In the last chapter we left silicon mid-transformation: an enormous data-center humming in Virginia, eighteen trays of cooled metal carrying out a kind of work the rest of nature has never managed. To understand how any of that work happens — how a sliver of patterned rock, the moment electricity touches it, becomes arithmetic, then logic, then memory, then a thought — we have to step back into physics. Specifically, into the strange behaviour of an electron inside a crystal.
This is the chapter where we earn the word semiconductor.
A strange middle ground
Almost every material on earth is either a conductor or an insulator. Copper, aluminum, gold — push a voltage on them and electrons flow effortlessly. Glass, rubber, ceramic — push the same voltage and nothing happens, because their electrons are locked into chemical bonds and have no place to go.
Silicon is different. Push a small voltage on a piece of pure silicon at room temperature and a trickle of current flows. Heat it up and the trickle grows. Cool it to liquid-nitrogen temperatures and the silicon becomes nearly an insulator. Shine light on it and the current jumps. Pure silicon's behaviour is conditional in a way that copper's is not. It almost seems to decide.
That conditional behaviour — the fact that we can ask silicon "are you conducting right now?" and get a different answer depending on what we did to it — is the entire foundation of the digital age.
The band gap
Quantum mechanics gives us the explanation. Inside any solid, electrons cannot have any energy they like. They are restricted to bands — broad ranges of allowed energy — separated by forbidden gaps. The lower band, called the valence band, holds electrons that are bound to atoms. The upper band, the conduction band, holds electrons that are free to roam.
In a metal, these two bands overlap. There is no gap, so electrons are always free to move. That is why copper conducts.
In an insulator, the gap is enormous — about 9 eV in glass — far larger than the thermal energy available at room temperature (~0.026 eV). No electron can muster the energy to leap across, so none ever joins the conduction band. That is why glass insulates.
Silicon's gap is 1.12 electron-volts. Big enough that very few electrons cross it spontaneously at room temperature — pure silicon is a poor conductor — but small enough that with a modest amount of help (heat, light, or a carefully placed neighbour atom), enormous numbers of electrons can be promoted across. This is the band gap of choice: large enough to keep silicon stable, small enough to make it manipulable.
Conductors say yes. Insulators say no. Semiconductors say "depends on what you do." Our entire civilization runs on what they say next.
Doping — the masterstroke
Pure silicon is a curiosity, not a technology. The masterstroke that turns it into a switch is doping: deliberately introducing a few foreign atoms — one part in ten billion at the lightest, one part in ten million at the heaviest — to flood the conduction band with carriers.
Silicon has four valence electrons; it sits in column IV of the periodic table. Slip in a phosphorus atom (column V, five valence electrons) and four of phosphorus's electrons participate in bonds with neighbouring silicons. The fifth has nowhere to go — it is loosely bound, easily kicked into the conduction band. Add enough phosphorus, and the silicon now has a sea of mobile electrons. We call this n-type silicon (n for negative carriers).
Slip in a boron atom (column III, three valence electrons) and the situation reverses. There is now a missing electron — a "hole" — in the bonding lattice. Holes behave, mathematically, as if they were positive charge carriers, drifting through the crystal as electrons hop into them from neighbour to neighbour. This is p-type silicon.
Modern chips dope silicon at concentrations as low as 1013 dopant atoms per cubic centimeter — about one foreign atom per billion silicon atoms. This is why Chapters 1-3 of this book obsessed about purity. You cannot dope to one-in-a-billion if your starting material already contains one-in-a-million of the wrong thing.
Rocks that switch
Place a slab of n-type silicon next to a slab of p-type silicon — what physicists call a p-n junction — and remarkable things happen. Free electrons from the n-side rush into the p-side to fill holes; holes drift the other way. A region empty of mobile carriers forms at the boundary. An electric field builds up, opposing further migration. Equilibrium settles. You now have a one-way valve for current — a diode.
The p-n junction was demonstrated by Russell Ohl at Bell Labs in work culminating in February 1940, and it is the conceptual ancestor of every device in this book. Once you can build a region of crystal whose conductivity depends on which way you push, you can build a region whose conductivity depends on a third electrode hovering nearby. That third electrode gives us the transistor — the gate that decides whether current flows or doesn't.
What we have, when all this comes together, is the trick we have been after the whole time: a rock whose ability to carry electricity is no longer a property of the rock but of what we have done to a particular spot of it. Silicon has stopped being a material and become a stage on which voltages can play.
In the next chapter we walk on that stage and watch a single transistor turn on.