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In this video we will discuss Contact Potentials.

The electric potentials that develop when you join 2 dissimilar materials together.

So let us assume we have 2 materials, M1 and M2, well separated from each other.

And we want to find out what happens when the 2 materials are Join together.

First of all I would like to define something called the work function of a

material. The work function is the energy it takes

to go from the Fermi level to the so called vacuum energy level.

Which corresponds to the energy-level of an electron, removed far away from the

material so that it is not influenced by it.

In this particular example, you can see that the work function of the first

material is large, smaller than the work function in the second material.

Now, the formula, well, loosely speaking, are a measure of how energetic the

electrons are in the corresponding material.

And as we have seen when we discussed semiconductors, they're also a measure of

how heavily populated the materials are with electrons or with holes.

Let's assume that we have plenty of electrons in material M1.

When you join the two materials together, as we have done here, the electrons that

are in, a large supply in M1 have a tendency to move towards M2 so they

diffuse in this direction. But as they do that, they leave behind, in

M1, positive charges because M1 was initially neutral, now electrons,

negatively charged, have moved to the right so they leave behind positive

charges. These positive charges now have a tendency

to attract the electrons that have moved into M2, back into M1.

In other words to go in this direction. And finally, an equilibrium is reached

where a certain number of positive charges has been revealed in M1 and it is such to

just counteract the farther diffusion of electrons from M1 to M2.

Sometimes people say that in this case drift current exactly cancels diffusion

current. Anyway, after you reach certain

equilibrium, instead of having two different Fermi levels, you must have a

single Fermi level. As we already know from our discussion of

equilibrium. And to make the two Fermi levels equal,

the rest of the banked edges, a conduction banked edge and the balanced banked edge

must bent. And they do, in order to support the

electric field. So what happens is that the energy band

bending has a corresponding electric potential change shown here.

As phi M1 comma F2. In the particular example, that I gave

you. The M1 material is more positive than the

M2 material, in terms of potential. So, the contact potential from one to the

other which we denote here with an arrow phi M1 M2 is positive.

And the total potential is the difference between these 2.

In the particular example here phi WM2 is larger than phi WM1 as you can see.

On the left, and therefore, the contact potential from M1 to M2 is positive.

Now, there is another way to see this. Let's assume that M1 and M2 are already in

contact. So we're trying to calculate their contact

potential phi M1, M2. We place the materials in a loop with

another reference material. But I will cheat, actually, and instead of

the reference material I will have in mind the vacuum level.

Then instead of the contact potential between the reference material and

material M1, we have the work function potential of M1.

An extent of the contact potential between the reference material and M2, we have the

word function potential of material M2. If you're not considering this as a loop,

as if it were a circuit for which you can write a [inaudible] of voltage law, you

sum all the contact potentials in the loop and they must add up to zero, so we have

phi M1, M2 is equal to phi WM2 minus phi WM1, which is the same result as we got

before. Now, let's look at something interesting.

Let's take several materials in series. M1, M2, M3, and so on.

All the way to M sub N. And let's look at the potential between

points K and L, something we will call psi KL.

What is the value of that? Well, we can find it by adding the contact

potential from M1 to M2 plus the contact potential from M2 to M3 plus and so on.

Plus the conduct potential of M, M minus 1, to MN.

So adding all these potentials, for example I show the first two.

We see that the first conduct potential, according to the formula I showed you

before, is phi W and 2 minus phi W and 1. The second potential over here is phi W

and 3 minus phi W and 2 and so on. Yo can see that Fi w and 2 appears here

with a positive sign and here with a negative sign so the 2 cancel out.

Similarly this one will cancel out with another term over here and so on.

And in the end the only terms that will appear Is phi w,m1 and, and phi m,n.

In other words, only this and this will have an influence in the overall

electro-static, electric, electric potential of psi k,l.

So, the result then is this. So, what have we shown here.

We have shown that sum of conduct potentials, only depends on the first

material and last material. All of the other contact potentials in the

loop cancel out. That will turn out again to be important

when we discuss those transistors. Now let us consider the same combination

of materials as before. And ask this question.

Can the potential we just calculated be measured?

So I'm going to take a volt meter. And attach these two terminals like this.

What will be the voltage measured by the voltmeter?

You might be tempted to say it's going to be psi KL, the, the mater, the vo,

potential we just calculated, but that's not the case because you don't have only

the materials M1, M2, M3 and so on and Mn, you also have the material of the

voltmeter. Lead.

And that material, let's call it mu, could be aluminum, could be copper, you name it,

is the same for the two leads. Now you have to apply what we just learned

before, that the total quan-, potential from one material all the way through

other materials back to this material, has to do only with a difference of work

function potentials between the first and the last material.

But the two are the same. And therefore, the total potential of the,

the volt meter measures is zero. This is why we can not measure contact

potentials with volt meters. You can measure them, but you need

elaborate techniques that are discussed in the physics handbooks.

Even if the two leads were made of the similar materials, eventually inside the

volt meter you would still have to take into account that you have to end up with

the same materials and then, the total voltage the voltmeter will measure is

zero. Finally let's take this first case.

Where we know that the potential at CKN is given by this.

Let's interrupt this and insert the battery here, as I showed you here.

Now, as we go around the loop. The potential that you see is higher than

before. By the battery voltage.

So instead of seeing this, you actually see the same thing plus the voltage of the

source. And if you now attach a volt meter here

and there. Before you were seeing 0.

Now you will actually see, the voltage of the source.

So this is why a volt meter measures the voltage of a battery.

And it doesn't matter what other materials you may be using, if they have wires to

connect to the battery. So in this video, we discuss contact

potentials. And in the next video, we will apply what

we learned here to a very important contact for us, the p-n junction.