Photovoltaic effect Laboratory Report IM2601 Solid State Physics spring 2012

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1 Photovoltaic effect Laboratory Report IM2601 Solid State Physics spring 2012 Axel Kurtson Sandrine Idlas Joakim Jalap May 8, Introduction 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 Hz, corresponding to the 1

2 wavelength 1100nm, which lies in the infrared spectrum. Thus shorter wavelengths 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 table 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 positioned 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 V p = 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 I av 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 = I av U. The power output depends on the distance l from the lamp to the solar cell as P (l) = P 0 /(l/l 0 ) 2 2

3 Measurement l 0 /l P/P Table 1: Theoretical results from measurements of solar cell power output where P 0 is a reference value of the power output calculated with the lamp at distance l 0 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 2l 0 so that the measurements were made according to Table 1. 3

4 3 Measurement results Figure 1: Current plotted against voltage for different distances from light source to solar cell 4

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

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

7 Figure 4: Power as a function of 1/r 2. Meassured data and the fitted equation 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: P max = k f(r), where f(r) = 1 r 2 function and k is a proportionallity coefficient.thus we try fitting the k (r r err), where r err is a correction term to handle any systematic meassuring error that might have been made, to the aquired data. The 7

8 values given by the fit were k = 4.39 and r err = This fitted function is also shown in figure Voltage at maximum power We can consider the applied voltage of the cassy as a resistor, and thus replace it with a corresponding resistance R c. The solar cell gives a voltage U 0, and it also has an internal resistance R 0. This gives a current I = U 0 R+R 0 flowing through the circuit. At the load the power is P = RI 2. This gives P = R ( U0 R+R 0 ) 2, then taking dp dr = 0 to get the maximum yields R = ±R 0, but resistance cannot be negative, so the value R = R 0 is discarded. The voltage corresponding to this is U max = R 0 I = R 0 U 0 2R 0 = U 0 2. When I = 0 then it must be the case that U = U 0. 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 U max 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: E g k b T 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 E g = 1.17eV for T = 0K and E g = 1.11eV for T = 300K, which makes it an excellent material 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 x g = Eg k b T = 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 8

9 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 ) = 119W/m 2. Say the solar cell has an area of about 6cm 3. It will then be hit by about 0.071W. So P out /P in = 0.011/ % for our solar cell. 4.4 The diode equation In figure 3 the meassured data is ploted together with the fitted diode equation I = I sat e f ) V ( k (1 e b T = I sat 1 e V v 0 ). Fitting the data to this equation with respect to I sat and V 0 gives: I sat = A and V 0 = 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. 9