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•• In the so-called direct-gap semiconductors, such as GaAs, an electron near the bottom of the conduction band can drop into a hole near the top of the valence band and emit a visible photon. The corresponding process is forbidden in an indirect-gap semiconductor, such as Si or Ge. To show why, consider the following. In a direct-gap semiconductor the initial and final states of the electron can both have momenta near zero (so that ∆ p can be very small); in the indirect case these two momenta are very different (∆ p is comparable with the momentum of the conduction electron, in fact.) (a) Compute the momentum of a visible photon. (b) Find the momentum of an electron with wavelength about 0.3 nm (which is typical for a conduction electron in a semiconductor), (c) Explain why the emission of a photon in an electron-hole recombination is forbidden in an indirect-gap semiconductor.
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