Direct versus indirect band gap semiconductors

A semiconductor is direct band gap if the minimum of the conduction band and the maximum of the valence band occur at the same crystal momentum k; it is indirect band gap if they occur at different k values.

   Direct (GaAs)          Indirect (Si)
  E                      E
  |   \   /  CB          |        \   /  CB
  |    \_/               |         \_/
  |     |  hv            |  ___      ^
  |    /^\               | /   \  phonon
  |   /   \  VB          |/     \ needed
  +---------- k          +------------ k
      same k              k(max) != k(min)

Comparison

Key point

In a direct gap material an electron at the bottom of the CB can recombine with a hole at the top of the VB and give out a photon of energy $h\nu \approx E_g$ while conserving momentum. In an indirect material the photon carries almost no momentum, so a phonon must take part; this three-body process is unlikely, which is why silicon cannot be used to make efficient LEDs or lasers.