Fundamentals of Solar Cell Operation

In a crystal of pure silicon, the 4-coordinated atoms are bonded to each nearest neighbour covalently, so that no free mobile electrons are available. To control the electrical properties of the material, a small proportion of lattice sites are substi­tuted, or “doped”, with elements of a different valence. If a pentavalent dopant is employed, only four electrons for each atom inserted on a silicon lattice site are incorporated in covalent bonding, and the excess electrons (one per dopant atom) provide mobile electrons as charge carriers; this type of donor dopant therefore makes the semiconductor n-type. Where positive charge carriers are required, an acceptor dopant such as boron may be employed, with only three valence electrons when fourfold covalency is required in the silicon crystal; the electron deficiency or hole then effectively provides a mobile positive charge carrier. One consequence of the excess or deficiency induced by doping is that the Fermi level, the energy of the highest occupied electron state, in the silicon is determined by the small propor­tion of dopant inserted, rather than by the bulk properties of the host material itself. With excess electrons in an n-type material, the Fermi level is close to the con­duction band edge, and conversely for a p-type material the Fermi level descends towards the valence band edge. On contact between two such materials, p – and n-, the Fermi levels equilibrate, so the electronic band structure is displaced, positively in the n-type material and negatively in the p-type, as shown in Figure 5.5. This then provides an electric field capable of separating oppositely-charged carriers, as

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Fig. 5.5 Electron band structure at a p-n junction in darkness, showing equilibration of the Fermi level and consequent “band-bending” representing an internal electric field. An electron with higher energy is at a more negative potential. (right) schematic of a p-n junction photovoltaic cell.

required for the exploitation of the converted solar energy represented by the photo­generated carrier pair. Electrons can descend to the n-type side of the junction where they accumulate, while holes rise to and accumulate on the p-type side; the electrons are therefore available to transit an external circuit, returning to the p-type zone to combine with and neutralise holes. The maximum potential difference generated under illumination, that is under open-circuit conditions, is therefore somewhat less than the band gap of the semiconductor material. In the silicon case, for example, yoc is approximately 600 mV, for a band gap of 1.1 eV. Figure 5.6 shows the electrical characteristics of a silicon solar cell, which shows only slight dependence of Voc on the intensity of illumination. As for the maximum available current under short- circuit conditions, it corresponds to harvesting of the carrier pairs photo-generated by absorption of sufficiently energetic, or “actinic” photons, and therefore is directly proportional to the incident light intensity.

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