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```University of California at Santa Cruz
Electrical Engineering Department
EE-145L: Properties of Materials Laboratory
Lab 6: Solar Cells
Fall 2014
Nobby Kobayashi
1.0 References
Sections 6.1-6.3 of S.O. Kasap. Principles of Electrical Engineering Materials and Devices
. 3rd Ed. 2005.
The Semiconductor applet Service – List of Simulation Applets
http://www.acsu.buffalo.edu/~wie/applet/applet.old
#4 PN Junction Diode at Equilibrium
#5 PN Junction Diode under Applied Bias Voltage
Includes interactive applets on:
Semiconductor statistics
PN junction diode (In equilibrium, Applied bias, Fabrication)
Also includes parameters, mathematical analysis, and detailed explanations.
Solar Electricity – How Solar Cells Work
http://www.soton.ac.uk/~solar/intro/tech0.htm
Includes solar cell simulations and general theory
Institute of Electrical Power Engineering - Renewable Energy Sect.
http://www.user.tu-berlin.de/h.gevrek/ordner/ilse/impressindex_e.html
Includes theory as well as interactive components
Center for Photovoltaic Engineering, University of New South Wales, Australia
http://www.pv.unsw.edu.au/node/573
Useful tables, current research in photovoltaics.
2.0 Theory
2.1 Formation of the pn Junction
A pn junction is formed when a p-type semiconductor material is brought into
contact with an n-type material. The p side has an excess number of holes, whereas the n
side has an excess number of electrons. When the two materials come into contact a
concentration gradient is formed on each side due to the excess charges. The holes begin
to diffuse toward areas of low concentration in the n side, and the electrons diffuse to the
p side. Eventually, a region in the middle becomes devoid of any electrons or holes because
1
they have diffused to the opposite sides. Within the middle region are the ionized acceptor
atoms in the p side and donors in the n type. This forms a negative charge on one side and
a positive charge on the other, creating an electric field between. The built in equilibrium
potential is given by V0. Figure 1 below illustrates the pn junction.
Figure 1
The middle region containing the electric field is referred to as the space charge
region, or the depletion region. Due to the electric field, electrons and holes experience a
drift current. Equilibrium is reached when the drift current exactly opposed the diffusion
current. The net current flow is therefore zero. The total current density for either electrons
or holes is given by:
J nTotol = J nDrift + J nDiff
(1)
J pTotol = J pDrift + J pDiff
The current densities are therefore given by:
dn ( x )
dx
dn ( x )
J p = qpµ p E − qD p
dx
J n = qnµ n E + qDn
(2)
Where n and p are the electron and hole concentrations respectively, μ is the drift mobility,
E is the electric field, and Dn,p are the diffusion coefficients.
2.2 Forward Bias
When a positive voltage is applied to the p-type material there is a net current flow
in the positive direction. Figure 2 below demonstrates the pn junction under forward bias:
2
Figure 2
The applied voltage, V, results in an electric field that opposes the internal field across the
space charge region. This effectively lowers the potential barrier by the amount V-V0. In
equilibrium, some of the majority carriers in the conduction band have a high enough
energy to surmount the barrier. Under forward bias, the barrier is lowered, increasing the
probability for majority charge carriers to diffuse across by a factor of e(qV/kT). As the
majority charge carriers cross the junction they are injected into the other type of material,
becoming minority charge carriers. This is referred to as minority carrier injection. Unlike
the diffusion current, the drift current remains fairly insensitive to the applied bias. This
current is caused by minority carriers wandering toward the barrier and then being swept
away by the field. Comparatively, there are very few minority carries compared to the
doped regions, therefore very few charges contributing to drift current.
The total current is given by adding the diffusion and drift currents, with the
diffusion current dominating. During equilibrium diffusion current is equal in magnitude
to the absolute value of the drift current. Under forward bias, the diffusion current can be
given by:
I diff = I drift e qV
kT
(3)
The total current is then the diffusion current minus the absolute value of the drift current,
since the drift current is in the opposite direction. The current is therefore given by:
qV
I = I 0  e kT − 1


3
(4)
Where I0 is the absolute value of the drift current. This equation is referred to as the ideal
diode equation. Using equation 2 and solving for the minority injection currents leads to a
more accurate diode equation given by:
 qV
 Dp
D
I = qA
p n + n n p  e kT − 1

L
Ln


 p
(5)
Where Lp,n are the diffusion lengths of the holes and electrons, pn and np are the minority
charge concentrations, V is the applied voltage, and A is the area of the device.
2.3 Solar Cells
2.3.1 Generation of photocurrent
With semiconductors, it is possible to convert the energy of the solar radiation into
electric energy. Theoretically, each absorbed light quantum (photon) could generate an
electron-hole pair. If the energy of the photon surpasses the band gap, then such a
generation takes place. The surplus energy is converted into heat. In order to generate more
than one electron-hole pair(EHP), the photon must provide a multiple of the energy of the
band gap.
Figure 3 Generation of electron-hole pairs
4
Figure 4 Generation of photocurrent in a diode
If the minority carrier created from the EHP diffuses toward the junction, it will be
swept to the opposite side by the internal field. Due to the larger number of charges
crossing the junction, the drift current increases. The charges then begin to build up on the
other side, holes on the p side and electrons on the n-side, making the p-side positive and
the n-side negative. This resembles the forward bias and creates the same diode current
from equations 4 and 5. The excess majority charge carriers begin diffusing away from
the junction. This creates diffusion current, called the photogeneration current (IPH) that
opposes the diode current.
2.4 Important characteristics of solar cells
Two important characteristics of a solar cell are its open circuit voltage (VOC) and
short circuit current (ISC).
Under short circuit conditions, the charges are free to travel through the circuit and
no build up bias is produced. The photogeneration current assumes a maximum since there
is no opposing diode current. Because the minority carriers are produced from the EHP’s,
the photogeneration current is directly proportional to the intensity of the sunlight. Under
direct sun conditions, the ISC is at its maximum.
Under open circuit conditions there is a charge buildup on each side creating a diode
current. The device reaches equilibrium when the diode current is equal and opposite to
the photogeneration current. In order for the diode current, otherwise referred to as the
internal or injection current, the internal potential barrier is lowered. This further
demonstrates the forward bias characteristics. Figure 5 below demonstrates the short
circuit and open circuit conditions.
5
Figure 5 Short Circuit Current
Figure 6 Open Circuit Voltage
Under illumination, the total current is given by the diode current minus the
photogeneration current:
I = I 0 (e qV
kT
− 1) − I Ph
(6)
Where IPh is the photogeneration current. The typical current for a solar cell is around 1mA
and the typical voltage for a silicon cell is about 0.5V. Figure 6 below shows the IV curve
for a cell.
6
Figure 7
Berlin University of Technology, Institute of Electrical Power engineering, Renewable Energy Section
The power output of the cell is the product of the current and voltage. A measure
of the quality of a cell is given by the fill factor (ff). The fill factor is defined as the ratio
of the maximum power to the product of the open circuit voltage and the short circuit
current:
ff =
I M VM
I SCVOC
(7)
Typical values of the fill factor range from 0.75-0.85. If the IV curve were in the shape of
a rectangle, the fill factor would be 1. The efficiency is a measure of the maximum power
over the input power.
η=
Pout
Pin
(8)
Where Pout is the maximum power point and Pin is the power due to the photons incident
on the cell, given by:
E = ∫ N ph (hc λ )dλ
(9)
The value of E with the sun perpendicular to a solar cell’s surface is referred to as the solar
constant. Its average value is approximately 1kW/m2.
The efficiency can then be rewritten as:
η=
ff ⋅ I SCVOC
E⋅A
7
(10)
2.5 Factors Affecting Efficiency
Typical values for solar cell efficiencies are 10-15% for thin film cells, 15-20% for
crystalline silicon cells, and 30% or more for concentrating systems (focus sunlight onto
small area sun, up to 1000 sun concentration). The best theoretical values for efficiencies
are 20-28% for normal cells. The reason for this low value is simply that not all of the
energy reaching a solar cell from sunlight can be converted into electricity. About 25% of
incoming photons have energies below the bandgap energy and cannot produce an EHP.
About 30% of the photons will have too much energy and will either be re-emitted or
wasted as heat. This accounts for a total of 55% of the energy that can’t be used. Of the
~75% of absorbed photons, about 43% of the energy from absorbed photons is lost as heat.
In addition to this, electrons can be lost due to recombination with in the semiconductor
material. The extent to which this is a problem depends on the type and purity of the
material. Without treating the cell, about 30% of incoming photons can be reflected off
the surface. For this reason the surface is texturized in the shape of pyramids, maximizing
the chance that a photon is reflected back into the cell. Antireflection (AR) coatings are
also applied. The combination of both can result in reflection losses of less than 1%.
Another problem is the natural resistance to electron flow. Large metal contacts on the
surface of the cell can minimize this, but will block the incoming light. The contacts are
therefore designed as a grid with conducting fingers. Research is also being applied to
creating back only contacts as well as transparent contacts. Temperature can also greatly
affect a solar cell’s efficiency. The warmer the cell, the less it behaves as a semiconductor
and the efficiency falls.
2.6 Types of Solar Cells (Reference Reading)
Types of solar cells fall into three categories. Table 1 below shows the different
types of cells.
Crystalline
Crystalline Silicon
(c-Si)
Gallium Arsenide
(GaAs) and Alloys
Thin Film
Other
Amorphous Silicon
(a-Si)
Quantum dot solar
cells
Thin film Silicon
Dye sensitized
photochemical cells
Copper Indium
Diselenide (CIS)
Polymer cells
(CdTe)
Photoelectrochemical
Cells
Crystalline silicon currently makes up about 86% of the photovoltaic market. The
reason for this dominance is that the material, technology, and equipment come right out
the electronics industry. Whatever is wasted is used in the PV industry. The development
8
of c-Si cells is very energy intensive. It is therefore very expensive to process these cells
and the technology is leaning toward the production of polycrystalline Si cells and thin film
technologies.
Polycrystalline silicon cells use less energy to produce. Molten Si is allowed to
solidify under specific conditions. The solidified Si is then sliced into rectangles and then
individual square cells. This process eliminates the time and energy intensive step of
growing a single ingot and then slicing wafers. The end product leaves small crystalline
silicon areas separated by grain boundaries. The grain boundaries decrease the efficiency
of the cell. However, the benefit of lower energy consumption and cost make up for this
loss.
Gallium arsenide can be alloyed with indium, phosphorous, and aluminum to
produce multijunction cells with very high efficiencies. In forming multiple junctions with
decreasing bandgap energies, the incoming photons can be sifted through with the longer
wavelength photons being absorbed at the bottom. Currently two junction devices are used
for spacecraft with GaInP as the top layer and GaAs as the bottom. Research is being
conducted to make a four-junction device boosting its efficiency to more than 40%.
Thin film semiconductors are only a few microns thick and therefore use much less
material than their crystalline counterparts. These materials are cheaper to manufacture
and likely to lead solar energy into a competitive market. Thin films are made by
depositing the semiconductor material directly onto a low cost substrate.
Amorphous silicon makes up most of the remaining 14% of the PV market. Stable
modules have efficiencies of 6-9%. The minimal material used and therefore the
inexpensive price of modules account for this low efficiency. The p and n regions are made
very thin with a thicker intrinsic layer between in order to lengthen the space charge region.
To maximize light absorption and minimize recombination, the layers need to be thinner
than that needed to absorb the light. Several layers are therefore stacked on top of each
other. Germanium is added to each successive layer in order to decrease the band gap
energy and therefore absorb wavelengths previously unabsorbed.
steps. With time it is thought to be the most promising thin film to meet the cost goals
needed for PV to be a competitive market. Laboratory cell efficiencies are around 16%
with module efficiencies between 6-9%. Some benefits to CdTe are its high absorption
coefficient, minimal amount of material, only 1μm, and the 12 or more manufacturing steps
that can be used to make the modules.
CIS and its alloys is also a promising thin film material with laboratory efficiencies
of 18% and module efficiencies greater than 11%. This product is currently on the market
and boasts 20+ years of research and development. Some problems include immature
manufacturing step, slow vacuum steps, and a more complex structure than the other thin
films.
Another type of thin film is thin film crystalline silicon in which the inexpensive
amorphous silicon is combined with the more efficient crystalline silicon. This is a new
technology that is in the experimental stages.
Among the “other” category include quantum dot solar cells in which a
nanocyrstalline CdSe semiconductor is embedded in the conductive polymer/C60
composite. This has the potential for low-cost, large-area production. Dye-sensitized
photochemical cells have a dye sensitizer that absorbs light and generates EHP’s in a
9
nanocrystalline titanium dioxide semiconductor layer. Only certain wavelengths can be
absorbed but because the device is clear, research is being conducted to create a clear
window that will absorb and convert UV light into energy.
3.0 Experimental Procedure
3.1 Overview
In this experiment we will plot the IV curve for a solar cell, using the open circuit voltage
and short circuit current for the limits. Data will be taken along the IV curve using a
variable resistor. Next perform a linear regression line and determine the maximum power
point.
3.2 Questions to answer before starting the lab:
1. Read through the first three references above. Next go to the last reference from
the Institute of Electrical Power Engineering, Berlin. Run through the simulations
on series and parallel resistance, and temperature effects. What are your
observations?
2. Will the current be positive or negative?
3. What values of current and voltage should you expect to measure?
4. What values will you use for the photocurrent and the voltage from the diode
equation?
5. How will you determine the fill factor and the efficiency?
6. What are the factors to affect Isc and Voc, how about temperature, is it a factor?
3.3 Equipment
•
•
•
•
•
Solar cell
Multimeters
Variable resister
Light source
Light intensity meter
3.4 Schematic setup
Figure 8 below gives the schematic setup for measuring the IV curve for a solar
cell.
Figure 8
10
3.5 Procedures
1. Set up the circuit from figure 8.
2. Set up the light source directly above the circuit.
3. Set the resistance to zero in order to measure the short circuit current. Record the
current and the voltage.
4. Turn off the light and observe the effect of decreased illumination on the short
circuit current.
5. Increase resistance until current is very close to zero. This corresponds to the open
circuit voltage. Record the current and voltage.
6. Turn off the light and observe the effect of decreased illumination on the open
circuit voltage.
7. Vary the resistance and take a few current and voltage measurements along the
curve.
a. To get a good fit of the I-V curve, you need to measure most of your points
near the elbow of the I-V curve;
b. The strategy here is to start with the short circuit condition, and increase
resistance until the current falls a few percent, take a measurement, then
repeat.
c. When the current drops by 30%, then it passed the elbow of the I-V curve
and only need a few more measurements
3.6 Questions to answer after completing the lab
1. Calculate the fill factor.
2. Calculate the efficiency of the cell. Does this seem reasonable? Why would your
value be incorrect? (What is the E value used?)
3. Why is the voltage not equal to zero when measuring ISC?
11
```
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