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112 CHAPTER 8. SEMICONDUCTOR DEVICES Figure 8.8: Theoretical I-V characteristic from (8.5). p n incoming photon, E = h f eφ j μ e-h pair generated in junction region, separated by junction field E j . E j Figure 8.9: Operation of a p − n junction based solar cell. When illuminated, electron-hole pairs are generated. Pairs generated away from the junction will recombine rapidly, but those electrons and holes generated near the junction will be separated by the in-built electric field. Electrons flow towards n-side, holes towards p-side, which is equivalent to increasing the generation current, which flows in the reverse direction (n to p). I ph I d V d R load solar cell equivalent circuit Figure 8.10: Equivalent circuit of a solar cell. We can model a solar cell as p − n diode with a current source in parallel, which produces the photocurrent.
8.3. SOLAR CELL 113 -I load I d (V) I d (V)-I ph max. -I ph power E g /e V load Figure 8.11: Current-voltage characteristic of a solar cell. How much power can be extracted is given by the product of voltage and current. These are limited by the size of the band gap and by the photocurrent. will separate them - the potential gradient pulls electron and hole in opposite directions. The resulting current is in the same direction as the generation current mentioned above, namely from n to p, or in the reverse direction. The separation of the charges across the depletion layer adds an extra internal dipole to the system - like charging a capacitor - and therefore generates an overall electrical bias. The induced voltage is in the forward direction - because it is opposite in sign to the built-in potential. This is the photovoltaic effect, which can deliver power to an external circuit. Large arrays of p-n junctions of Si are used to make solar panels, converting solar radiation to electrical power. We can model the effect of this process as a current source added in parallel to the diode normally associated with a p − n junction (Fig. 8.10). The current delivered by this current source, the photocurrent I ph depends on the amount of light falling onto the junction area. Fig. 8.11 illustrates how much power can be extracted from a solar cell, by considering the I − V characteristic of the full device – current source plus diode. Note that for zero load resistance (short circuit, I load = I ph but V = 0) and for infinite load resistance (I load = 0), no power is extracted. What is the open circuit V d Its upper limit is given by the band gap E g , because if V d exceeds φ j (∼ E g /e), then the in-built junction field vanishes and photo-generated carriers are no longer swept out of the junction area. The maximum power extracted for the ideally chosen load resistance is therefore determined, up to a factor less than one but of order one, by the product I ph E g /e. Shockley-Queisser limit: How far is it possible to optimise solar cells by tuning the gap energy E g Shockley and Queisser made a careful analysis of the maximum efficiency of solar cells, which considered, among other influences, the matching between the semiconductor band gap and the intensity spectrum of sunlight. Their considerations are outlined in Fig. 8.12. The key point is that photons can only be captured by the solar cell, if the band gap is lower than the photon energy. On the other hand, the power extracted is given by the size of the band gap, not by the photon energy. This is evident from the preceding argument that the open circuit voltage is related to the band gap, but also from the fact that electrons and holes excited into states far away from their
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