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Solar energy conversion

Physical Background

The basis of a photovoltaic cell is a semiconductor diode, usually based on a PN junction. Its voltage-current characteristic in the dark, ideally without the influence of series and parallel resistance, is:

where J is the current flowing through the diode, J₀ is the reverse current, U is the voltage, k is the Boltzmann constant, T is the absolute temperature, n is the diode ideality coefficient, which is related to the charge transfer mechanism through the diode, e is the electron charge. When illuminated, the diode turns into a source of electric current. An equivalent circuit diagram of an illuminated cell as a current generator J_L with a diode connected in parallel is shown in Fig. 1 on the left. In reality, in addition to the load resistance R, it is necessary to take into account the series resistance R_S and the parallel resistance R_SH. The resistance R_S represents the resistance of the volume of the semiconductor and the contacts, while R_SH is usually related to a leakage current. The voltage-current characteristic then has the form:

This dependence is shown in Fig. 1 on the right in the 4th quadrant; U_OC and J_SC are the values of the open-circuit voltage and short-circuit current, which are influenced by the series and parallel resistance. The area of the largest inscribed rectangle indicates the maximum power that can be obtained from the cell (U_m·J_m). The efficiency of the cell is then the ratio of this power to the power P of the incident light. The reflection of light from the surface of the material, characterized by reflectivity, which is about 35 % for silicon, also plays a role. Assuming a large parallel resistance, the value of the series resistance can be obtained directly from the slope of the volt-ampere characteristics at the U_OC point. The inverse values of the resistances R_S and R_SH are shown in the figure by the tangents.

From the measured dependence of the current on the voltage, the so-called fill factor (FF) can also be determined as:

The maximum power is P_max = J_SC·U_OC·FF and the efficiency of the cell is then P_max/P.

Authors of the study text: doc. RNDr. Jana Toušková, CSc. and doc. RNDr. Jiří Toušek, CSc. (Charles University in Prague, Faculty of Mathematics and Physics)

Literature

1. D. K. Schreder, Semiconductor material and device characterization, Chapter 8, A Wiley Interscience Publication, John Wley & Sons, Inc. New York 1990.
2. M. A. Green, Solar Cells, Prentice Hall, Inc., Englewood Cliffs, N.J. 07632, 1982.
3. H. Frank, Fyzika a technika polovodičů, SNTL, Praha 1990.