External Parameters of an Ideal Solar Cell

The diagram above is self explanatory.  V_oc is found when current density is zero.  J_sc is found when voltage is zero.  The 2 circuit diagrams are shown below.  Note that where I is used, it also refers to J.

Based on the equation:
J = J_PH - J₀[ exp(qV/kT) - 1 ]

When J = 0:
V_oc = (kT/q) ln (J_PH/J₀ + 1)

When V = 0:
J_sc = J_PH

This shows that V_oc is dependent on J_PH, T and J₀.  When more light is shone on the solar cell, meaning there's higher irradiance, the increase in J_PH will increase V_oc as well.  When there's higher temperature T, J₀ will be strongly affected and there will be more leakage current.  This is not shown in the equation, and will overwhelm the increase in T in the equation and cause V_oc to reduce.

The diagram above shows the power density curve, where a negative power density shows that the solar cell is generating power.  A positive power density shows that the solar cell is consuming/dissipating power, and the solar cell heats up.  There is a point of maximum power density generation called the maximum power point, where the power density is P_max, with corresponding voltage V_mp and current density J_mp.  The points where power density is zero is at V_oc and J_sc.

Hence: P_max = V_mp J_mp
And the shaded area in the diagram represents the power density generated.

Another external parameter called the fill factor FF is defined as follows:
FF = J_mpV_mp / J_scV_oc

Lastly, the conversion efficiency η of a solar cell is defined as follows:
η = P_max/P_in = J_sc V_oc FF / P_in

where P_in = 1000W/m² = 100mW/cm², the irradiance (power density of light) under STC (AM1.5, 25°C).

Hence, efficiency is expressed all in external parameters.

Reference:
3.2.1 External Parameters of an Ideal Solar Cell, Delft University of Technology, https://www.youtube.com/watch?v=ZyedIjJ6frI