Solid-state physics
A four-lesson path from energy bands through charge transport and Hall measurements to the Zener diode.
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Before you begin
Solid-state physics explains why copper conducts, glass insulates and silicon sits in between. The lessons start with energy bands, then use the drift of charge carriers to explain resistivity, measure the carriers with the Hall effect, and finish with the Zener diode. This topic goes beyond the H3 Physics syllabus.
Be comfortable with: current electricity and the photon energy E = hf.
Learning goals
- Connect energy bands, carrier response, Hall measurements, and semiconductor-device behaviour.
Lessons
Work through them in order.
- Energy bands in solidsExplain how energy bands form in solids and use band gaps to classify metals, semiconductors and insulators.
- Charge transport and resistivityModel conduction with drift velocity and the Drude model, and explain how metal resistivity varies with temperature.
- Hall effectUse the Hall voltage to find the sign and density of the charge carriers in a conductor.
- Zener diodeExplain reverse breakdown in a Zener diode and use it to regulate a voltage.
Practise and check
Topic reference
Quick reference
| Idea | Relation | Notes |
|---|---|---|
| current and drift | I = n|q| Avd | n carriers per unit volume |
| Drude conductivity | σ = nq²τ/m, ρ = 1/σ | τ is the mean time between collisions |
| resistance | R = (ρ L)/A | |
| Hall voltage | VH = BI/nqt | t is the thickness along B |
| Hall coefficient | RH = 1/nq | its sign is the sign of the carriers |
| band gap and light | hf ≥ Eg | to excite an electron across the gap |
Core knowledge to remember
- In a solid, atomic energy levels spread into bands separated by gaps.
- A full band carries no current. Metals have a partly filled band; insulators have a full band and a large gap; semiconductors have a small gap.
- A semiconductor’s resistivity falls as its temperature rises; a metal’s rises.
- Carriers of either sign are pushed to the same face in the Hall effect, so the sign of the Hall voltage shows the sign of the carriers.
- A Zener diode in reverse breakdown keeps an almost constant voltage over a wide range of current.
Common mistakes
- Confusing resistivity, a property of the material, with resistance.
- Using the width instead of the thickness along the field in the Hall voltage.
- Saying a full band can carry current.
- Connecting a Zener diode in forward bias in a voltage regulator.