Recombination and open-circuit voltage in solar cells

[Mayan Fung]

TL;DR

How does recombination in solar cells reduce the open-circuit voltage?

From the ideal diode model, we can derive the open-circuit voltage (Voc) as:

$$ V_{oc} = \frac{nkT}{q} ln(\frac{I_L}{I_0} + 1) $$

where $I_0$ is the dark saturation current and $I_L$ is the light generated current. From the model, if the recombination rate increases, the dark saturation current also increases, thus resulting in a smaller Voc.

I wonder if there is a more intuitive explanation on the Voc loss. As a naive picture, I am thinking that the original voltage is determined by the bandgap of the material. When recombination occurs, the hole-electron pair annihilates and release heat (or radiative recombination). It seems that in this picture, it is the current but not the voltage which is affected by recombination. Is there any intuitive explanation to address the Voc loss?

 

[Henryk]

The current across a regular diode is given by the Schottky formula $I = I_0 ( e^{\frac{eV}{nkT}})$. When you short the diode terminals and shine a light on the junstion, it will produce light current $I_L$. Open circuit voltage means no current, that is the light current cancels exactly the forward current of the diode. That's how you get the forumula for the open circuit voltage