# Why is the necessary energy for a photon to lift an electron higher than the band gap energy?

The band gap energy of silicon is around 1 eV and though the required energy for a photon to lift an electron up into the conduction band is around 3.6 eV.

Why is this?

Is the Energy of an absorbed photon exactly the energy of the band gap? is quite similar but - whyever - they do not answer it respectively do not use any material.

• Huh. 1064nm Nd:YAG gets absorbed just fine in silicon, and it isn’t anywhere near 3.6eV. Something is wrong with your sources. – Jon Custer Aug 17 at 17:10
• researchgate.net/post/… – Ben Aug 17 at 17:19
• Look, if your Si CMOS camera in your phone only responded to light above 3.6eV your pictures would look very different. – Jon Custer Aug 17 at 17:34
• Maybe 3.6 eV is the direct band gap of Si. Below that is indirect, requiring, e.g., a phonon to complete the absorption process. 1.1 eV is the indirect band gap of Si. – Gilbert Aug 17 at 19:18
• Page 8,10 and 11 in that PDF show the Si gap as 1.1eV which is roughly 1micron IR light (and above, including visible) – Bob Jacobsen Aug 17 at 22:02

Silicon has an indirect band gap. This means that although there is a conduction-band state which is only 1eV above the top of the conduction band it occurs at a different Bloch momentum $${\bf k}$$. The nearest state with the samae $${\bf k}$$ value is 3.6eV above the top of the valance band. Photons have a wavelength $$\approx 600\mu$$ that it is much larger than the inter-atom spacing and so their crystal momentum $${\bf k}$$ is much smaller than the size of the Brillouin zone. Their momentum is therefore effectively zero as far as band theory is concerned. Therefore, for single-photon absorbtion with none of the energy going into phonons (to make up the momentum change) you need 3.6 eV photons.
LED's and other devices that play well with light are made of III-V or (or even II-VI) materials such as Gallium Arsenide or Indium Arsenide that have direct band gaps, meansing that the lowest energy conduction-band state has the same $${\bf k}$$ as topmost valence band state.