In this video, we will continue our review of basic semiconductor concepts.

As I already mentioned, we're not really explaining things in this background

review. I just give you some basic, background

that you will need to know in order to follow the rest of the course.

And again, I promise you once we get to the meat of the course you will see things

developed in the rigorous way. So, in this video we will talk about the

energy concepts as applied to non-equilibrium situations.

And we will also talk about the relation between charge density, electric field and

electric potential. So non-equilibrium, non-equilibrium

basically means that you have energy exchange with the external world.

And for us, this would imply current flow. The equation that gives you the hole

concentration in terms of energy levels looks almost exactly the same as we've

seen with the, in equilibrium but instead of E sub F which was a single Fermi level

valid for both electrons and holes, you have something else, E sub Fp.

And, for the concentration of wholes, you have to get something else called E sub F

n. E sub F p and E sub F n are not Fermi

levels. They're called Quasi-Fermi levels, or

imrefs. Imref you can read it as Fermi, spelled

backwards. It also stands for imaginary reference.

So what basically we do here is we, we replace the Fermi level in the equations

that were valid for equilibrium with just the right quantities to give you the right

value for p and n. In general, the two Quasi-Fermi levels are

different for holes and electrons. And this is why when you multiply p times

n, the two exponents do not cancel out and you no longer have np call to an i square,

np calls to an i square and applies to equilibrium.

Otherwise in general the product here is different from a nice square.

We will now talk about the relation between charge density, electric field,

and potential. Many of you will have seen this material

in your physics or electrical engineering classes.

I will just give you a very brief one slide review.

And if you would like more information, you can consult appendix A in the book.

We will concentrate on the 1-dimensional case.

So here we have a piece of semiconductor. We assume that the charge varies

vertically, and we will consider a point y at which, the charge density, will be

denoted by row over y, the electric field by.

Script e of y, and the potential by c of y.

The total charge density can be due to holes, electrons, dome or atoms, and

acceptors. In the most general case all of these can

be present at the same time. Now, each of these 4 types of charges

carries an electronic charge. For example, one pole has a charge of q,

an electron has a charge of minus q, an ionized donor atom has a charge of plus q

And that ionized acceptor atom has a charge of minus q for reason that we have

already described. So, if you add all of this charges, you

end up with a total charge density which is the whole minus the electron density

plus the donor density minus the acceptor density all multiplied by the magnitude of

the electronic charge. In what we are about to write we will also

use something called the- The permittivity of the semiconductor, epsilon sub s, and

that is the permittivity of free space, epsilon zero, multiplied by the dielectric

constant of the semiconductor. And values for those quantities will be

given shortly. Now to relate electric field to charge

density, we have this relation. You may have seen it in the general form

in electro magnetic theory classes but here we show it in simplified form just.

In that 1 dimensional case. So the derivative of the electric field

with distance is proportional to the charge density.

And the constant of her personality's 1 over the permativity.

We can also relate the electric field to the potential If you combine these two

equations here. Specifically if you plug in this equation

into this, you end up with an equation that is called the Poisson equation, and

it is shown here. The second derivative with respect to

distance, is minus the charge density divided by the permativity.

We will have use for all of these equations in our discussion of

the[UNKNOWN] transistor. Now notice that in these equations you

ahve derivatives, but you can also have the equivalent Integral formulas.

So for example if you take the first equation here and you integrate both sides

from a point y0 which will be our reference point.

For example it could be equal to y equal 0 but in general we call it y0.

To a point y. You end up with this equation.

Which says that the electric field to y is equal to electric field at our reference

point. Plus 1 over the[UNKNOWN] times the

integral of the density between these two points.

This will be seen to be nicely illustrated graphically when we discuss The PN

junction. Let's now go to the second equation that

relates the electric field to the potential.

Integrating this equation, we get that the potential of point Y is equal to the

potential of our reference point minus the integran of the field from the reference

point to the point in question. Finally here I show you the a reminder of

what these various quantities mean. And also I gave you, values for the

quantities. So in this, video, we have discussed,

non-equilibrium in semiconductors very briefly and we also discussed the charge

density. Electric field and potential relations

that we will be using in our development of the [unknown] transistor

characteristics. In the next video, we will start talking

about conduction in semiconductors.