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where J ph is the photo current given by
A number of approximations have been made in order to derive the analytical
expressions for the current–voltage characteristics of an ideal p-n junction in the dark and
under illumination. These approximations are summarized below:
the depletion-region approximation;
the Boltzmann approximation;
low level injection conditions;
the superposition principle;
infinite thickness of doped regions;
uniform generation rate.
The derived expressions describe the behaviour of an ideal p-n junction and help us
understand the basic processes behind the operation of this junction. However, they do not
fully and correctly describe real p-n junctions. For example, the thickness of a real p-n
junction is limited, which means that the recombination at the surface of the doped regions
has to be taken into account. The thinner the p-n junction, the more important surface
recombination becomes. The surface recombination modifies the value of the saturation
current density. Further it was assumed that there are no recombination-generation
processes in the depletion region. However, in real p-n junctions, the recombination in the
depletion region represents a substantial loss mechanism. These and other losses in a solar
cell are discussed in Chapter 10.
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