# Why is the energy for an electron-hole pair for $\rm CdTe$ bigger than the band gap energy?

Let's take the indirect semiconductors Si, Ge & Diamond. All these semiconductors are indirect, meaning that the maximum of the valence band is not directly under the minimum of the conduction band. This is how we can explain that the band gap for Si is $$1.12$$ eV, whereas the average required energy to cerate an electron-hole pair is $$3.65$$ eV (basically, the energy difference goes into phonons, heat).

But then, for the direct semiconductor $$\rm CdTe$$ (Cadmium-Tellur), why is the required energy for the creation of an $$e/h$$ pair $$4.43$$ eV, whereas the band gap is $$1.44$$ eV!? Very similar numbers also hold for GaAs (reference: Kolanoski-Wermes "Particle Detectors. Fundamentals and Applications. 2020. p. 261").

Edit:

From the text:

I thought that for direct semiconductors, we don't have phonon excitations.. But okay, I was probably wrong here.

• Context matters. Why do you believe this, given a wide range of papers on, say, solar cell performance? – Jon Custer Mar 3 at 16:46
• @JonCuster Well, it's not a matter of belief. I quoted numbers for CdTe and GaAs. The context is Particle Physics/Detector Physics. – user248824 Mar 3 at 16:51
• Yeah, what are you referring to? That band gap value is the same energy where light absorption begins. Is light not creating electron-hole pairs? – Gilbert Mar 3 at 16:52
• @MathIsFun - well, the context absolutely does matter. The issue with particle detectors is you look at how much current (e-h pairs) you get out of the device for the total electronic stopping that occurs in the active volume. Because the energy deposited along a particle track is quite high, the carrier densities are high enough that there is significant in-device recombination of the free carriers. Ballpark is you divide total electronic stopping by the bandgap, then divide that by a factor of order 3-10 that you must figure out based on geometry, particle, energy, etc. – Jon Custer Mar 3 at 17:32
• Notice all the numbers are ~3x the band gap, direct or indirect. – Jon Custer Mar 3 at 21:29