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Design and optimization of Solar Cells
EE 332 Research Paper
Anna Grimley, Josh Luff, Francis Ferrer, Richard Page
We were able to find the parameters and set the design elements to create a solar cell of 22.7653% efficiency
and less than 10% power loss. This required a detailed objective that we found to be the key principles that
create effective solar cells: Increase the amount of light collected, increase the collections of photons generated,
minimize shadowing current or darkness, and optimize the extraction of current in the cell with minimal
resistive loss.
We then took these objectives and gained a knowledge base about basic solar cell parameters: Solar cell
IV curve, Fill Factor, Efficiency and Tandem Cells. This lead us to the development of our bar design and
screen printing ink selection. It was also very clear to have a thorough understanding of the potential of screen
printing design and the key fabrication points that make this fabrication technique such a staple for cost
effective solar cells.
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Table of Contents
I. Introduction

1.1 Prompt Introduction

1.2 Loss Parameter

1.3 IV-Curve
o
1.31 Open Circuit Voltage
o
1.32 Short Circuit Current
o
1.33 Fill Factor
o
1.34 Efficiency
o
1.35 Tandem Cells

1.4 Thin Film Ink Selected

1.5 Buss Bar Design
o

1.51 Benefits of Schottky Barriers
1.6 Design for Power Loss
o
1.61 Sheet Resistance Loss
o
1.62 Resistive Power Loss from Grid Fingers
o
1.63 Power Loss in Buss Bars
o
1.64 Shadowing Power Loss
II. Modern Screen Printing

2.1 Screen Printing Technology

2.2 Inks Used in Solar Cells

o
2.21 Model and Company of Ink Used For Front Side Contact
o
2.22 Model and Company of Ink Used For Back Side Contact
2.3 Cost Effectiveness of Ink used
III. Calculations of Solar Cell

3.1 Open Circuit Voltage

3.2 Short Circuit Current

3.3 Fill Factor
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
3.4 Efficiency of Solar Cell

3.5 Design for Power Loss
o 3.51 Sheet Resistance Loss
o 3.52 Resistive Power Loss in Grid Fingers
o 3.53 Buss Barr Power Loss
o 3.53 Shadowing Power Loss
IV. Evaluation
V. References
VI. Appendix
I. Introduction
1.1 Prompt Introduction
When asked to create a solar cell for the purpose of increasing efficiency similar to what we face with this
research paper and being limited to the idea of a single junction cell there are a few principles we must follow
as electrical engineers in the area. They are simple, but are as follows:
●
Increase the amount of light collected by the solar cell that can then be turned into carriers
●
Increase the collection of photons generated by the p-n junction
●
Minimize any form of shadowing current or darkness effecting our cell
●
Optimize an effective way to extract the current in the cell without a large number of resistive losses
This is a general diagram of a solar cell being built, next to this one however is a CAD design of our designs
using Google SketchUp and an external rendering system to better show each material in the design.
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Figure 1: Solar Cell Diagram
Figure 2: Our Designed Solar Cell using CAD Rendering
We will encounter many forms of losses in the construction of this cell and our current goal is to minimize those
losses, they are as follows:
●
Sheet Resistance loss
●
Resistive Power loss in grid finger
●
Power loss in the bus bars
●
Shadowing loss due to fingers and bus bars
Our team then encountered the choice of what to set our values at for our cell with the given parameters from
our design objective paper. After some careful research and time we came up with these dimensions for our
system:
1.2 Loss Parameters
Voc = 0.749 V
Isc = 3.58 A
Jsc = 35.8 mA
FF = 0.849
η=22.7653%
Buss bar width = 700 um
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Finger width = 100 um
Buss bar/finger height = 20 um
Finger length = 9.8 cm total
Each side of buss bar = 2.415 cm
Fingers placed .3 cm apart
1.3 IV Curve
The IV curve for a solar cell is slightly different from that of the standard IV curve due to the light generated
current from darkness this current is represented by IL. This new current acts as a vertical shift in the negative Y
direction. This equation is as follows:
Equation 1: Current of a Diode
Figure 3: Normal IV Curve
Figure 4: Normal IV Curve with Light applied
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Figure 5: Normal IV Curve with More Light Applied
Figure 6: Normal IV Curve with More Light Applied Inverted
1.31 Open Circuit Voltage
The Open Circuit Voltage, also referred to as Voc, is the maximum voltage that can be achieved in the solar cell.
This occurs when there is zero current in the system. This is correlated to the amount of forward bias voltage on
the cell from the biasing of the junction from the light generated current.
Figure 6: Open Circuit Voltage VS Short Circuit Current
In order to solve for your Voc value you must equate the following equation to zero, the net current in the solar
cell.
Equation 2: Open Circuit Voltage
1.32 Short Circuit Current
The Short Circuit Current is the current running through the solar cell when you have a value of zero volts on
the cell, i.e. shorted out. This value is denoted by Isc. The short circuit current is from the generation and
collection of the light carriers or photons. For the ideal solar cell the short circuit current should equate to the
light generated current from above. The short circuit current can depend on a numerous parameters though such
as but not limited to:
● They area of the solar cell, to remove this parameter you must stop thinking of the short circuit current
and see it as the short circuit density with units generally of (mA/cm2). This is denoted by Jsc generally.
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● Number of photons, or the power of the incident light source. Isc is directly correlated to the light
intensity from the source.
● Spectrum of the light source, this must be considered due to different light wave lengths giving different
values of energy
● The solar cells optical properties, this depends mostly on the surface of the cell as well as the minority
carries lifetime for the system
When designing the solar cell you must compare the material type and
parameters of the material, most
importantly the diffusion length. When you have a cell with perfect surface design and uniform generation of
carriers, the equation can be written as follows:
Equation 3: Generation Current
Since the discovery of this equation there has existed a spectrum to base results on from relating the band gap of
a material to the Jsc. This is called the AM1.5 Spectrum. This spectrum says the maximum possible current
achievable is about 46 mA/cm2. The largest recorded in laboratories is slightly larger than 42 mA/cm2. Current
commercial solar cells range from 28 mA/cm2 up to 35 mA/cm2.
1.33 Fill Factor
The ISC and VOC are the maximum values you can receive from the solar cell in the each respected area however
they are not linear in terms of each other. Due to each of these values coming from the other value equaling zero
you receive a power of zero. You must find the “optimal” location of the two values to maximize your power
out of the system. This is when there thought process of Fill Factor comes in, denoted by FF in all equations.
This value determines the maximum power of the two parameters. You can graph Fill Factor as follows:
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Figure 7: Fill Factor for Current and Voltage with Max Power
The Fill Factor is defined as the maximum power achievable divided by the ISC * VOC or as follows:
Equation 4: Fill Factor
The typical solar cell however has a FF between .85 and .83. This can be changed though pending on your
materials used, such as GaAs may yield a FF of near .89.
1.34 Efficiency
Efficiency of solar cells is the basis of all production of the solar cell. There are many factors that influence the
Efficiency of a solar cell however it is in short based on the fundamental ideas of VOC (Voltage of the Diode
from the Open Circuit) and ISC (Current running through the system when you short out the Diode.) You must
also consider the idea of Fill Factor for a given system to determine the percentage of the photons absorbed.
There are many other factors for the efficiency of a solar cell but these are the underlying main ones.
Maximizing Power and the efficiency of a system can be found using these two equations:
Equation 5: Max Power
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Equation 6: Solar Cell Efficiency
1.35 Tandem Cells
There are other methods besides the open circuit voltage and short circuit current that can be optimized
individually in a solar cell, one such way of doing this by utilizing the idea of Tandem Solar Cells. In short it is
the idea that you can use multiple cells that are optimized for each section of the visible light spectrum.
Tandem solar cells can be individual or multiple connected in a series style connection to absorb different
energy of photons. When constructing the series version of this tandem cells it is much easier than the other
even though each one has the same amount of current running through the two ways to attack this idea. The
most common way of creating the tandem cell is to grow the layers of each substrate on top of each other and
create a tunnel between the junctions, however in order to achieve multiple band gap energies their must exist a
semiconductor material at that level which do not generally exist.
Figure 8: Tandem Cell Design Band Gap Efficiencies
As you can see the ability to create tandem cells will greatly increase the efficiency of your solar cell system
with no real optimization of the cell itself.
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1.4 Thin Film Ink Selected
The front side contact carries the duties of light absorption as well as generating the majority of the electrical
carriers. We chose to use the DuPont Solamet PV16A photovoltaic metallization for the design. We chose the
front side contact to be n-type silver and the back side contact to be p-type silver. We ultimately decided to
follow DuPont and all of their recommendations on our final ink selection due to the similarity between their
different products as well as the strong name DuPont has as group.
1.5 Buss Bar Design
The Bus Bar is used on the Solar Cell to effectively distribute the current and voltage throughout the solar cell.
It is the transfer medium of basically all items in the cell as far power input is related. We generally use
Schottky Barriers to create these so that they may have a metal-semiconductor contact point.
1.51 Benefits of Schottky Barriers
The use of Schottky barriers in solar cells can be very useful. The barrier has a lower junction voltage, and can
be used to gain more of an ideal diode setting. Also, because one material is metal in the Schottky diode you
can lower the resistance in semiconductor devices. Along with lowering resistance the use of one dopant needed
simplifies fabrication. Solar cells use diodes in series with them. A voltage drop in the cell will result in a
reduction of efficiency, so a low voltage drop diode is useful here. Schottky diodes are also used for protection
from an electrical discharge if the solar cell is connected to a battery.
1.6 Design for Power Loss
We used a mesh type grid design for our solar cell. In the design we took into account the sum of four losses
that would affect our cell’s output performance. The losses were power loss in the sheet resistance of the n+
layer, resistive power loss in fingers, resistive power loss in buss bar, shadow loss in finger, and shower loss in
buss bar. The sum of all the losses was supposed to be less than 10%.
1.61 Sheet Resistance Loss
For emitter layers the resistivity value is often unknown and difficult to calculate. Aside from this the sheet
resistivity can be calculated and be measured from the n+ layer that is uniformly doped. It is essentially the
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resistivity divided by the thickness. Using the sheet resistivity you can calculate the power loss due to the
emitter resistance. It is based on the finger spacing of the contacts. From using the current density at max
power, voltage at max power, emitter sheet resistivity from the ink and finger spacing you can calculate the
power loss percentage.
1.62 Resistive Power Loss
Resistive Power Loss is closely intertwined with Sheet Resistance and for our purpose of this design it is
unnecessary to attempt to decipher the differences between them.
1.63 Power Loss in Buss Bars
Contact resistance loss happens at the interface of the silicon and the metal contact. To keep contact losses low
one can dope the n+ layer very heavily. To have higher conductivity the fingers should be spaced at a consistent
length apart. Usually the fingers are placed closely to reduce the resistance level. There is a balance of fingers
and spacing. The same principles apply for the buss bars also.
1.64 Shadowing Power Loss
The shadow losses are caused by the covering of the buss bars and fingers on the top of the solar cell. This
prevents light from entering the cell at these points. The equations that were used in our calculations were
dependent on the bus bars and fingers width and thickness.
II. Modern Screen Printing
This process is used to deposit the metal fingers and buss bars on to the solar cell. There are many different
ways of doing this but due to pricing we are limited to how we do it between the processes. They are
Phosphorus Diffusion, Surface Texturing to Reduce Reflection, Antireflection Coating and Fire Through
Contacts, Edge Isolation, Rear Contact, and, Substrate. We chose to use the area of Antireflection Coating and
Fire through Contacts due to pricing of the cell.
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2.1 Screen Printing Technology
Using screen printing to fix the bus system to the solar cell is pretty standard practice and has been in
use since the 1970's. Although there are more refined practices available screen printing is very cost effective
and is used often in "terrestrial", common user, solar cell applications.
For screen printing a "squeegee" is used to force metal paste/ink through a mesh grate to unmasked
areas. So the width of the fingers relies on the sizing of the mesh grate used to adhere the metal paste. The
finger widths can range from 100μm to 400μm. The spacing between the fingers can vary from 1μm to 5μm.
After the fingers are created a metal contact strip is soldered to the buss bar to lower series resistance.
Figure 9: Omron Linear Squeegee Slider
Firing is the process of getting the metalized pastes on to the Si to form the contacts of the photovoltaic
cell. The four stages of the firing process are: drying, burn out, firing, and cooling. The drying process is
around the range of 150 C and is use to remove the solvents that can cause cracks in the wafer. Burn out gets rid
of the organic material used in the paste, ranges from 300 C to 400 C. The actual firing process is around 700 c
to 800 c and the silver starts to form a bond with the silicon to form the metal contact. The last step is for the
cell to cool. The firing process has a large impact on the efficiency of the cell because the series resistance,
shunt resistance and the leakage current of the junction rely are impacted by the contact.
2.2 Inks Used in Solar Cells
2.21 Model and Company of Ink Used for Front Side Contact
The front side contact carries the duties of light absorption as well as generating the majority of the electrical
carriers. We chose to use the DuPont Solamet PV16A photovoltaic metallization for the design. The Solamet
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for n- type Silver Metallization features; Low contact resistance, High conductivity, Good line resolution, Good
solderability. The product PV16A offers high efficiency, and emitter resistance up to 85 ohms. The below
figures include the physical properties of the DuPont Solamet 16A photovoltaic metallization as well as the
graph the Firing profile
Figure 10: Physical Properties of DuPont Solamet 16A
Figure 11: Table Properties of DuPont Solamet 16A
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2.22 Model and Company of Ink Used for Back Side Contact
The back side contact has the responsibility of interconnecting part of the second electrode in the cell. We
chose the front side contact to be a n-type silver so, the back side contact is a p-type silver. DuPont
recommended using a Solamet PV3XX and PV5XX in conjunction with the PV16A due to rapid and fast
cofiring as well as firing properties.
Figure 12: Physical Properties of DuPont Solamet PV3XX
2.3 Cost Effectiveness of Ink Used
Some reasons that make screen printing so cost effective are its simplicity and ability to easily refine. Screen
printing is such a long standing process that there is a wide variety of reliable and fast equipment available. For
example DEK solars’ PV1200 line screen printers can process up to 1200 wafers per hour. Also it’s adjustable
because of the ease of replacing mesh grates whenever need be. Also screen printing can be on many different
kinds of substrates where as other processes are too specific for this to be possible. Screen printing allows for
different thicknesses. Optical lithography, which requires so much precision and resources, does not really work
for any more than 1m.
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III. Calculations of Solar Cell
3.1 Open Circuit Voltage
Equation 2: Open Circuit Voltage
With Given Inputs of:
1. n=1
2. k*T/q= .0259
3. IL=10^-12
4. I0=3.58 A
Voc= .749 Volts
3.2 Short Circuit Current
Equation 1: Current of a Diode
With Given Inputs of:
1. n=1
2. k*T/q= .0259
3. IL=10^-11
4. VOC= .749 Volts
ISC=3.58 A
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3.3 Fill Factor
Equation 4: Fill Factor
Equation 7: Normalized Open Circuit Voltage
Using equation number 7 we must first solve the “normalized” Open Circuit Voltage which then gives us the
ability to solve for empirical form of the Fill Factor Equation, equation number 8, which assumes a voltage
dropof .72 across the diode.
Equation 8: Fill Factor with Normalized Voltage
Which brings us a Fill Factor of .8439 from use of VOC=.749 V and vOC=26.59 V
3.4 Efficiency of Solar Cell
Equation 57: Max Power
Equation 6: Solar Cell Efficiency
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By use of the earlier determined values of VOC(.749 V) and ISC (3.58 A) and the Fill Factor (.8439) and the
given 10 x 10 cm2 with input power of 100mW/ cm2 x 100 cm2 equaling 10 W in and using equation 5 and 6 we
calculate PMAX=2.2765 W and η=22.7653%
3.5 Design for Power Loss
Using the earlier found design parameters given below we were able to calculate each portion of the losses in
the cell for optimal minimization.
o η=22.7653
o Area = 100 cm
2
o VOC = 0.749
o ISC = 3.58 A
o JSC= 35.8 mA/cm
2
o Fill Factor = 0.84
o POUT= 2.2765 W
o PIN = 10 W
o n+ doping (Na) = 1 16 /cm
E
3
o n+ layer thickness = 100 µm
o p type layer thickness = 600 µm
o Buss bar (2) width = 700 µm
o Finger width = 100 µm
o Buss bar/Finger height = 20 µm
o Finger placement = 3 mm apart
o Finger length = 9.8 cm total
3.51 Sheet Resistance Loss
n+ Layer Resistive Power Loss
Current density at max power,
Jsc = 38.5 mA/cm2
Voltage at max power,
Vmp = 0.749 V
Emitter Sheet Resistivity,
ρ= 50 Ω/
Finger Spacing,
S = 3 mm
Fractional Power Loss,
Pn+f = 2.06%3.52 Resistive Power Loss in Grid Fingers
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Finger Resistive Loss
psmf <sheet resistivity> = (25 µmΩ/sq.)/20µm = 12.5 mΩ
Wf <finger width> = 100 µm
b <finger length> = 2.415 cm
S <finger/buss bar thickness> = 20 µm
= 0.0373%
Equation 9: Power Loss in Grid Fingers
3.53 Buss Bar Power Loss
Buss bar Resistive Loss
psmf <sheet resistivity> = (25 µmΩ/sq)/20µm = 12.5 mΩ
Wb <buss bar width> = 700 µm
b <finger length> = 2.415 cm
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S <finger/buss bar thickness> = 20 µm
= 1.46%
Equation 10: Power Loss in Bus Bars
3.54 Shadowing Power Loss
Finger Shadow Loss
Wf <finger width> = 100 µm
Fs <finger spacing> = 3 mm
= 3.30%
Equation 11: Power Loss Finger Shadowing
Bus bar Shadow Loss
Wb <bus bar width> = 700 µm
b <finger length> = 2.415 cm
= 1.44%
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Equation 12: Power Loss in Bus Bar From Shadowing
3.53 Total Power Loss
Total Power Loss = resistive loss + shadow loss
Total Power Loss = ( Pn+f + prf + prb) + ( psf + psb) = 8.30%
Table 1: Sum of All Loses
Power Loss Factors
Percentage of Loss
n+ Layer Resistive Loss
2.06%
Finger Resistive Loss
0.04%
Buss bar Resistive Loss
1.46%
Finger Shadow Loss
3.30%
Buss bar Shadow Loss
1.44%
Total Resistive Loss
3.42%
Total Shadow Loss
4.74%
Total Loss
8.30%
IV. Evaluation
We determined this to be a quality research prompt for our given area of study due to who would be evaluating
this article when we were all finished with it. We evaluated our purpose to be to educate others as well as show
our knowledge of solar cells fabrication, design, and all around work. We have also determined that we properly
addressed the research question in use by our ability to minimize our losses of power from our cell and keep
our efficiency as high as possible. We discovered the amount of work necessary to create a solar cell, not to
mention the extensive quantum physics used by the designers. Our general conclusion was that this was an
exciting paper to be assigned as well as a good way of understanding an area that will be very beneficial to the
future of mankind. We as a group feel very strong about our final piece of work for this paper and we hope that
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anyone who reads it will have a stronger understanding of the area. As well as not be entirely confused with the
amount of physics required for something like this.
V. References
Cell Parameters Template
http://onlinelibrary.wiley.com/doi/10.1002/%28SICI%291099-159X%28200003/04%298:2%3C237::AIDPIP309%3E3.0.CO;2-C/pdf
Glunz, S. W., Köster, B., Leimenstoll, T., Rein, S., Schäffer, E., Knobloch, J. and Abe, T. (2000), 100
cm2 solar cells on Czochralski silicon with an efficiency of 20·2%. Progress in Photovoltaics: Research and
Applications, 8: 237–240. doi: 10.1002/(SICI)1099-159X(200003/04)8:2<237::AID-PIP309>3.0.CO;2-C
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Cost Effectiveness
Honsberg, Christiana B., and Stuart Bowden. "Manufacturing Si Cells.” PVCDROM. National Science
Foundation, July 2008. Web. 10 Apr. 2011. <http://pvcdrom.pveducation.org/>.
http://www.electroiq.com/index/display/photovoltaics-article-display/2438273560/articles/PhotovoltaicsWorld/thin-film_solar_cells/amorphous-silicon/2011/1/why-less-is-more-how-thin-film-manufacturing-isfinding-momentum.html
Ink Front Contact ( Print For REF)
http://www2.dupont.com/MCM/en_US/assets/downloads/prodinfo/PV16A.pdf
Ink Back Contact ( Print For REF)
http://www2.dupont.com/MCM/en_US/assets/downloads/prodinfo/PV506.pdf
PVeducation.org-Multiple articles used...
Honsberg, Christiana B., and Stuart Bowden. "Solar Cell Operation." PVCDROM. National Science
Foundation, July 2008. Web. 10 Apr. 2011. <http://pvcdrom.pveducation.org/>.
Honsberg, Christiana B., and Stuart Bowden. "Design of Silicon Cells." PVCDROM. National Science
Foundation, July 2008. Web. 10 Apr. 2011. <http://pvcdrom.pveducation.org/>.
Honsberg, Christiana B., and Stuart Bowden. "Characterisation,” PVCDROM. National Science
Foundation, July 2008. Web. 10 Apr. 2011. <http://pvcdrom.pveducation.org/>.
Technical Data sheet citations
Dupont Solamet PV16A; Technical Data Sheet; Dupont Microcircuit Materials: Research triangle Park, NC,
Feb. 2011
http://www2.dupont.com/MCM/en_US/assets/downloads/prodinfo/PV16A.pdf (accessed April 2011)
Dupont Solamet PV505; Technical Data Sheet; Dupont Microcircuit Materials: Research triangle Park,
NC, Aug. 2010
http://www2.dupont.com/MCM/en_US/assets/downloads/prodinfo/PV505.pdf (accessed April 2010)
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VI. Appendix
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