The Direct bandgap reference article from the English Wikipedia on 24-Apr-2004
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Direct bandgap

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In semiconductor physics, a direct bandgap means that the conduction band lies directly above the valence band, in momentum space (see E-k plots). A semiconductor with a direct bandgap can be used to emit light. Indirect bandgap semiconductors such as crystalline silicon cannot.

The prime example of a direct bandgap semiconductor is gallium arsenide - a material commonly used in laser diodes.

See indirect bandgap for an explanation of the connection between bandgap offset and light emission.