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Can someone please explain why Indirect band gap semiconductor can not be used for LED creation. Can you also please give me some reference link for details.

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Isn't indirect-bandgap gallium phosphide used for LEDs??? – Steve B Sep 25 '11 at 20:03

Because they do not emit light.

And they do not emit light because:
massless photon has (almost) zero momentum. In indirect semiconductor holes and electrons have different momenta. Thus, to recombinate and fulfill momentum conservation law they need to do something with this uncompencated momentum. While in direct gap semiconductors hole+electron pair momentum is zero can be zero and they are able to "just recombinate".

Read wikipedia, use google.

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I'd like to add that the extra momentum can be obtained from a phonon, but clearly that is just dumping unhelpful energy to be dissipated into the material, and losses a lot of efficiency. As a rule of thumb, photon transitions are "vertical" in dispersion, and phonons are "horizontal". So by combining the two, you can get any direction you want. – genneth Sep 25 '11 at 23:54
@genneth, there are few ways to get this extra momentum. Phonons, impurities, interfaces. Probability is highly reduced in any case. – Misha Sep 26 '11 at 3:40

The premise of this question is wrong. Indirect bandgap semiconductors CAN be used for LEDs. Gallium phosphide is the most famous example.

Other things equal, direct-bandgap materials make better LEDs than indirect bandgap materials. (Why? Start by reading Misha's answer or wikipedia. If you're still confused then you can ask a new stackexchange question.) Well, then why is gallium phosphide used in commercial green LEDs, even though it has indirect bandgap? Because "other things equal" is not the case in the real world. Every material has advantages and disadvantages -- cost, bandgap, ease of material growth, crystal defects, etc. etc. An indirect bandgap is unfortunate when you're making an LED, but it's not the end of the world.

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Indirect bandgap semiconductors do not emit as well as do not absorb light for photon energies close to band gap due to reasons described above. Namely, the main reason is the momentum conservation law. However, it is possible to make photodetectors (absorbers) on such semiconductors utilizing interband electron transitions with energies much higher than the bandgap. In this case, such transitions occur at the center of the Brillouin zone with zero or small changes of the momentum.

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