In this video, we will discuss the conduction mechanisms in semi conductors. In other words, the mechanisms responsible for the flow of electric current. Let's consider a bar of semiconductors shown in white over here. Sandwiched between two conducts. Assume that this made perfect contact with a semiconductor. And we're mostly interested in what happens inside the semiconductor here. Let's say that for some reason, electrons are moving toward the right, as you see here. Negative electrons, moving to the right, are equivalent to a positive charge, moving to the left. That's why when we define the current in this way it is positive. The total charge inside this bar of semiconductor will be denoted by Q. And I will assume uniform motion with transmit time tau. So I'm assuming that all of these electrons, move smoothly, which, actually, in practice they don't. But for now, assume they move smoothly, and that it takes an electron a time tau, to go from the beginning to the end. So let's start counting time. An electron found here, after tau seconds, moves all the way out. And that means, all of the charge that was ahead of it, also has moved up. That means that the total charge that has moved is Q, in time tau. And the current, which is, basically, the rate of change, the flow of charge with respect to time, will be Q over tau. And I'm putting an absolute value sign because, as I said before, the current is positive, in this case. Solving this equation for tau, we get tau equals to charge magnitude over the current. And sometimes this equation is actually used as the definition of transit time. Now, conduction is due to two mechanisms. One is called drift, and it has to do with carriers moving because of the presence of an electric field. And the other is diffusion, that is caused by concentration gradients. We will discuss each mechanism separately, starting with drift. So let us talk about drift. Let us consider a bar of semiconductor, the white area, shown here. And it is sandwiched between two contacts, the dark regions. We apply a potential on the right hand contact, with respect to the left hand contact V, and V is assumed to be positive. Now this will create and electric field in this direction, and consequently the electrons, being negatively charged, will move towards the right, towards the plus of the battery, if you like. Now the movement of electrons is something very complicated, because it has to do with the thermal agitation of the crystal lattice of silicon, at temperatures above absolute 0. And as the electrons collide with the atoms, they acquire a complicated type of motion. We will not need to describe this complicated motion. And instead, we will assume that the average velocity towards the right is the same for our electrons. And we call this velocity, drift velocity, and denoted by V sub d. Now, drift velocity depends on the electric field. You expect that the higher the electric field, the more the drift velocity will be. And, indeed, that turns out to be the case. Here, we have plotted drift velocity versus electric field. And although both quantities are positive, in the particular example we are discussing, I have placed absolute values here, so that this plot is valid in other cases, as well. So you can see that at low field, the drift velocity is proportional to the field itself. But at high fields, the velocity tends to saturate. This phenomenon is called velocity saturation, and it is due to the fact that if the fields are very high, although this means that the electrons try to accelerate very much. They hit atoms that collide with them with force, and they lose their energy and their momentum, after one collision. Then they accelerate again, they collide again, they lose energy, and the interplay between the energy they get through the field, and the energy they lose because of the collisions reaches a balance. And after that, the drift velocity cannot increase anymore, so you reach such a ratio like this. So at low fields, this straight line represents the drift velocity, and can be described by an equation of the 4 mu sub V times the magnitude of the electric field intensity, where mu sub V is a constant of proportionality called the mobility. And the subscript B stands for bulk, and this is the bulk mobility that is valid when electrons are moving, in the bulk of the semiconductor. And we use the subscript B to distinguish this from the so called surface mobility that we will find at the surface of semiconductors later on, when we discuss utmost transistor. Continue with drift, here we have the same situation as before, but I have indicated geometrical dimensions. A is the length, B is the width, and C is the depth of this bar. As we have shown, the current is the magnitude of the charge, at any given moment in the semiconductor, divided by the transit time. Now the transit time is the length of the bar divided by the drift velocity. And, therefore, if you plug in this into tau, you end up with this. What I have multiplied and divided by the same quantity b, and I did this in order to make ba up here, ba, as you can see, is the product of this dimension times this dimension. So, in other words, it is this area over here, it's the surface area. So now q over A, A standing for this area, is the charts per unit area, which we will denote by q prime. Like this. So now you can see that the current is the width of the bar, times the charge per unit area, times the drift velocity. This equation will be useful for us when we discuss utmost transistors. Continue with drift velocity. Again, I repeat the previous plot, velocity versus selected field, and now, I will concentrate on the low field case, in other words, we are in this region over here, where this equation applies. This is the equation we derived on the previous slide, the current is the width of the bar, times charge per unit area, times v sub d, the drift velocity. The drift velocity's mobility times electric field, and the field itself is the voltage from the right to the left contact, divided by a. So this is in volts per meter, which are the proper units for electric field. So you replace electric field by this, and the result into here, and you end up with this equation. Which says that the current is the mobility, times the charge per unit area, times the ratio of the width to the length, times the voltage. Now once we apply this equation to the utmost transistor, b will be the width of the transistor channel, and a will be the length of the transistor channel. So you see now here appearing the ubiquitous w over l. That if you have used any equation for the utmost transistor, you have already seen. So all of these equations will become directly useable for us once we start discussing immersed transistors. Now let's take everything in front of v, and call it G. Then, this equation reduces to I is equal to G times V. This is nothing but Ohm's law with G being the conductance. So you, we have derived Ohm's law. It is clear that we were able to do that, because we limited ourselves in the region, where drift velocity is proportional to electric field. At higher values of the field, Ohm's law would not apply, but for low fields, it does apply. Now, as I mentioned before, the transit time is the length of the bar divided by the velocity. If you now replace the drift velocity by mu times e, and replace e by V over a, you end up with this equation for the transit time. So in this equation, let's see if it makes physical sense. The larger the mobility, the smaller the transit time, because larger mobility means that for a given field, the electrons move faster. The larger the voltage, the smaller the transit time, because for a larger voltage for a given horizontal dimension here, we have a larger field. And in the numerator, we have the length of the bar squared. Why is it squared? Let's say you double the length. If you double the length, then the electrons have to go twice the distance, so they take longer. But, in addition, the field being V over a, becomes half as much. So, the motivation for electrons to move becomes half as much. So, in other words, increasing the length hits you in two ways, and this is why you have a squared over there. Later on, we will find that the a is the length of the transistor channel, and then, you start seeing why we tried to make transistors as small as possible. When the channel length is large, the transit time becomes large, and the device becomes slow. In this video, we have discussed the first mechanism of current conduction, drift, which is due to the presence of electric fields. In the next video, we'll discuss the second conduction mechanism, that has nothing to do with electric fields, namely, we will discuss diffusion.