Conductors and Band Theory

The unfunny meta joke

I like how the title suggests this could be about music; it's about physics.

The basic introduction

Every substance is a conductor, when you think about it. Heat up glass to a high enough temperature and it will start conducting electricity - that is, letting electrons pass through it, like a distorted wire. This will be due to the temperature causing the electrons to gain more kinetic energy, which thus causes them to become overexcited and start moving more quickly - but more on that in a bit.

There are two basic types of material - conductors and insulators. Insulators cannot conduct electricity as well as conductors, because the electrons are more fixed in place, and need more energy to be freed and allowed to move around and conduct a charge. Conductors, however, don't have this problem - metals contain delocalised electrons, so can always conduct a charge whenever. Or in other words, to conduct electricity, you need free electrons. 

The chemistry aspect

Those free electrons will always come from an atom's valence electrons - they're easier to dispose of because the electrostatic attraction between them and the atom's nucleus is far weaker than if they were closer. It's easy to consider an atom as containing a series of orbitals, where if electrons gain more energy they get further away from the nucleus by going up in energy levels. So now it's clear as to why insulators can become conductors as you increase its temperature. 

Band theory

These energy levels, however, could further be split into separate electronic bands. There are two main ones - the valence band, and the conduction band. The valence band consists of the electrons on the outermost orbital of an atom, and should the electrons get excited, they might be able to become delocalised and thus enter the conduction band. They are separated by a band gap in insulators, which is essentially another band of energy levels which electrons cannot occupy, whereas in conductors, the valence and conduction bands overlap - the electrons can freely move between the bands.

 

Insulators will only ever fill the valence band - the band gap is far too big, and you'd need to increase the energy in the system to bridge that gap. Conductors don't have this problem due to the overlap, which is why metals in all states can conduct electricity.

Semi-conductors

Say you started to close that gap, though...there'd obviously be a blurry grey transition state. This state contains semi-conductors, which have properties similar to conductors and insulators. The gap is small enough for electrons to be able to transfer between the bands. These are all over the place in tech, such as in microchips and transistors. The Semiconductor Industry Association says "a single semiconductor chip has as many transistors as the Great Pyramid of Giza has stones", in today's strange analogy.

The best part is, though, that by adjusting the chemical makeup of these semiconductors by doping (adding impurities of other metals to it), you can also adjust its ability to conduct electricity. This is as the impurities will either add or remove electrons from the semiconductor's lattice structure - the more electrons (which are charge carriers) present, a greater charge can be conducted. And vice versa.

Holes and charge carriers

For completion, I may as well mention the formula for calculating the drift velocity:

I = nAqv

Here, I is the current and n is the number of charge carriers. For the sake of this blogpost, I'll only focus on those two aspects, but I may as well also mention that A is the cross-sectional area of the wire measured, q is the charge of an electron (-1.6e^-19), and v is the drift velocity. But that could be a blogpost of its own in the future.

As you increase n and keep all the other variables constant, you will increase the current across it. So obviously conductors will have more charge carriers than semi-conductors, which will have far more than insulators would. Charge carriers could include electrons or ions, but most importantly they must be free. This is why solid table salt (NaCl) won't conduct electricity, but molten or dissolved table salt will - the ions are freed from their ionic lattice and can thus conduct a charge. 

And then there's another charge carrier - the hole - which I have neglected to mention. 

When electrons move from the valence band to the conduction band, they will leave an empty space behind, which is called a hole. An electron will subsequently move to take its place; except that will leave another hole. This will thus continue, and the hole will move in the opposite direction to the flow of electrons through the valence band. Therefore, empty space could be thought of as having a charge. 

As this crude diagram shows:

 

The epilogue

 

There isn't really a true insulator - it just so happens that, with a high enough temperature, everything can become a conductor. However, even those conductors can act in a strange manner, and even then, physics can still get a bit too abstract for my liking.

And this is the unsatisfying final sentence.