Some important notes on semiconductor physics

Integrated circuit technology is easily my most difficult class right now -- it manages to use up every IQ point I can throw at it and still want more -- so I'm going to write down some of the essential stuff to get it straight in my own head. This isn't really intended to entertain readers, but hopefully it will help me. And not be too wrong.

The first thing to understand is how current flows in a semiconductor. I'll focus on a (possibly doped) crystalline silicon lattice here, rather than slightly weird stuff like III-IV semiconductors, for simplicity -- but most of the same stuff applies universally.

The Si atoms are covalently bonded to four of their neighbors in a regular pattern. Remember all that stuff about energy levels in the good ol' Bohr model of hydrogen? Well, forget that; in a crystal like silicon, those energy levels bifurcate and get all crazy, turning into energy bands. There are two big ones: the valence band and the conduction band. The valence band is the lower one, the energy levels that are filled at 0 degrees Kelvin. Those are the electrons that stick to the atoms or are shared between neighbors. The conduction band is higher energy; electrons there are free to move around through the crystal. If you want to ignore all the quantum stuff and stay far away from Schrödinger's equation, then you can think of those electrons as being little charges balls bouncing around.

But how do electrons find their way up to the valence band? There is a gap between the bands, creatively named the bandgap, which contains states that electrons cannot occupy. To get from one band to another, they have to jump across by either gaining or losing energy. Fortunately we're not operating at a temperature of absolute zero, so thermal fluctuations will kick electrons back and forth across the bandgap all the time. Don't trouble your beleaguered head about "phonons"; just think of the crystal as being kind of vibratey.

Since electrons are always going back and forth across the bandgap, how do we determine how many electrons we have in the conduction band, ready to do useful things? The answer is Fermi-Dirac statistics. Don't ask me to derive it, or even to explain it, but you can use a simple formula for the concentration of electrons in the conduction band in a pure ("undoped") semiconductor at a given temperature. This is called the "intrinsic concentration of charge carriers n_i".

The concentration of charge carriers determines how well a material conducts electricity. If there are lots of carriers (as in a metal, with no bandgap), then current can flow easily. If there are a tiny number of charge carriers (as in an insulator, with a big bandgap), then current has a deuce of a time flowing at all. But for semiconductors, the bandgap is middling thickness and the conductivity could go either way.

I should probably mention something about charge carriers now. The term refers both to electrons and to "holes", which are not really particles at all. Holes are gaps in the valence electrons. They move by being filled with electrons, thus leaving another gap in the electrons nearby. They're bubbles, essentially. Bubbles are just gaps in water, and they bubble up by being filled with water. If holes are moving then it also means that valence electrons are moving the other way. Both are perfectly valid ways of transporting charge. In undoped silicon, the number of holes is the same as the number of free (i.e. conduction band) electrons. This is because of the way that both are created: thermal fluctuations knock an electron out of the valence band, and this leaves a hole behind.

This isn't the whole story, though. To do useful things, we need to add small concentrations of impurities to the silicon, called doping. This can be done quite precisely, so let's not worry about how they manage this feat. For now, just consider what it does to the lattice. The impurities in silicon have either one more or one less electron in the outer electron shell than silicon. In other words, they come from one of the two neighboring columns of the periodic table. Once one of these impure atoms (like Boron or Arsenic) bonds to the crystal lattice, it either has an extra loosely-bound electron or a hole for an electron to fall into. These are called donor and acceptor impurities, respectively.

When you go introducing holes or weakly bound valence electrons into the lattice, you're going to play hob with that "intrinsic carrier concentration" stuff I talked about above. Since impurities are so much more likely to donate or trap conduction electrons than silicon, just a tiny dash of impurity comes to dominate the carrier concentration. The doped silicon becomes filled with either free electrons or with holes, and whichever dominates is called the majority carrier. Doped silicon in which electrons are the majority carrier is called N-type (the N is for "negative"), and where holes are the majority carrier we call it P-type. The carrier concentration in doped silicon depends almost entirely on the net concentration of donor or acceptor impurities. That is, donor and acceptor impurities cancel each other out and whichever side is left standing contributes the vast majority of the charge carriers.

At this point it's worth explaining how to visualize current in a semiconductor. If you're using my favored silly-bouncing-balls model of how charge carriers behave, then this should be fairly easy. Electrons and holes are always bouncing around like a bunch of flying bumper-car Pokémons or something. If there's no electric field, then this random movement does not make them go in any particular direction on average. It's a random walk. But when you put a voltage across, and there's an electric field pushing carriers in one particular direction, then they tend to shuffle and bounce more in one direction than the other. This produces motion of the electron cloud, though very slow. Think of it as being like water pressure in pipes: the individual water molecules don't have to move very far for an increase in pressure to be felt several meters away.

Charge carriers in doped silicon do this too. There's a key difference, though. In wires, you have a sea of electrons and that's how your current flows. In doped silicon, it's pretty much all electrons or holes. This only really starts to matter when we stick P-type and N-type silicon right next to each other, as we do in transistors and diodes. When that happens, the free electrons in the N-type silicon start filling the holes in the P-type silicon, and there forms a thin layer of silicon without enough charge carriers to conduct. This is called the depletion region. It stops current from flowing across the p-n junction (where the P-type and N-type silicon touches), but the depletion region can be made to shrink by putting an electric field across it.

This is how diodes work: they put P-Si (P-type silicon) next to N-Si, which creates a depletion region and shuts off current. But if you give the P-Si a positive voltage with respect to the N-Si, this pushes the electrons and holes closer together and makes the depletion region so narrow that charges can move again! This is why, after you put a voltage of about 0.6 to 0.7 V across a typical diode, it becomes essentially a conductor -- but it needs that voltage drop. And if you put the voltage across in the other direction, it doesn't make the depletion region narrower, so it doesn't lead to current flowing.


(Corrections will be welcomed with open arms.)