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The band gap of Diamond, Silicon and Germanium is 5.5, 1.12, 0.66 eV while the average energy to produce an electron-hole pair for the same semiconductor is namely 13, 3.6 and 2.9 eV. This ratios are ranging from $\sim4,4$ to $\sim2$. Is there a simple rule connecting all indirect semiconductors band gaps to their electron-hole pair generation threshold? I cannot find any reference paper discussing this specific relation...

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  • $\begingroup$ In the surface barrier detector world (and radiation effects in electronic devices) there have been a few attempts to put it on some sort of theory basis, but as far as I can tell none have been much more than handwaving. For the moment, its just one of those things that looks like it should have a simple explanation, yet doesn't (yet). $\endgroup$ – Jon Custer Jan 3 at 21:31
  • $\begingroup$ I find it hard to see how there could be. The average energy to produce an electron-hole pair tells us a lot about the overall difference in energy between bonding and anti-bonding orbitals. However the band gap is sensitive to where ever the lowest conduction and highest valence states are, and this is very sensitive to details of the crystal structure and bonding. You can even have semi-metals where the band gap is negative enough though the average energy to create a pair is quite positive. $\endgroup$ – Paul Young Jan 3 at 22:21
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I finally found a paper addressing this correspondance between band gap and electron hole pair energies. I hope this will help some other.

As you can read on the paper there is such a simple law to link the two. You may refer to the image:

electron-hole-pair creation energy is about 3 times the semiconductor band gap

The deal here is to use momentum conservation. Read the paper for further infos (don't want to break some copyright).

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