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In this video, we will discuss an important combination of materials for us,

the pn junction, a junction between a p and an n region.

We start with pn junctions with zero and forward biased.

Let's start with zero biased. To biased the junction with 0 volts, we

connect an external wire, as you can see here, between n and p.

All of this region is n. And all of the regions is p.

I'm assuming that this is a Step junction, which means that we have uniformly doped n

region and a uniformly doped p region, and there is a sharp boundary between them.

Now, because you have plenty of electrons here, electron, and very few electrons

here in the p region, electrons tend to diffuse downwards and at the same time,

holes are in plenty of supply in the p region and they tend to diffuse upwards.

When electrons diffuse downwards, they leave behind positively charged donor

atoms and when holes diffuse upwards, they leave behind negatively charged acceptor

atoms. The region here, consisting of positively

charged donor atoms and negatively charged acceptor atoms, is called the depletion

region. We will make the simplifying assumption

that the edges of this depletion region are sharply defined, as shown in the

figure. Overall, the structure is neutral, because

these pluses cancel these minuses. Now, why doesn't this process continue?

Why don't even more electrons diffuse down and holes diffuse up?

The reason is that you have now developed an electric field in this direction, which

tends to prevent holes from moving up and also tends to prevent electrons form

moving down. You have a charged density in the

depletion region and when you integrate it twice, you end up with a potential across

the depletion region. This would be called the built-in

potential of the junction. Now, how is it that we have a potential

here despite the fact that we have 0 potential difference between the contact

of the junction? Well, the reason is understood if you use

the material in the, the contact potential lecture, there is not only a contact

potential between n and p, but there is a contact potential between n and this

material here, that I used to contact n. There is a contact potential from here to

there, to the y, similarly here. And if you start this point and end up

with this point, the sum of all contact potential is 0, which is consistent with

the fact that you have sorted the junction.

If you break the wire here, the situation remains the same as when you have the

junction sorted. Now, let's see how the energy bands look

like in this structure that is in equilibrium.

Since it is in equilibrium, we have a single Fermi level throughout.

And locally, in the inside, by the way, this is the energy band that you get when

you take this structure and you rotate it 90 degrees in this direction.

So, n comes to the left and p comes to the right.

This is the n-side and this is the p-side. Now, let us look at the situation on the n

and p sides, away from the diffusion region.

Locally, on the n -side, the situation looks like I have shown to you for

equilibrium and type material in the past. And luckily over here, this usually, this

situation looks like it should for p-type material.

For this to be consistent with the fact that the Fermi level is constant

throughout, the bands have to bend, as shown like this.

And as we know, the bottom of the conduction band represents potential

energy for electrons. And if it goes up, it means that the

corresponding potential goes down because the charge of an electron is negative.

Energy per unit energy divided by the negative charge, will give you a delta C

that will be the opposite from delta EC, the change in the conduction band level.

The total change in potential is the built-in potential.

It's this quantity over here. And therefore, in the energy band,

multiply by 2 and you get the corresponding energy band bending here.

We know already that the contact potential of this region with respect to this region

is going to be the difference between the corresponding work functions, but an

easier way to see what happens here is this.

The total band bending here is the sum of this distance here which is q phi Fn.

Q is the electron charged band [unknown] and phi Fn is the Fermi potential for the

n-type region, which we have discussed before.

And the total distance here is correspondingly q phi Fp.

Phi Fp being the Fermi potential for the p-side.

So then, the total bending, the total bending for this or for this level, is the

sum of this and that. But because they have opposite signs, you

have to take this one and subtract this negative quantity to get the total.

So phi Bi is the built-in potential of the junction and depends, of course, on the

doping concentration because the Fermi potentials depend on doping concentration.

It can be several tenths of one volt, close to a volt depending on doppler

concentration. Let us know look at the same junction but

forward biased. So, we apply a voltage V between the

p-side and the n-side. Now, this positive terminal here has a

tendency to make holes moving in that direction and the negative terminal here

has a tendency to make the electrons moving the opposite direction.

What I'm saying is just the fundamental logical way of explaining things to help

you remember things. The, the actual physics of this are rather

complicated. The net result is that now, the depletion

region width becomes less than before. And because we are pushing through the,

the, the supplication of potential, we are pushing holes go up and electrons go down,

there's a net positive current that flows through the junction.

And if you plot I verses U, you find the well-known exponential relation for pn

junctions or diode. Now, let's look at the energy band because

we are a non-equilibrium. And why are we non-equilibrium?

Because now, the structure can exchange energy with the external world.

The external world being the, the voltage source that we have applied.

The energy bands now look this. Far away from the divisional region and

the n material we still have the same situation as before.

And far away from the depletion region, we still have on the p-sides, the same

situation as before. Because of the polarity of the externally

voltage which has the plus connected to the p and the minus connected to the n

there is a higher energy on the n-side, for the electrons there.

And therefore the quasi-Fermi energy level e sub Fn on the n-side is higher than the

corresponding quasi-Fermi level is e sub Fp on the p-side.

For this to happen, the bands must bend. You will recall in the previous slide when

we had zero bias, that bending was q times phi Bi, the built-in potential.

So now, they will bend, but they will bend less by an amount corresponding to the

difference of the two Fermi levels. And that difference is basically V, the

externally applied voltage. So, instead of q phi Bi, you now have q

times phi Bi minus V. That means that the corresponding change

in potential versus distance is now phi Bi minus V, which shows that the total band

bending decreases by an amount which depends on the externally applied voltage,

V. Large currents can flow and one way to

describe this effect is to say that before the band bending was larger, which means

that from the n-side, the electron phase, the energy barrier which was large enough

to prevent many of them from flowing. But now, the energy barrier has been

reduced, the band bending is less, so more electrons can make it to the other side.

Correspondingly, more poles can make it to the left.

So, in this video, we have seen pn junctions under zero biased and under

forward biased. In the next video, we will talk about

reverse biased pn junctions, which is actually the case of most [unknown].