# Exercise 3.4.1

Lets consider a solar cell as an ideal pn-junction, for simplicities sake even without the current contributions from the space charge region, but with a built in series resistance Rser and a shunt resistance Rshunt
We have the following equivalent circuit diagram (also defining what is meant by a shunt resistance). See also the "Solar Cell Primer" in a basic module

The shunt resistance takes into account that the huge area of the pn-junction of a solar cell might have weak points (locally, e.g. at the edge) which short-circuit the junction somewhat. These defects are summarily described by a shunt resistor.
The constant current source mimics the current generated in the junction by light. it simply defines a current value Iphot (not to be mixed up with the terminal current I) that is given by the light and added (with a negative sign) to the junction current, i.e. Ijunct = Idiode(U) – Iphot. Iphot thus simply moves the total characteristics of the diode downwards on the current scale.

Take the following schematic curve of I-U-characteristics as a reference and for the definition of the following terms

The fill factor is the relation between the area of the yellow rectangle to the pinkish area under the characteristics.

Derive the complete current-voltage relationship.
Discuss qualitatively the influence of the two resistors with particular respect to:
The open-circuit voltage UOC
the short-circuit current ISC
The fill factor FF (the degree of "rectangularism" of the characteristics).
The efficiency h which is proportional to UOC, ISC, and FF, i.e.

h  =  const · UOC · ISC · FF