Question

The current density of an ideal p-n junction under illumination can be described by:

J(V)=Jph−J0(eqVkT−1)
where Jph is the photo-current density, J0 the saturation-current density, q the elementary charge, V the voltage, k the Boltzmann's constant, and T the temperature.

A crystalline silicon solar cell generates a photo-current density of Jph=40mA/cm2 at T=300K. The saturation-current density is J0=1.95∗10−10mA/cm2.

Assuming that the solar cell behaves as an ideal p-n junction, calculate the open-circuit voltage Voc (in V).

Answer 1

0.674

Answer 2

J0=1.95∗10−10mA/cm2=1.95*10^-9A/m^2
Jph=40mA/cm2=400A/m^2
Voc=kT/q*ln(Jph/J0+1)
T=300K
k=1.35*10^-23J/K
q=1.6*10^-19C
J(V)=Jph−J0(eqVkT−1)
The open-circuit voltage is the voltage at which the net current is zero where J(Voc)=0
Solving for Voc we have
Voc=0.0253*ln((400+1.95*10^-9)/(1.95*10^-9))
Voc=0.659 V