Band Theory, Defects and Why Some Solids Conduct
Combining orbitals from a very large number of atoms produces bands rather than levels. Whether a band is full, empty or partly filled decides whether a solid is a metal, a semiconductor or an insulator, and small defects shift the answer.
What a learner can do afterwards
- Explains how discrete orbitals become a band as the number of atoms grows
- Uses band filling and gap size to classify a metal, a semiconductor and an insulator
- Explains n-type and p-type doping in terms of where the extra levels appear
- Links a point defect or a non-stoichiometric composition to ionic conductivity or to colour
1 · Read
One lonely atom holds its electrons on neat separate levels. Pack billions of atoms into a solid and each atom brings its own levels, packed so tightly that they blur into continuous bands of allowed energy. Between the bands sit gaps where no electron may go.
How full the bands are decides conduction. In a metal the top filled band is only partly full, so electrons have empty states next door and drift when pushed. In an insulator a full band meets a wide gap, and electrons cannot jump across, so nothing moves. A semiconductor has a small gap: heat or light kicks a few electrons across, leaving holes behind, and both carriers move. That is why warming silicon raises its conduction, while copper, already a metal, gains no new carriers from warmth.
Tiny additions shift the answer a lot. Impurity levels just below the conduction band give an n-type solid, while levels just above the valence band give a p-type solid, and conduction changes sharply. Missing or extra atoms do similar work: a point defect or an off-ratio composition can open ionic conduction or paint the solid a new colour.
Partly filled bands conduct, wide gaps block, and small gaps plus impurities tune the answer.
2 · Watch
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Where it sits
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.