Indirect Bandgap Semiconductors
Not all semiconductor materials have the minimum of the conduction band above the top of the valence band in the E-k bandstructure.
These materials are known as indirect semiconductors. Examples include Si, Ge and AlAs. For indirect bad gap semiconductors, the conduction band can be crudely approximated by the following equation near the conduction band minimum.
where k0 is the offset in the conduction band minimum. For light emitting devices, indirect band gap semiconductors are not at all promising. To see why, consider the band edge diagram of an indirect band gap semiconductor. The momentum of an electron in the conduction band is different from a hole in the valence band. Momentum is conserved by quantised lattice vibrations known as phonons. Phonons have substantial momentum, but energies in the far infra-red, which are negligible on the scale of Eg. For a transition to occur, requires both a photon of frequency w and also a phonon of frequency W.Clearly, the probability of these two events happening is less likely than an electron making a single direct transition, as occurs in direct bandgap semiconductors.
A measure of how well a semiconductor material is at converting carriers into photons is the internal quantum efficiency h i. It is the ratio of the number of photons produced to the number of carriers crossing in the junction. Indirect semiconductors have a poor internal quantum efficiency.