Series and Shunt Resistance

In a real, non-ideal solar cell, there are electrical losses, which can be represented as parasitic resistances in an ideal solar cell electrical circuit.  2 important resistances are the series and shunt resistance.

Consider a crystalline silicon c-Si solar cell.  The series resistance R_s results from the semiconductor materials of the p-n junction, the interface between the p-n junction and the metal terminals/contacts, and finally, the metal terminals/contacts themselves (see diagram below).

The shunt (or parallel) resistance R_SH results from a macroscopic defect in the solar cell, such as a crack through the semiconductor layers or a current path along the edge of the solar cell.  These are alternate paths for the photogenerated current (see diagram below).

Ideally, the series resistance should be as low as possible to minimise voltage losses, while the shunt resistance should be as high as possible to minimise leakage of photocurrent.

Hence, the circuit diagrams below show the outcome:

V = V_ideal - JR_s

J = J_PH - J_D - J_SH

J_SH = (V+JR_s) / R_SH

The effects of increasing R_s and decreasing R_SH are separately shown in the diagrams below.  The J-V curve will change.  Increasing R_s and decreasing R_SH will also reduce the maximum power point, and correspondingly, the FF, because V_oc and J_sc are unchanged.

The J-V curve of a solar cell has current density and power density varying with voltage.  To determine the point on the curve that the solar cell operates at, a load must be connected (see diagram below).

A load of low impedance means current density is high and voltage low, leading to a P_out lower than the maximum power point P_max.  A load of high impedance means the reverse: the current density is low and voltage high.  It also leading to a P_out lower than P_max (see diagrams below).  Hence, solar cells must have maximum power point trackers (MPPT) to tune the impedance of the load to ensure proximity to P_max.

In the 2 diagrams above, the lower right corner of the red rectangles point to the point on the J-V curve of the solar cell's operating parameters.  Extending a vertical from the voltage parameter will intersect the power density-voltage curve at a point to indicate the P_out.

Finally, it must be noted that the slope of the J-V curve at V_oc can be estimated as:
dJ/dV = 1/R_s

And the slope of the J-V curve at J_sc:

dJ/dV = 1/R_SH

Reference:
3.2.2 Series and Shunt Resistance, Delft University of Technology, https://www.youtube.com/watch?v=HnpDaYINCKY