# Solar Cell Temperature and Efficiency

It is a common misconception that higher the temperature higher is the output of the solar cell. This is not true as the efficiency of a solar cell decreases with increase in temperature and lower efficiency results in lower output power. So in fact a bright sunny day, with sun rays perpendicular to the solar panel and a cool weather is the ideal combination for higher performance of a solar panel.

Let us now look at this in a bit more detail. There are two basic reasons for decrease in efficiency due to increase in temperature.  One is the decrease in the band gap energy (Eg) and the other is the decrease in open circuit voltage (Voc) with increase in temperature. The relationship between band gap energy and and temperature is quite straightforward and is given as.

$E_{g} = E_{g}(0)+\genfrac{}{}{1}{0}{\alpha T^2}{T+\beta}$ One might argue that the decrease in band gap would allow for more carriers to be transferred to the conduction band and yield a higher output power. However this is not true as the output power is the product of current and voltage and a lower voltage would reduce the power. In fact there is an ideal range of band gap which produces the maximum energy. Going too high or too low would not yield the optimum results.

Next we turn out attention to the open circuit voltage Voc. The relationship between temperature and open circuit voltage is not that straightforward. At first it might seem the open circuit voltage increases with increase in temperature as shown in the expression below.

$V_{oc} = \genfrac{}{}{1}{0}{k_{B} T}{e} ln \biggl[1+\genfrac{}{}{1}{0}{J_{L}}{J_{s}}\biggr]$

But in reality this is not the case. Increase in temperature results in increase in intrinsic carrier concentration n which in turn results in higher reverse bias saturation current Js. There is a squared relationship here so increase in intrinsic carrier concentration would cause a very large increase in reverse bias saturation current. And as is evident from the above formula this causes a decrease in open circuit voltage. This is also shown in the figure below. So to conclude a bright sunny morning in winter might not be the worst time to produce some solar energy (provided you have got your solar panel tilt right 🙂 ).