It’s been a long time since I updated this blog. I keep saying I want to get back to it, but every time I post anything, it leads to a stream of abuse from trolls and crackpots, and the frustration drives me away. But I shouldn’t let a pack of bullying assholes do that! So I’m going to give it another try. I’m going to be a bit more aggressive about policing the comments, and probably write more longer, but less frequent posts, instead of trying to keep a pace of 3 or 4 per week like I used to.

To get started, I’m going to do some writing about computers.

Last week, my son was saying that he loves programming, and understands on the code level how a computer works, but he has no idea of how a bunch of electrons moving around actually make that happen.

My father was a semiconductor physicist, and when I was a kid, he spent a lot of time teaching me about math and physics, and he did a great job explaining how computers worked to me. I don’t remember exactly the way that he taught it, but I remember a lot of it, so I thought I’d try to pull it together with other material, and see if I could rebuild what he taught me.

As usual, we need to start with some basics. To be clear, a lot of what I’m going to say is an extreme simplification. This isn’t a simple area – the real, full depth of it involves pretty deep quantum physics, which I don’t pretend to understand. And even for professionals, there’s a lot of craziness and inaccuracy in how things are explained and taught.

Conduction

The most basic thing to understand is: what is an electrical circuit? What does it mean for something to conduct electricity? From there, we can start building up our understanding of basic components like resistors and diodes and transistors, and then how to put those together into the building blocks of computers.

We all know from school that matter is made up of atoms. The atom has a core called the nucleus which is made of a collection of positively charged protons, and neutral (chargeless) neutrons. Whizzing around the nucleus are a bunch of tiny negatively charged particles called electrons. (Remember what I said about simplifications? This is very much one of them.)

The electrons aren’t just whizzing about willy nilly – there’s a structure to their behavior, which is described by some of the most introductory parts of quantum physics. Electrons fall into specific states around a nucleus. The states are divided into shells, where the first shell is closest to the nucleus; the second shell is a little further, and so on. Every electron associated with an atom is associated with one shell. An electron can only be in a shell – it’s impossible to be in between shells; that’s what the quantum of quantum physics means: there are discrete states with nothing between them.

Each of the shells can contain a certain number of electrons. The first shell can contain at most two electrons; the second shell can contain eight electrons; the third can contain 18 electrons.

Once a given shell is complete, it becomes very stable. For example, helium is an atom with two protons, and two electrons. It’s only got one shell of electrons, and that shell is complete (full). That means that it’s very difficult to add or remove electrons from a helium atom, and helium won’t form compounds with other atoms.

The inner, complete shells of an atom are almost inert – you can’t get the electrons in them to move around between different atoms, or to be bound to multiple atoms in a chemical bond. Only the outmost shell – called the valence shell really interacts.

Now we get to another of those simplifications. There’s a whole area of theory here that I’m just handwaving to keep this comprehensible.

In addition to the valence shell, there’s something called the conduction band. The conduction band is the next electron shell out from the valence shell. When energy is added to an atom, it can push electrons upwards by a shell level in a process called excitement. When an excited electron is in the conduction band, it’s got enough energy to move around between different atoms.

The conductivity of a material is determined by the difference between the energy band of its valence electron shell and its conduction band. When the valence shell and the conduction band overlap, the material conducts electricity well, and it’s called a conductor. All metals are conductors. When there’s a significant separation between the valence shell and conduction band, it’s a non-conductor. Most non-metals fit into this category. Finally, there’s a third group of materials that fits in between – where its valence shell and its conduction band are close, but not overlapping. These are the semiconductors. We’re going to talk a lot about them, but we’ll come back to that in a little bit. Before we can really talk about them, we need to understand how an electrical circuit works.

So let’s think about a simple circuit – a battery connected to a light bulb. We’ve got two terminals – a positive terminal, and a negative terminal, with different electrical fields. If there’s a path that electrons can move through between the terminals, then there will be an electromotive force produced by the field that pushes the electrons from the negative to the positive until the fields are equalized. In between, we have the light bulb, which contains something that isn’t a very good conductor – but there’s that electromotive force pushing the electrons. If it’s strong enough to push through the weak conductor, it will heat it up, and cause it to glow, consuming some of the energy that’s contained in the difference between the fields of the battery terminals. So electrons get pushed from the negative terminal through the wire, through the bulb, and all the way to the positive terminal. In this circuit, we call the strength of the difference between the electrical fields of the terminals voltage, and we call the number of electrons being moved current.

We tend to think of it as if electrons are moving from the negative terminal to the positive, but that’s not really true. Electrons don’t move very far at all. But the force propagates through the cloud of electrons in a conductor at nearly the speed of light, and since individual electrons are indistinguishable, by convention we just say that an electron moves through the circuit, when what actually moves is something more like a wave of force produced by the differing electrical fields.

Semiconductors

The behavior of semiconductors is at the heart of a lot of modern electronics. But we don’t really use them in their pure state. What makes semiconductors particularly valuable is that we can change their properties and conductivity using a process called doping. Doping is just impregnating the crystal structure of a semiconductor with another atom (callod a dopant) that changes the way it behaves. The crystal structure of semiconductors provide two ways of doping that are relevant to computers: N-doping, and P-doping.

Doping converts a semiconductor to a conductor – but a conductor with particular properties that depend on the dopant.

Let’s look at a model of a silicon crystal. This isn’t really how it looks – it’s a 2D model to be readable (but this is the standard way that it’s illustrated in textbooks.) Each silicon atom has 4 valence electrons. So it forms into a crystal where each silicon atom is surrounded by 4 other silicon atoms, and each atom of silicon shares one of its electrons with each of its neighbors – so that the crystal behaves almost as if the valence shells were complete.

When we N-dope silicon (producing an N-type semiconductor), we add something that changes the way that electrons get shared in the crystal structure so that some of the electrons are more mobile. For example, a really common N-dopant is Phosphorus. Phosphorus has 5 valence electrons. When it gets infused into a silicon crystal, each atom of phosporus is surrounded by four atoms of silicon. The atoms share electrons in the same way as in a pure silicon atom – each atom shares an electron pair with each of its four neighbors. But the phosphorus atom has an extra valence electron which isn’t paired. That unpaired electron can easily jump around – with it and the other semi-free electrons around phosphorus atoms in the crystal lattice behaving almost like the cloud electrons in a metal. When you apply a force using an electric field, the free electrons will move in response to that force – the semiconductor is now a peculiar conductor.

When we P-dope silicon (producing, you guessed it! – a P-type semiconductor, we’re doing something similar – we’re creating a “free” charge unit that can move around in the crystal, but we’re doing in in a sort-of opposite direction. We introduce something which doesn’t have quite enough electrons to fit perfectly into the silicon lattice. For example, Boron is commonly used as a P-dopant. Boron only has 3 valence electrons. So when it’s integrated into a silicon crystal, it shares a valence electron with three of its neighbors – but there’s one missing – a hole where an electron can fit. We can think of that hole as a pseudo-particle with a positive charge. In the same way that the “free” electron of the N-doped silicon can move around the crystal, this free electron hole can move around the crystal – but it moves in the opposite direction than an electron would.

An important thing to understand here is that doped silicon is still electrically neutral. A piece of N-doped silicon doesn’t have a negative charge, and P-doped silicon doesn’t have a positive charge. Doping the silicon hasn’t changed the fact that the charges are balanced – the silicon is has a neutral charge both before and after doping! Instead, N-doping has converted a semiconductor to a conductor that allows electrons to move through the crystalline lattice; and P-doping has converted it to a conductor that allows positive charges to flow through the lattice.

N-type and P-type silicon by themselves aren’t all that interesting. They are semiconductors that have been chemically altered to conduct electricity better, but they’re not as good at conducting as a nice piece of metal. What makes them interesting is what happens when you start to put them together.

The simplest example (or, at least, the simplest one that I understand!) example is a diode, which is just a piece of N-doped silicon connected to a piece of P-doped silicon.

Where they contact, a bunch of electrons from the N-type silicon will jump across the gap to fill holes in the P-type silicon. This creates a region along the boundary that doesn’t have free electrons or holes, This region is called the depletion zone. Some of the holes on the P-side are filled by electrons from the N-side, so that now, on the P side, we’ve actually got a slight negative charge, and on the N side, we’ve got a slight positive charge. This creates an electric field that prevents more electrons on the N side from crossing the depletion zone to fill holes on the P side.

What happens if we apply a voltage to the negative side? This pushes electrons to move – and with enough force, they’ll start to jump the gap created by the depletion zone. It takes some voltage to get it started, because of the electrical field around the depletion zone, but with some force (typically a bit less than a volt), the electrons will start moving, almost as if you had an open circuit.

But what happens if you reverse the terminals? Then you have a force pushing electrons in the opposite direction. We’ve got an electrical field trying to push electrons into the P side of the diode. Electrons start filling holes in the P-type side, which just increases the size of the depletion zone, making it even harder to push a current across that gap. The more voltage we apply, the larger the depletion zone gets, and the more voltage we would need to apply to get a current across.

The diode conducts electricity from N to P, but not from P to N. By combining N and P type silicon, we’re able to create a one-way valve – a component which only conducts current in one direction!

This is the first step towards a computer: control how electrons move through a circuit, preventing them from following certain paths.

Next time we’ll look at transistors, which are where things start getting dynamic! The transistor is a switch without moving parts, and it’s the heart of modern electronics.

References

I’ve been looking at a lot of places to help put this together. Here’s some good links that I used. I’m sure I missed some, so I apologize in advance!

• Conduction Bands
• Semiconductor Doping
• Transistor basics (for material about how depletion zones work)
• More transistor basics
• Diode basics
• Wikipedia on diodes