Photovoltaic effect Laboratory Report IM2601 Solid State Physics ...

Photovoltaic effect Laboratory Report
IM2601 Solid State Physics spring 2012
1 Introduction
Axel Kurtson akurtson@gmail.com
Sandrine Idlas idlas@kth.se
Joakim Jalap jjalap@kth.se
May 8, 2012
A solar cell is a large variant of a so called p-n junction. The p-n junction
is composed of two parts of doped semiconductors, with acceptor atoms on
the p-side and donor atoms on the n-side. In a region between the p and
the n-side the electrons of the donor atoms will move to the acceptor atoms.
The diffusion of electrons leaves the p-side negatively charged and the n-
side positively charged which will give rise to an electric field. When the
cell is illuminated by light of sufficiently high energy to overcome the band
gap, electrons will be excited and a free electron and a hole will be created.
These are accelerated in opposite direction by the electric field and a current
is generated. The voltage that occurs when a p-n junction is illuminated is
called the photovoltaic effect.
In this lab we will study a solar cell made of a thin film of Silicon (Si). The
band gap of Si, i.e. the energy needed to lift an electron to a conduction
band, is 1.11eV at T = 300K.
Say that a monochromatic light source is to power the cell. The minimum
frequency needed to create a voltage is 2.7 · 10 14 Hz, corresponding to the
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wavelength 1100nm, which lies in the infrared spectrum. Thus shorter wave-
lengths of electromagnetic radiation, such as visible light, will be able to drive
the cell.
2 Experimental Procedure
The solar cell was connected to the Power Cassy, which applies a selected
voltage over the solar cell and measures the current output. The Cassy was
connected to a computer to presents the data. The Cassy Lab software was
started and the settings were adjusted according to the instructions. A ta-
ble lamp which was used for the later measurements was placed above and
facing the solar cell. Our first measurement was made with the table lamp
turned off and as expected the current and voltage was next to zero.
Our next measurement was made with the table lamp turned on and po-
sitioned close to the solar cell. The data plot showed a sine curve with a
frequency of 100Hz. This is as expected since the regular wall electric outlet
outputs an alternating current (AC) to the lamp at 50Hz, so that the power
output of the lamp has a frequency of 100Hz.
We now changed the settings so that the Cassy produces a triangular wave
with amplitude Vp = 57 V and frequency 0.2Hz. Measurements were again
made, first with the lamp turned off and then with the lamp turned on. To
avoid the sine like curve due to the electrical outlet AC we used the average
value Iav over 10 ms from now on.
For our next measurements we plotted the power delivered from the solar cell.
The power is given by the simple relation P = Iav × U. The power output
depends on the distance l from the lamp to the solar cell as P (l) = P0/(l/l0) 2
2

Measurement l0/l P/P0
1 1 1
2
√
2 2
3
√
4 4
4
√
6 6
5
√
8 8
6
√
10 10
7
√
12 12
8
√
14 14
9
√
16 16
10
√
18 18
Table 1: Theoretical results from measurements of solar cell power output
where P0 is a reference value of the power output calculated with the lamp
at distance l0 from the solar cell.
10 measurements was now made with the lamp at different distances from
the solar cell. Beginning from the longest distance at 87 cm the lamp was
lowered for every measurement with √ 2l0 so that the measurements were
made according to Table 1.
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3 Measurement results
Figure 1: Current plotted against voltage for different distances from light
source to solar cell
4

Figure 2: Power plotted against voltage for different distances from light
source to solar cell
5

Figure 3: Current plotted against voltage without illumination, and the
fitted diode equation
6

Figure 4: Power as a function of 1/r 2 . Meassured data and the fitted equa-
tion
4 Discussion
4.1 Power as a function of distance
The power of the light reaching the solar cell is inversely proportional to the
distance from the solar cell to the lamp squared: Pmax = k · f(r), where
f(r) = 1
r 2 and k is a proportionallity coefficient.Thus we try fitting the
function
k
(r−rerr) , where rerr is a correction term to handle any systematic
meassuring error that might have been made, to the aquired data. The
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values given by the fit were k = 4.39 and rerr = −0.26. This fitted function
is also shown in figure 3.
4.2 Voltage at maximum power
We can consider the applied voltage of the cassy as a resistor, and thus
replace it with a corresponding resistance Rc. The solar cell gives a voltage
U0, and it also has an internal resistance R0. This gives a current I = U0
R+R0
flowing through the circuit. At the load the power is P = RI 2 . This gives
P = R
U0
R+R0
2 , then taking dP
dR = 0 to get the maximum yields R = ±R0,
but resistance cannot be negative, so the value R = −R0 is discarded. The
voltage corresponding to this is Umax = R0I = R0 U0
2R0
= U0
2 .
When I = 0 then it must be the case that U = U0. From figure 1 it can be
seen that at the minimum distance (which gives the maximum power), when
I = 0A U ≈ −0.55V . In the figure 2 it can be seen that Umax ≈ −0.35V .
This is in a reasonable agreement with the theory.
4.3 Maximum efficiency of pn-junction solar cell
The equation for the maximum efficiency of a solar cell is: Eg
kbT
≈ 2.3. Given
that the sun has a temerature of ≈ 6000K, the most efficient semiconductor
would be one with an energy gap of 1.19eV . Silicon has Eg = 1.17eV for
T = 0K and Eg = 1.11eV for T = 300K, which makes it an excellent mate-
rial to use for a solar cell.
If a lightbulb burns with a temperature of about 3000K, assuming it can
be approximated with a black body, this gives xg = Eg
kbT
= 4.29. From figure
7 in the lab compendium, we can see that the upper limit on a pn-junction
solar cell will be about 0.3 or 30%.
If the lightbulb converts 100% of the electric power inte radiation that
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can be used to generate current in the solar cell, and that it is a 60W
bulb, at 20, 5cm it will give 60/(4π · 0.205 2 ) = 119W/m 2 . Say the solar
cell has an area of about 6cm 3 . It will then be hit by about 0.071W . So
Pout/Pin = 0.011/0.071 ≈ 15% for our solar cell.
4.4 The diode equation
In figure 3 the
meassured
data is ploted together with the fitted diode equa-
−ef V
k tion I = Isat 1 − e bT = Isat 1 − e −V
v0 . Fitting the data to this equa-
tion with respect to Isat and V0 gives: Isat = 1.32 · 10 −5 A and V0 = 0.061V .
4.5 Sources of errors
One approximation that was made was that the light from the lightbulb was
distributed spherically, but since there was a lampshade, this approximation
might not hold. The lampshade actually focuses the light into a cone.
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