In 1839 Becquerel observed that certain materials, when exposed to light, produced an electric current [Becquerel (1839)]. This is now known as the *photovoltaic effect*, and is the basis of the operation of photovoltaic or solar cells. When light falls onto semiconductor material, photons with energy more than the band gap energy (the difference in energy between electrons in the valence and the conduction bands) interact with electrons in covalent bonds, creating "electron-hole" (e-h) pairs. The generation rate of e-h pairs per unit volume can be calculated as a function of the photon flux (photons/unit area/sec), the absorption coefficient, and the distance travelled before absorption. Optimum use is made of incoming sunlight if the semiconductor bandgap lies in the range 1.0-1.6 eV. This effect acts to limit the maximum achievable efficiency of solar cells to 44% [Shockley and Queisser (1961)]. Silicon, the most commonly used solar cell material, has a bandgap of 1.1 eV.

When not illuminated, the system returns to a state of equilibrium and the electrons and holes move around until they meet up and *recombine*. Any defects or impurities within or at the surface of the semiconductor promote recombination. The *carrier lifetime* of a material is defined as the average time for recombination to occur after e-h generation. Similarly, the *carrier diffusion length* is the average distance a carrier can move from point of generation to recombination. These two parameters give an indication of material quality and suitability for solar cell use.

A *silicon solar* cell is a diode formed by joining p-type (electron deficient, typically boron doped) and n-type (with excess electrons, typically phosphorous doped) silicon. At the p-n junction, excess electrons flow from n- to p-type leaving behind exposed charges on dopant atom sites, fixed in the crystal lattice. An electric field (Ê) builds up in the so-called "depletion region" around the junction to stop the flow. Depending on the materials used, a "built in" potential V_{bi} due to Ê will be formed. If a voltage is applied to the junction, Ê will be reduced. Once Ê is no longer large enough to stop the flow of electrons and holes, a current is produced. V_{bi} reduces to (V_{bi} − V) and the current flow increases exponentially with the applied voltage. This phenomenon results in the *Ideal Diode Law*, expressed as:

where I_{o} = "dark saturation current", the diode leakage current density in the absence of light; V = applied voltage; q = absolute value of electronic charge; k = Boltzmann's constant; T = absolute temperature.

"IV" curves for a diode are generated by plotting I against V. Illumination of a cell adds to the normal "dark" currents in the diode and has the effect of shifting the IV curve such that power can be extracted. The IV curve characterizes the cell and is most often shown reversed, as in Figure 1. The two limiting parameters used to characterize the output of solar cells for given irradiance, operating temperature and area are the *short-circuit current*, I_{sc}, the maximum current at zero voltage, and the *open-circuit voltage*, V_{oc}, the maximum voltage at zero current. Ideally, if V = 0, I_{sc} = I_{L}, the light generated current. I_{sc} is directly proportional to the available sunlight while V_{oc} increases logarithmically with increased sunlight.

**Figure 1. Typical IV curve, showing short circuit current (I _{sc}), open circuit voltage (V_{oc}), and maximum power point (V_{mp}, I_{mp}).**

For each point on the IV curve, the product of the current and voltage represents the power output for that operating condition. A solar cell can also be characterized by its *maximum power point*, the maximum value of V_{mp} * I_{mp}. The maximum power output of a cell is graphically given by the largest rectangle that can be fitted under the IV curve. The power output at V_{mp}, I_{mp} under strong sunlight (1 kW/m^{2}) is known as the "peak power" of the cell.

Photovoltaic panels are usually rated in terms of their "peak" watts, W_{p}. The *fill factor*, FF, is a measure of the junction quality and series resistance of a cell. It is defined as the maximum power/ I_{sc} V_{oc}. The nearer FF is to unity, the higher the quality of the cell. Ideally, it is a function only of V_{oc}. The spectral responsivity of a solar cell is given by the amps generated per watt of incident light.

Ideally this increases with wavelength, making cell performance strongly dependent on the spectral content of sunlight. The operating temperature of solar cells is determined by the ambient air temperature, the characteristics of the module in which it is encapsulated, the intensity of sunlight falling on the module, and other variables, such as wind velocity. The main effect of increasing temperature for silicon solar cells is a reduction in V_{oc}, FF and hence the cell output. I_{o} increases with temperature according to the equation:

where B is independent of temperature; E_{GO} is the linearly extrapolated zero temperature band gap of the semiconductor [Green (1992)]; and γ includes the temperature dependencies of the remaining parameters determining I_{o}.

#### REFERENCES

Becquerel, E. (1839) On electron effects under the influence of solar radiation, *Comptes Rendues*, 9, 561.

Green, M. A. (1992) *Solar Cells—Operating Principles, Technology and System Application*, University of NSW, Kensington, Australia. DOI: 10.1016/0038-092X(82)90265-1

Shockley, W. and Queisser, H. J. (1961) Detailed Balance Limit of Efficiency of p - n Junction Solar Cells, *Journal of Applied Physics*, 32,510-519.

Wenham, S. R., Green, M. A., and Watt, M. E. (1994) *Applied Photovoltaics*, Centre for Photovoltaic Devices and Systems, University of NSW, Australia.