We just discussed in the next three,

the p-n junction at equilibrium.

Now we will calculate the current as a non-equilibrium p-n junctions.

In particular, we will demonstrate the Schockley's law.

Recall that for example electrons,

the current consist in two contributions,

the current drift on a diffusion current.

In fact at equilibrium,

these two terms are both large.

The electric field is very strong in the space charge region at the interface.

On either, there is a high concentration difference between the n and p regions,

the diffusion currents are also very large.

Both contribution are capacities completely are at equilibrium.

Out of equilibrium, we will consider that

the resulting current is negligible as compared to both contributions.

This assumption will be contentatively checked at the end.

We will determine the current is a junction as well as

a minority carrier concentration as the boundary of the space charge regions.

In particular, it will be shown that when applying an external potential to the junction,

the concentrations at the limits of the space charge zone

vary from equilibrium conditions.

This variation of concentration at the edge of the space charge region

induces a diffusion current thus,

explaining the behavior of the junction in the case of the reverse bias.

I remind you that we have the Einstein relations also.

Therefore, by using the above relations at the limit of the p region,

we obtain the following expressions in the presence of an external voltage, Ve.

So applying a voltage, Ve,

creates a concentration different as compared to equilibrium N X equals D prime P,

that is to say as the limit of the space charge region,

the variation in concentration is given by this expression.

This change in concentration at the boundary of the space charge region,

will therefore induce a diffusion of minority carriers.

This is what explains the current of the minority carriers in the case of reverse bias.

According to the sign of Ve,

we see that there is injection or extraction of minority carriers.

Therefore, the p region in fact,

behaves as a system wherein the surface

is maintained at different as refered to the equilibrium concentration

for the minority carriers which creates a diffusion current as seen in appendix two.

We can make a similar argument for the holes at X equal N plus

D prime N. We obtain the following expression for the minority areas.

Finally, we obtain the total current of electrons on holes,

neglecting recombination in the space charge region.

We obtain the Schockley's law,

which is given by this expression,

where Js is called the saturation current.

So, the total current is given by Js multiply by exponential,

eVe, is the external voltage on kT minus one, Schockley's law.

So when Ve increases,

the current increases exponentially.

That explains the asymmetric behavior of the diode used in an inverter.

Finally, this numerical calculation shows

the resulting current is actually of the order of 10 order of magnitude,

smaller centigrade current for example.

So, the current that appears in non-equilibrium is very small compared to

the two contribution drift on diffusion than compensated at equilibrium. Thank you.