So in this video, I'm going to try to give an overview of semiconductor physics. And I'm going to be talking about, for electrical engineers at least, the central questions in semiconductor physics. The first of which is, how many charge carriers do I have?
So if I've got a certain piece of semiconductor, so maybe it's silicon, maybe it's some other more interesting one. Let's say it's silicon. We want to know within this block how many charge carriers, so electrons are an example of a charge carrier, how many of these do I have available to conduct current?
So if I just had a metal, we know that... the number of electrons available to conduct current in the metal is roughly equal to the number of atoms, but in semiconductors that's not the case and the reasons for that will become become clear as we go through the course. So this is the central, one of the central questions in semiconductor physics. The second question is where are they and how are they moving? So if I've got the same semiconductors above, say I've got some silicon with some electrons floating around, and say I want to apply an external electric field, I want to know how these charges or how these charge carriers are going to respond to that.
I want to know how the charge concentration is going to change within the semiconductor, what are other effects that I have to worry about, and how... How is this all going to play out in time? And lastly, sort of the underlying question of both of these is, how can I change these? And more than that, how can I make useful things out of them? So we're engineers, we're interested in primarily the practical applications of any physics or mathematics that we learn.
And so we're going to learn about in the later parts of these videos and in semiconductor physics in general, how you analyze things like MOSFETs, diodes, BJTs, among other things. So these are just the... Semiconductor physics is the starting point for analyzing all of these.
So up next, I'm going to give a little roadmap. So what's this adventure going to look like? Where are we going to start? So as you may have guessed, we're going to start with quantum mechanics, because everything starts with quantum mechanics.
And to a lesser extent, statistical mechanics. or STATMEC. And then with these tools, which are probably the most powerful tools we have at our disposal, including in addition to the conservation laws kind of sitting over here on the side, those are sort of an ever-present force in anything you do in physics.
So along with these two tools we're going to analyze semiconductors and in order to do that we're going to calculate things called the density of states. So electrons, how many states do they have to occupy within the semiconductor? And this is a quantum effect.
Basically, how much room is there for electrons? We're going to derive something called the energy momentum. And that's a k, but k is a stand-in for momentum.
Band diagram. And we're going to use these, and we're going to use band diagrams very heavily in semiconductor physics. If you understand band diagrams, you understand almost everything there is to understand about semiconductor physics. And we're going to use these band diagrams to calculate things like the effective mass. So...
As you might imagine, applying an electric field to a charge within a semiconductor is a little more complicated than just applying it to a charge in free space. So if I've got an electron and I apply an electric field to it, we want to know... what is its effective mass within a semiconductor?
So if it's within a piece of silicon. In other words, how do we easily relate what we know about how charges move in free space to how they move in silicon? And then the last thing we're going to go over is what are called Fermi statistics.
And these are closely tied to the density of states. And we're going to use all of these things so the band diagrams, density of states, and Fermi statistics, to answer the question, how many, or how many charge carriers do I have? And we're going to do that with an integral, basically. So we're going to integrate the density of states multiplied by our Fermi statistics over our energy band.
diagram. So all this is sort of brought together in order to answer our first question of how many are there. So you might ask, why have I been using the term charge carriers? Seems like an awfully complicated term for electron.
But in fact, in semiconductors, in addition to having the electron, we have what's called the hole. Which just acts like a positively charged electron and I'll have a video on this later But just to give you a sense of what's to come and to give you to prepare you for this rather bizarre Bizarre concept and so that is all to answer our question of how many so how many? Charge carriers are there in the semiconductor? The second question we want to ask is Where are they?
and how do they move? And in order to answer these questions, we're basically going to start with Maxwell's equations and probability theory. And don't worry too much if you're not super comfortable with these, because these are just sort of just the underlying fundamentals. We're not going to heavily use them other than in derivations.
And we're going to use these things to figure out how... how do carriers move in semiconductors? And the main mechanisms are called drift and diffusion. And so we're going to go over both of these. And as you might guess, one is sort of a slow motion along.
The other one has to do with concentration gradients and how things diffuse. And we're also going to go over carrier generation. and recombination. In other words, carriers aren't just sitting there, they're constantly being created and destroyed. And if we're interested in knowing how things vary with time, then it's important to understand this.
And interestingly, if you understand carrier drift, that leads directly to Ohm's law. So this is actually where Ohm's law comes from. And when I first took this class, this was probably one of the cooler things.
that I found out of it. It's like, oh, that's the bridge between circuit theory and semiconductor physics. And we're going to use all of these mechanisms after learning about them to derive what's called the continuity equation and the ambipolar transport equation.
And both of these things are nothing but a massive hammer. So they're just a differential equation sledgehammer that we're going to use for various semiconductor problems. And we're going to use that sledgehammer essentially to, and you'll see why I call it that.
It's rather complicated. We're going to use that to analyze p-n junctions. Once we analyze p-n junctions, we'll be able to understand things like diodes, which often are just p-n junctions.
Things like MOSFETs and BJTs, which collectively are known as transistors. There's other kinds of transistors as well, but these are two of the big ones. We'll also be able to understand optical devices.
So things like solar cells and photodiodes and LEDs. How do these things work and how do we use them? I hope you found this video interesting.
It's sort of an overview of semiconductor physics, where we're going to go with it. If you didn't understand anything in this video, most things in this video, you're not expected to, don't worry. We'll be going over them one by one, but this is sort of just to give you a flavor for what's to come.
And at the very end, this is probably going to be the latter half of all the videos I end up making, is the analysis and figuring out how to make these devices. And this is sort of the culmination of semiconductor physics is, okay, how do we actually understand transistors, diodes, optical devices, and how do we use them? And how do we apply our fundamental physics to fundamentally understand them?
So in the next video, I'm going to be talking about the very first topic, and that's going to be quantum mechanics.