EC-5.2 Atoms, Quantisation, and Why Electrons Sit in Levels

What this is and why it exists

Everything about semiconductors rests on one fact: an electron bound to something cannot take any energy it likes. It has a list.

That single restriction produces the sharp lines in a spectrum and the shape of the periodic table. It also produces the way atoms bond, and eventually the band gap that makes a transistor possible.

This topic exists so the band diagram in the next one arrives as a consequence rather than as a picture to memorise. It is deliberately physical rather than mathematical. You are not going to solve anything here; you are going to understand why the next diagram looks the way it does.

The vocabulary

• Quantisation — the restriction of a quantity to particular values rather than a continuous range.
• Energy level — one of the allowed energies an electron in an atom can hold.
• Ground state — the lowest arrangement, the one an undisturbed atom sits in.
• Excited state — any arrangement above the ground state.
• Shell — a group of levels at roughly the same energy.
• Orbital — a region where an electron of a given state is likely to be found.
• Valence electrons — the electrons in the outermost occupied shell.
• Covalent bond — a bond made by two atoms sharing a pair of electrons.
• Electron volt — the energy an electron gains crossing a potential difference of one volt.

The mental model

Start with the analogy that actually explains it. A guitar string fixed at both ends can only vibrate at certain frequencies, because only some wavelengths fit between the ends. Any other wavelength cancels itself out.

An electron confined near a nucleus behaves as a wave. Only some wavelengths fit, so only some energies are allowed. Everything between them is not merely unlikely; it is impossible.

That is the whole idea, and the evidence for it is direct. When an electron moves from one allowed level to another it takes in or gives out exactly the energy difference. That energy arrives as light of one particular colour. Heat a gas and it emits a handful of sharp lines rather than a smooth glow. If the energies were continuous the spectrum would be continuous, and it is not.

Electrons fill the levels from the bottom, and no two can occupy the same state. That filling rule produces the shell structure, and the shell structure produces the periodic table. Elements in the same column behave alike because they have the same number of electrons in their outermost shell.

Only the outermost electrons matter for anything you care about. Inner electrons are held tightly and take no part in chemistry or conduction. An element's entire electrical and chemical personality comes from its valence electrons.

Silicon has four. That number is why the rest of this module happens.

When atoms come together they can share electrons, hand them over, or pool them. Sharing gives a covalent bond. A silicon crystal is every atom sharing one electron with each of four neighbours: every valence electron accounted for, none free to move. That is why pure silicon barely conducts. Pooling gives a metal, where the electrons are common property and move freely, which is why a metal conducts well.

One practical note. Energies here are quoted in electron volts, because in joules the numbers are unusably small. Carry one figure forward: a semiconductor band gap is around one electron volt. You will meet it constantly.

What you should now be able to explain or do

• Say why a bound electron has a list of allowed energies rather than a range.
• Explain what a spectral line is evidence of.
• Describe how the filling rule produces shells and the periodic table.
• Say why only valence electrons matter, and why silicon having four is significant.
• Explain why a covalent crystal barely conducts while a metal conducts well.

Check yourself