existing
gas, coals and oils reserves are almost depleted [9].
However, the sun will always shine. Photovoltaic solar cells are an obvious solution
since the only raw material necessary for producing solar power is sunlight, which
is abundant in many parts of the world and would never be depleted [3].
In addition, the sunlight falling upon earth contains much more energy than that
used by the entire human race, and can be converted into electricity using solar
cells. It is widely believed that a significant part of the future production of electricity will be the product of solar cells.
1.1.1
Introduction to How a Solar Cells Works
Photovoltaics, as the word implies (photo = light, voltaic = electricity), convert
sunlight directly into electricity. Once used almost exclusively in space, photovoltaics are used more and more in less exotic ways. Photovoltaic (PV) cells are
made of special materials called semiconductors such as silicon, which is currently
the most commonly used. Basically, when light strikes the cell, a certain portion of
it is absorbed within the semiconductor material.
This means that the energy of the absorbed light is transferred to the semiconductor.
The energy knocks electrons loose, allowing them to flow freely. Also, PV cells all
have one or more electric fields that act to force electrons freed by light absorption
to flow in a certain direction. This flow of electrons is a current, and by placing
metal contacts on the top and bottom of the PV cell, we can draw that current off
to use externally. This current, together with the cell’s voltage (which is a result of
its built-in electric field or fields), define the power that the solar cell can produce.
From the figure below we can see a circuit:-
4
I
hυ
I S (e
=
qV/kT
−1)
Iph
RL
RL
Figure 1: Equivalent Circuit of a Solar Cell
From the figure above we can see why solar cells act merely as a diode. The I-V
characteristics of a solar can be expressed as follows:qV
I = Io (e kT − 1) − IL
(1)
I
Dark
Voc
Vmp
V
Illuminated
IL
Imp
Isc
Figure 2: Terminal properties of a p-n junction diode in the dark and when illuminated. The light generated current (Illuminated) is superimposed upon the normal
rectifying current-voltage characteristic of the diode. This results in the region in
the fourth quadrant where electrical power can be extracted from the device.
Hence the illuminated characteristics are merely the dark characteristics shifted
down by a current IL . That is why this gives a region in the fourth quadrant of this
plot where power can be extracted from the diode.
However, there are three parameters which can be used to characterize solar cells
output. The first one is open-circuit voltage (Voc ), which can be expressed as below
5
after setting IL in(1) to zero:Voc =
kT
IL
ln( + 1)
q
Io
(2)
The second one is the short-circuit current (Isc ), which is basically the light generated currentIL . The third one is the fill-factor (FF). It is a measure of how square
the output characteristics are. The fill factor can be expressed as follows:FF =
Vmp Imp
Voc Isc
(3)
From the above equation we can deduce the energy-conversion equation as follows:-
η=
Voc Isc F F
Pin
(4)
However, it has been found that the maximum value of fill factor is a function of
Voc . Hence, only the limits of Isc and Voc need to be maximized.
1.1.2
Efficiency Losses
Many factors contribute to the efficiency losses in photovoltaic cells. From energyconversion equation of a solar cells below, we can deduce the parameters which
dictate the efficiency of a solar cell, which are open-circuit voltage (Voc ), shortcircuit current (Isc ) and fill-factor (FF) :η=
Voc Isc F F
Pin
(5)
Hence, we can categorize the efficient losses in accordance to those parameters:Short Circuit Current Losses (Isc )
The losses associated with this category are :• Optical losses due to the reflection of the cell
• Shadowing which is caused by the front contact grid pattern of the cell
• The thickness of the semiconductor material used. Indirect band-gap semiconductors require more materials than direct band-gap materials
• Bulk and surface recombination
• Thermolization
6
Open Circuit Voltage Losses (Voc )
For the case of Voc ,the important factors are:• Recombination through trapping levels in the depletion regions
• Low doping levels, hence high minority carriers at the junction edge
• Low diffusion length in the material
• No passivation of the surface, hence high localized recombination sources
within a diffusion length of the junction
Fill Factor Losses (F F )
• Recombination in the depletion region can also reduce the fill factor
• Series resistance, which is caused by the bulk and contact resistance
• Shunt resistance, which is a function of the leakage across the p-n junction
In this project we will tackle these losses by considering the design of the top
metal contact grid [2]. We plan to develop a design which will reduce these losses,
hence increase the short circuit current of our cell. Henceforth this will increase
the efficiency of the solar cells.
2
The Solar Sell Front Contact
The top contact design of the cell becomes increasingly important as the size of
the individual cells increases. The power losses associated with the top contact
of the solar cell are lateral current flow in the top diffused layer of the cell, series
resistance of the metal lines and the contact resistance between the lines and the
semiconductor [1]. Hence, losses are due to the shadowing of the cell by these
metal lines, which are also known as fingers.
The project aims at developing the shape of the top contact grid, which will lead
to minimization of electrical and optical losses endured by the solar cell [4]. That
is, optimal width and spacing of the grid fingers will be found at the end of the
project.
It has been shown by scientists that, by choosing the proper pattern of the of the
front contact grid [1], and optimizing of the grid parameters, a considerable increase in the efficiency of the solar cell can be achieved [1].
In addition, optimal spacing between the grid lines will be developed, so as to
overcome the loss due to the lateral current flow. Although theoretically this would
increase the sheet resistivity of the cell, it is not of significance to this project,
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because the major factor determining the sheet resistivity is the depth of the solar
cell of which is considered to be constant in our design [1].
However, the sheet resistivity determines the minimum spacing required between
the grid lines of the top contact. Hence, the project aims to reach the theoretical
limit which would be set forth by the design of the front contact of the silicon solar
cell. This would allow maximum extraction of carriers from the bulk, hence more
electrical current.
The minimum spacing technique agrees with theory, since another key parameter,
the diffusion length, is taken into consideration among the parameters to be optimized in the design. This is so, because the minority carrier lifetime is the major
factor forcing the spacing to be small, since the closer the grid lines, the higher the
probability that the carriers will be extracted from the bulk before recombination
of the pair occurs.
Furthermore, the contact resistance losses were not taken into consideration into
this project, since they are generally not very important for silicon under one sun
operation. The depth of the junction was not of relevance to this project either,
although in practice it is a very important parameter. That is, since the generation
rate is very high near the surface where the probability of collection is low, it is
obvious that the deficiency is minimized if the junction is as close to the surface as
possible.
In addition,the busbars of the front contact grid were also not the focus of this
project. Our main focus was the fingers of the front contact grid. The study of the
busbars could be a continuation of the project at hand, so as to develop a design of
whole front contact grid, and not just fingers.
It is also a worthy-mention that there are some practical limitations in the printing
of the heights and widths of the grid lines. Henceforth the conventional printing
technique used in the solar cell industry would set the limit for the minimum losses
unless an alternative method is developed.
2.1
The Front Grid Pattern
The maximum power output of this unit cell can be seen to be given by ABJmp Vmp ,
where AB is the area of the unit cell. Jmp and Vmp are the current density and
voltage respectively at the maximum power point. The resistive losses can be calculated using the same method used in the calculation of power loss on the top
layer
prf =
Jmp S
1 2
B ρsmf
m
Vmp WF
8
(6)
prb =
Jmp 1
1 2
A Bρsmb
m
Vmp WB
(7)
ρsmf and ρsmb are the sheet resistivities of the contact metal layers for the fingers
and busbars. WF and WB are the average width of the fingers or busbars lying
within the unit cell, and S is the spacing of the fingers.
Hence, the fractional losses due to fingers and busbars are:psf =
WF
S
(8)
psb =
WB
B
(9)
Furthermore, we can deduce that, the power loss due to the contact resistance is as
follows:Jmp S
(10)
pcf = ρc
Vmp WF
where ρc is the specific contact resistance. Hence the optimal occurs when:s
ρsmb Jmp
WB = AB
(11)
m Vmp
and the minimum value of fractional power loss is:s
ρsmb Jmp
(prb + psb )min = 2A
m Vmp
(12)
However, in practise the front contact design has long busbars and short fingers
because ρsmb < ρsmf . It is also a worthy-mention that there are some practical
limitations in the printing of the heights and widths of the grid lines. Henceforth
the adopted technologies set the limit for the minimum losses.
It can be observed from the above calculations that the major contribution towards
the total loss comes from resistive and shadowing loss of busbars. The combined
losses due to the front contact design is about 15%. This is due to the fact that silver
resistivity (screen printed contact) is high, hence wider busbar are preferable.
In our project we plan to develop a design, with optimal width and spacing of grid
fingers, which will lead to minimization of electrical and optical losses endured
by the solar cell. The losses could be brought down to about 10%, or more. Furthermore, our project focuses only on the fingers of the front contact of the solar
cell, even though busbars are part of the front contact, they were not taken into
consideration in this project.
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S
WB
WF
Figure 3: Schematic of a top contact design showing busbars and fingers. Where
WB is the width of the busbar WF is the finger width and S is the finger spacing
2.2
Influence of Fabrication Process
One major road block in developing nanostructures is the lack of a low-cost, highthroughput manufacturing technology. This problem is particularly serious for
structures with a size below 0.1µm.
In planar devices, the current screen printing technology used to print the front contact of solar cell has limitations in thickness (5µm and 10µm) and finger width (not
less than 100micron). At the moment, this is the most mature solar cell fabrication
process. Simplicity of the process makes it stand out from the rest[10].
However, other alternative fabrication processes are needed, for the case of finer
grid lines and smaller front contact designs. Some techniques have already been
introduced and others are making progress from the labs to the production lines.
Among them is the micro contact printing (µCP).
In µCP, just as in many conventional printing techniques, a patterned stamp is
brought into contact with a substrate to transfer an ink to and thus create an image
of the stamp pattern on the substrate surface. In a subsequent processing step this
image may be transferred into the substrate material by, for instance, an etching
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or a material deposition process. In the case of etching, the pattern formed by the
ink on the substrate surface can be utilized as an etch resist, whereas in the latter
deposition process it may serve as a template for further material growth.
The stamp is made from an elastomeric polymer, such as poly(dimethylsiloxane)
(PDMS). This material allows for conformal contact with the substrate combined
with advantageous chemical and physical properties important for the ink transfer
behaviour. Stamps are fabricated by casting a pre-polymer on a master with a
negative of the desired pattern, curing it, and peeling the cured stamp off the master.
µCP is a low-cost and technically feasible process. It has been tested and demonstrated by the Nanophotonics group under Prof. Dr. Dietmar Knipp [8]. Hence,
µCP could be used to print the front contact of the design suggested in this project.
The classical screen printing method is not viable for the design, since the design
has grid lines in the micron range.
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3
3.1
Simulation
Simulation Tool - OptiFDTD
OptiFDTD is a powerful, highly integrated and user-friendly software application that enables the computer-aided design and simulation of advanced passive
and non-linear photonic components. OptiFDTD enables you to design and analyze nonlinear photonics components for wave propagation, scattering, reflection, diffraction, polarization and the nonlinear phenomenon. The core program of
OptiFDTD is based on the finite-difference time-domain (FDTD) algorithm with
second-order numerical accuracy and the most advanced boundary condition - uniaxial perfectly matched layer (UPML) boundary condition.
The algorithm solves both electric and magnetic fields in temporal and spatial domain using the full-vector differential form of Maxwells coupled curl equations.
This allows for arbitrary model geometries and places no restriction on the material
properties of the devices. The automation of these processes dramatically improves
productivity of design engineers and reduces time-to-market for the product. [11]
3.2
The Design Parameters
The design parameters of our solar cell model were specified as follows.
• The thickness of the solar cell thickness T was 10µm
• The cell width P was set to 1.5µm
• Finger width (S), was the same as the finger height (D), and they both ranged
from 100nm to 500nm
• The back and front contact were composed of a material which was a perfect
conductor
• The mesh size used in the simulation were 3nm, which is considerably small
compared to the wavelength of the incoming light
• The profile of the input beam was rectangular
3.3
Input Field Parameters
• The wavelength of the incoming light source was 800nm, because absorption
profile of silicon at wavelength is better, relative to other lower wavelengths
• Incoherent light - Gaussian Modulated Continuous Wave
• Coherent light
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Our cell design will be within the above mentioned parameters. The preliminary
simulations will be for the flat case. The electric field profiles will be studied and
then will be compared for the later cases when several parameters are altered.
D
P
S
T
Figure 4: Solar Cell Design for the simulations. The black blocks are the back
contact and the front grid. They are composed of perfect conductor. The main
solar cell is composed of bulk silicon.
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4
Results
To obtain the optimum design for the front contact design, simulations were carried
on by varying the height(S) and width(D) of the fingers of the front contact of the
solar cell. The simulations showed the electric field distribution of the absorbed
light in the solar cells for different dimensions of heights and widths.
The preliminary simulations were for the flat case, that is the cell did not have a
grid. They were then followed by cases when the cell had a grid at the top. For
this case, simulations were done for heights and widths ranging from 100nm to
500nm. Finally, all the simulations were repeated with different input fields, that is
coherent and incoherent light source. The results obtained in the latter cases were
normalized with the flat case.
The power loss profiles were calculated by using Matlab [7] from the ASCII text
files, exported from the electric field profiles obtained from OptiFDTD. The light
absorbed by the solar cells was obtained by evaluating the integral over the whole
bulk silicon area where light is illuminated.
From the ASCII text files, the amount of light coupled into the cell, Pl was generated from a simple computation by using a simple Matlab code. The relationship
between Pl and Ē shown below was used in the post-processing steps of the ASCII
text files, from the electric field profiles from OptiFDTD:Pl = Ē. barJ
= Ē.σ J¯
= σ Ē.Ē
(13)
= σ[(Ex ).(Ex )]
= σEx2
Dimensions,
100x100
200x200
300x300
400x400
500x500
1000x100
SxD[nm2 ]
Power Loss
Geometrical Analytical
6.67
13.33
20
26.67
33.33
66.67
S
P *100
OptiFDtD
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21.2
30.5
38.4
44.4
70.6
Afterwards the results we obtained were compared with the power loss due to shadowing, from the geometrical analysis by using the geometry of the fingers. That is
power loss due to shadowing was simply calculated by finding the ratio between D
and P, that is D
P , as seen from the table above.
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P
T
Figure 5: Flat case when there is zero shadowing on the solar cell surface.
Finally, the results obtained from the OptiFDTD software and from the geometrical
analysis were plotted on the same graph. The above values were plotted in a graph
to compare them.
As we can see from the plot below, the graph we obtained from our simulations
software is above the Ideal line - the plot from the geometrical analysis. This shows
that the power losses in a real solar cell is higher from what we would expect from
the geometrical analysis.
The plots below, show light absorption in the solar cell,for two cases. The flat
case,and the case when you have a grid on the top of your solar cell. We can
observe that, for the flat case more light is absorbed compared to the case when the
cell has a grid. That conforms with what we would expect from theory.
However, we can also observe that, light is mostly absorbed within the cell, hence
no back contact reflection of the incoming wave back to the front contact.
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Figure 6: A graph of Power loss Vs dimensions. For both the theoretical analysis
from geomerty of the front grid and the case of OptiFDTD.
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Figure 7: Flat case
Figure 8: Grid 1000nm x 1000nm
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5
5.1
Conclusion
Summary
The project came up with an improved design of the fingers of the front contact.
The design consists of smaller fingers in the micron range. However, since the
conventional silver screen printing has limitations, an alternative printing method
which is µCP, was proposed.
However, although our design overcomes the shadowing effect, the electrical losses
overcome the gain caused by the design proposed by this project. This is due to
the fact that Resistance = ρ.l
A . Hence, as the cross sectional area of the fingers
decreases, the resistance of the fingers would increase, overcoming the gain caused
by less shadowing.
However, it has been observed analytically that, most losses from the front contact of the solar cells come from the resistive and shadowing loss of the busbars.
Hence, a new design of the busbars would be needed to complement the new design
proposed by this project.
5.2
Further Investigations
A detailed analysis of the theoretical optical and resistive losses has revealed that
the busbars play a major role in optical and resistive losses caused by the design
of the front contact grid of the solar cell.[4] Hence further work to this project
could be to find a busbar design which will complement the design of the fingers
proposed by this project.
Furthermore, alternative shapes and patterns of the front contact grid could be studied to further reduce the optical and resistive losses.
5.3
Acknowledgement
I would like to express my gratitude to all those who gave me the possibility to
complete this thesis. I am deeply indebted to my supervisor Prof. Dr. Dietmar
Knipp, whose help, stimulating suggestions and encouragement helped me at all
times during the project.
I also want to thank Rahul Dewan, for his help, support, interest and valuable hints,
without which this project would not have been possible. Last but not least, Hoi
Ching Mui, who looked closely at the final version of the thesis for English style
and grammar, correcting both and offering suggestions for improvement.
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5.4
Matlab Codes for Post-Processing
clear all;
load Ey.txt;
real = Ey(:,1);
imag = Ey(:,2);
[len col] = size(Ey);
output = zeros(2, len);
for i=1:len
Fc = sqrt((real(i))ˆ2 + (imag(i))ˆ2);
output(1,i) = Fcˆ2;
output(2,i) = 0;
end
fid = fopen(’Ey_dot_Ey.txt’, ’w’);
fprintf(fid, ’%12.8f %12.8f\n’, output);
fclose(fid);
%--------------------------------------------clear all;
load Ey_dot_Ey.txt;
Eyreal = Ey_dot_Ey(:,1); Eyimag = Ey_dot_Ey(:,2);
[len col] = size(Ey_dot_Ey);
output2 = zeros(2, len);
output = zeros(1,len);
for i = 1:len
output2(1,i) = Eyreal(i);
output2(2,i) = Eyimag(i);
end
fid = fopen(’Evec_400.txt’, ’wt’);
fprintf(fid, ’%12.8f %12.8f\n’, output2);
fclose(fid);
%--------------------------------------------------
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References
[1] M.A. GREEN, SOLAR CELLS: Operating Principles, Technology and System
Application. Kensington,NSW: The University of New South Wales (1998).
[2] H. B. SERREZE, ” Optimizing Solar Cells Performance by Simultaneous Consideration of Grid Pattern Design and Interconnect Configurations”, Conference Record, 13th IEEE Photovoltaic Specialists Conference, Washington,
D.C.,1978 pp. 609-614.
[3] E. Y. WANG, et al.,”Optimum Design of antireflection Coatings for Silicon
Solar Cells,” Conference Record, 10th IEEE Photovoltaic Specialists Conference, New Orleans, 2002, pp. 399-402.
[4] U.GANGOPADHYAY, et al., ”Front Grid Design for Plated Contact Solar
Cells,” Conference Record, 29th IEEE Photovoltaic Specialists Conference,
New Orleans, 2002, pp. 399-402.
[5] M.A. BUTTERI, et al., ”Contact Shadowing Losses Reduction by Fine Line
Screen Printing ,” Conference Record, 29th IEEE Photovoltaic Specialists
Conference, New Orleans, 2002, pp. 407-409.
[6] C. A. HAASE, Optics in nanostructed devices. PhD Proposal, International
University Bremen (2005).
[7] R. DEWAN, Optics in Nanotextured Solar Cells. MSc. Semester I Project Report, International University Bremen (2006).
[8] http://www.faculty.iu-bremen.de/dknipp/group/
[9] http://www.qcells.com
[10] http://www.research.philips.com/technologies
[11] http://www.optiwave.com/2007/products/optifdtd/
benefits.htm
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