# inability of indirect gap semiconductors to emit light efficiently

what is reason of inability of indirect gap semiconductors to emit light efficiently?

I imagine that by light emission you're talking about radiative recombination, which corresponds to a release of energy excess (a photon) resulted from the combination of a conduction electron with a valence hole.

To understand the following reasoning, please recall than band structure diagrams, also called dispersion diagrams, are composed of Energy vs Momentum (or $\omega$ vs $\mathbf{k}.$).

Direct gap: A semiconductor with direct gap is described by a band structure for which the minimum energy state in the conduction band is aligned vertically with the highest energy state of the valence band. This in turn implies that an electron transition from the conduction band to valence band comes only with a photon emission (energy conservation) and zero momentum change in the crystal.

Indirect gap: The radiative recombination becomes less likely to occur, because for an indirect gap semiconductor, the minimum energy state in the conduction band has a different corresponding momentum $\mathbf{k}$ (k-vector) than the highest energy state of the valence band that has $\mathbf{k'}\neq \mathbf{k}$. This difference implies that for a radiative recombination to occur, the transition process must also involve the absorption or emission of a phonon to account for the momentum difference $\Delta \mathbf{k}=\mathbf{k'}-\mathbf{k}$, where the phonon momentum equals this difference. To conclude, we know that momentum conservation cannot be violated, meaning in a crystal, the crystal momentum has to be conserved, one way of achieving this would be via a phonon emission or absorption associated with momentum $\hbar\Delta \mathbf{k}$. This added process to the transition of the electron makes the whole photon emission event less likely to occur, or more formally the radiative recombination cross section is reduced because such mechanisms will be attenuated at low temperatures when the needed phonons fulfilling the selection rules are no longer readily available (recall phonon state population is governed by Bose-Einstein statistics). Now you know e.g. why laser diodes are always made of direct gap semiconductors.

Such transitions are often called non-vertical transition. Whereby photon emission/absorption is accompanied by either creation/annihilation (respectively) of a lattice vibrational phonon. Illustrative diagram from wikipedia:

More on crystal momentum, see here and on phonons see here.

• Tnx for your answer." such mechanisms will be attenuated at low temperatures",u said. do u mean room temperature? – Mr. Nobody Jan 3 '15 at 18:32
• Can be at any temperature, to simplify even further: point is that if you compare two semiconductors, one with a direct gap and the other with an indirect gap, for a given temperature $T$, there are not infinitely available phonon states for the crystal, and whenever they are not available (probability of having a phonon at energy E and temperature T given by Bose-Einstein statistics), the one with indirect gap will not allow the electron-hole pair combination and no photon will be emitted, whereas with a direct gap, such selection rule on momentum is not even needed (no phonon creation) – Phonon Jan 3 '15 at 18:44
• U mean that density of states of phonons is limiting factor. according to your reasoning, photon absorbtion processes in solar cells and photodetectors(indirect gap) also should not be efficient, but i know that it is not true! – Mr. Nobody Jan 3 '15 at 19:00
• Yes density of states of vibrational crystal phonons. Please don't mix things up now, in your post you asked about photon emission, and I answered for photon emission via electron-hole pair combination! had you asked about solar cells specifically, I would have answered accordingly. – Phonon Jan 3 '15 at 19:05