Conductors, insulators and semiconductors.

Step 1 of 6

Bands of levels

A current is charge on the move, and in solids the charge is carried by electrons. But why do they flow easily in a copper wire, and hardly at all in diamond?

The answer is in the energy levels. In a single atom an electron has only certain levels. In a crystal billions of atoms sit close together, and their levels spread into bands: many closely packed levels, with gaps between them. In silicon, diamond and germanium the bonding electrons fill the valence band completely. Above it, across the Band gap, lies the empty conduction band. Show the energy levels draws the electrons at their energies. Here Band gap is set to Metal.

Step 2 of 6

The thermal shaking

As a material warms up, the atoms in the crystal shake harder. Most of the time the shakes are small, but now and then a very large one breaks a bond and lifts an electron across the gap. The electron becomes a free electron in the conduction band, and where it was it leaves a hole: an empty place in the valence band, which can also move and conduct. Band gap is fixed on Silicon, 1.12 eV, and Temperature is fixed.

Step 3 of 6

Warm silicon

How many large enough shakes are there? The share of electrons that heat lifts across the gap depends on the ratio between the gap and the energy of the shaking:

$n \propto e^{-E_g/2kT}$⁠

That is an exponential, and the exponent is large: for silicon at 300 K, $\dfrac{E_g}{2kT} \approx 22$$\dfrac{E_g}{2kT} \approx$$22$⁠. So a small change in temperature changes $n$⁠ a lot. Band gap is fixed. Predict, then look at the number on the board.

Step 4 of 6

The size of the gap

A material with a small gap is a semiconductor: it has a few free electrons, and their number depends on heat. Germanium, 0.66 eV, conducts better than silicon, because its gap is smaller. Temperature is fixed at Room. Change Band gap and look for the gap that gives a hundred times silicon’s electrons.

Step 5 of 6

Insulators

A material whose gap is wide, above about 4 eV, is called an insulator. In Diamond the gap is 5.47 eV, and at room temperature you could wait forever for a free electron: a diamond the size of the Earth would hold only a handful. Band gap is fixed. Predict what will happen when we heat it a lot.

Step 6 of 6

A cold metal

A Metal has no gap at all: the bands overlap, and it has free electrons at any temperature. What heat does do in a metal is add shaking, and the electrons bump more into the shaking atoms. So a metal’s resistance rises as it warms up, and a semiconductor’s falls.

Try it: after checking, choose Silicon and lower Temperature to Liquid nitrogen. Almost all the free electrons vanish, and silicon becomes nearly an insulator. The chips in a phone are made of silicon, with a tiny amount of other atoms added to set how many free electrons it has.

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