What is the physical explanation behind the decrease of open circuit voltage as temperature increases in an amorphous solar PV cell? I have researched and looked at several papers describing the effect of temperature on the $I_{sc}$ and $V_{OC}$, and seen many numerical explanations as to why the voltage drops, with reference to I-V curve and other equations, but none actually described why this physically happens. What causes voltage to drop at increased temperatures. Is it the decreased bandgap? It would be appreciable if you could link any related papers that explain this phenomenon physically.
Thanks
 A: We can begin with the equation for solar cell current
$I=I_0(e^{qV/kT}-1)-I_L$
The open circuit voltage is the voltage when current ($I$) is 0. Solving the above equation gives us
$V_{oc}=\frac{kT}{q}\ln\left(\frac{I_L}{I_0}+1\right)$
A temperature increase causes an increase in the intrinsic carrier concentration which in turn increases the diode saturation current $I_0$. Since $I_L\gg I_0$ the $+1$ can be ignored and this equation can be rearranged as
$V_{oc}=\frac{kT}{q}(\ln I_L-\ln I_0))$
The change in $V_{oc}$ can clearly be seen here as a function of temperature, both in the $\frac{kT}{q}$ term and in the $I_0$ term. These have opposing effects, and it turns out even inside $\ln$ the change in saturation current ends up dominating the temperature effect.
Part of the change in intrinsic carrier concentration comes from the reduction in bandgap, and part of it comes from the smearing of the Fermi distribution.
A: The saturation current is in a direction opposite to the illumination current and therefore an increase in temperature increases the saturation current and reduce voc.
A: The Fermi-Dirac statistical distribution expresses how carriers populate energy levels
$$\hat n(E) = \frac{1}{e^{{\epsilon-\mu}/{k_BT}}+1}$$
And this is how it looks like at different temperatures (taken from Wikipedia):

And this behavior represents the fact that electrons can be excited spontaneously by thermal energy (e.g., received from phonons), therefore they have higher chance of populating higher energy levels.
This smears the distribution and weakens the interatonic bonds (based on valence electrons), which effectively decreases the bandgap.
Since the open-circuit voltage is directly related to the bandgap (as the potential drop across a p-n junction is related to the band alignment), this also decreases the open-circuit voltage.
