# Do Numbers Make Sense

Press Release

"The Fraunhofer Institute for Solar Energy Systems ISE, Soitec, CEA-Leti and the Helmholtz Center Berlin have jointly announced that they have achieved a new world record for the conversion of sunlight into electricity using a new solar cell structure with four solar subcells. Surpassing competition after only over three years of research, and entering the roadmap at world class level, a new record efficiency of 44.7% was measured at a concentration of 297 suns. This indicates that 44.7% of the solar spectrum's energy, from ultraviolet through to the infrared, is converted into electrical energy. This is a major step towards reducing further the costs of solar electricity and continues to pave the way to the 50% efficiency roadmap".

"These solar cells are used in concentrator photovoltaics (CPV), a technology which achieves more than twice the efficiency of conventional PV power plants in sun-rich locations. The terrestrial use of so-called III-V multi-junction solar cells, which originally came from space technology, has prevailed to realize highest efficiencies for the conversion of sunlight to electricity. In this multi-junction solar cell, several cells made out of different III-V semiconductor materials are stacked on top of each other. The single subcells absorb different wavelength ranges of the solar spectrum".

## A Closer Look at the Numebrs

Let us now try to validate the numbers given above.

Power is the product of voltage and current.

Pideal=Voc Isc=(4.165)(0.1921)=0.8001Watts

Pmax=Pideal*FF=(0.8001)(0.8650)=0.6921Watts

This is the power produced by 5.20mm2 of solar cell.

1mm2 of solar cell would produce 0.1331Watts.

1m2 of solar cell would produce 133.1kW of solar energy.

This is the power generated due to 297.3 suns.

A single sun would produce 133.1kW/297.3=447.67Watts of power.

This gives us an efficiency of 447.67/1000=0.4477=44.77%.

# Solar Cell Temperature and Efficiency

It is a common misconception that the higher the temperature higher is the output of the solar cell. This is not true as the efficiency of a solar cell decreases with an 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 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 the decrease in efficiency due to the 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 the increase in temperature. The relationship between band gap energy 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 the 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 our 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 the 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. An increase in temperature results in an increase in intrinsic carrier concentration n which in turn results in higher reverse bias saturation current Js. There is a squared relationship here so an 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 🙂 ).