MATTER LogoIntroduction to Electrons in Crystals

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Density of States > Free Electrons

Description of Flash Animation.

This animation shows the E-p parabolas. The animation also shows the holes.

This resource requires Flash Player 9 or above available to download from

The shared valence band electrons in a crystal must occupy different energy levels - this is why the energy band forms. Each electron has a different energy and a different momentum.

Every valence electron in a crystal has a unique vector defining its momentum, p.

If electrons are free, their energy and momentum will be related by:

E=p2/2m   (Simple derivation)

Kinetic energy of a free particle = ½mv2 where m is the mass of the electron and v is its velocity.
Momentum p=mv so v=p/m
Substituting for v we get E=½mp2/m2, or


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E vs p should then be a parabola. You can see this plotted by clicking on the plot button. To consider the energies of holes click on the holes button opposite.

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