We see that this is a case of solar cells based on crystalline silicon.

The ideal operation involve several assumptions.

The first is perfect absorption of all photons

that have an energy greater than the bond gap which implies

the absence of reflection of the front surface of the semiconductor.

For example,

the second assumption is a perfect collection of a photogenerated carriers.

That is to say, lack of recombination in the p-n junction and

then perfect contact with the metallic electron.

The solar photon conversion mechanism is summarized in this field.

We have seen that from the electrical point of view a cell

behaved like a p-n junction out of equilibrium.

In parallel with the current source that corresponds to

the photogenerated carriers.

The characteristic of a non-equilibrium

diode follows the Shockley's law,

I = IS exponential- eV on kT- 1,

which is on parallel with source IL.

The final characteristic IV is presented here.

We also define two quantities, VOC which is open circuit voltage.

Which correspond to I = 0.

One the short-circuit current ISC corresponds to V = 0.

The solar cell acts as a generator in the third quadrant.

P = VI negative which is only illustrated here reversed.

The current per unit area JS depends on the characteristic of the semiconductor.

That is to say bond gap, diffusion constant of the carriers,

lifetime of electrons on holes, to n on to p, dumping densities and so on.

The VOC is obtained from the expression of the characteristic at I = 0.

We obtain an important cosecant from the solar cell operation.

VOC depends logarithmically on the photon flux IL.

Thus for example, VOC increases with the optical concentration.

The maximum of the power,

P equal VI corresponds to dP over dV = 0.

It can therefore be calculated analytically as shown here.

So short circuit current Isc corresponds to the photon conversion.

It is obtained from the interior of the spectrum of solar

photons integrated between Eg and infinity.

These quantities are reported in this figure, which again,

display the first quadrant of the curve IV.

We define the field factor FF, the ratio JmVm.

That is to say, maximum power divided by the area of the rectangle Isc, Voc.

The most characteristic will be close to the rectangle,

the greater the field factor will be.

In practical application FF can reach 80% or even above.

This figure shows a theoretical comparison of various semiconductors.

The two top curves correspond roughly to the crystalline germanium and silicon.

The more the bond gap decreases the more solar photons are absorbed,

leading to an increase of ISC.

We observe an opposite behavior for the Xs.

Voc depends on the bond gap still being slightly lower as we have seen previously.

We can evaluate the theoretical maximum conversion efficiency for

the various semiconductor.

Remember that the solar photons that have lower energy than

the bond gap are not converted.

More the gap is low, more this loss is weak.

In contrast losses by thermalization vary in the opposite way.

These opposing behaviors with EG lead to a compromise shown in this figure.

Bond gap of 1.34 slightly higher that crystalline silicon

corresponding to the better compromise between convection and degradation.

This corresponds to efficiency of 33% and

the ideal operating conditions is called the Shockley–Queisser limit.

It applies to the homojunction, that is to say a p-n junction,

based on single semiconductor material.

This limit is well below the thermodynamic limit, more than 80%.

The red dots correspond to the best yields actually achieved.