Calculating the Efficiency of the Solar Cells
Basic Definition of Efficiency:
(Power output per unit area of the cell) / (Power Input per unit area of the light source)
Power Input Measurements:
Input power is a result of the photons hitting the solar cell
surface. Several processes can happen to attenuate the light
reaching the material that absorbs the incoming light.
Also, there will be a distribution associated with the wavelength
dependence of light. AM1 AM0 other wavelength dependence of
the source.
The material, itself, has a wavelength dependence.
Are any of these taken into account when measuring the efficiency?
The efficiency of the solar cell is usually measured based on a source that mimics
a certain region of the spectrum. Combinations of lamps and filters are made such that
the wavelength dependence of the output is matched to AM0, AM1, or AM1.5 for
instance.
Once the lamp has been selected, it is important then to determine the power imparted
by the light on the surface area of the solar cell.
The measurement is typically in W/m2 or mW/m2
Figure
The measurement is made by a calibrated detector employing a photodiode or a
calorimeter.
Ideally the power meter would have the same surface area as the material, as there could
be non-uniformity in the light beam.
Once the measurement is made, the power per area is calculated by dividing by the active
surface of the detector.
Power Output Measurements
The output power is measured as a function of the resistance through an external load.
As we saw, there is a built in potential in the solar cell that can be used to drive current
through an external load. However, the current can be limited by the resistance of the
solar cell itself (its ability to conduct the electrons) as well as by the resistance in the
external load.
If the external load has zero resistance, then we have a measure of the current that can be
provided, essentially limited by the movement of the electrons across the junction
potential and through the doped semiconductor to the external contact.
This will be the maximum current that the solar cell could provide in a particular light
source, the short circuit current, Isc.
Conversely, if the external load has an infinite resistance, then no current can flow
through the external connection. The light then simply moves the electrons and holes to
opposite contacts creating the maximum potential possible from the solar cell for the
particular light source being investigated. The voltage available under no current flow
conditions is called the open circuit voltage, Voc. If current was flowing the potential
would be reduced as the electrons move away from the external junction.
Ideally, then, the maximum power that could be generated would be, if we could provide
as much current as is possible under short circuit conditions, Isc. Also, ideally, if the
current load did not pull down the potential, then the maximum voltage possible would
be the open circuit voltage, Voc.
The ideal maximum power then is the product of Isc and Voc.
In practice, however, an external load affects both the voltage and the current. A typical
IV plot made by varying the external resistance would look something like.
Dark
0.50
Blue
Green
Photocurrent (mA)
0.40
Yellow
Red
0.30
Solar
0.20
0.10
0.00
0
100
200
300
Bias (mV)
400
500
600
This curve was actually made by putting a reverse potential across the solar cell and
observing the current flow as a function of the bias. This is similar to imposing an
external resistance to the flow of electrons.
Where would the IDEAL MAX POWER appear or be calculated from this diagram?
The max power can be obtained from the diagram by looking at the current and voltage to
see where the maximum product occurs. It will occur at the “knee” of the curves on the
diagram.
It is often more helpful to look at a plot of power vs potential which is similar to the
figure here.
Power Curve 6N3- Normalized Intensity
0.45
0.4
0.35
P (uW)
0.3
Blue
Yellow
Red
Green
0.25
0.2
0.15
0.1
0.05
0
0
5
10
15
20
25
30
35
V (mV)
This diagram allows the maximum power to be determined more readily.
Calculating the Efficiency
Once the maximum power has been obtained, it is divided by the area of the solar cell to
get the maximum power per area. Then this number is divided by the power per area of
the incident light and multiplied by 100% to give the % efficiency.
% Efficiency = (Max Power/Area) (generated Solar Cell) / (Power/area) (incident light)
Another Quantity that is often quoted is the fill factor. The fill factor is defined as
Max Power per Area (from solar cell) / Ideal Max Power per Area