Homo-Lumo energy

[Wisam1222]

Dear All
When plot the band structure:
Is it possible to say that the valence band edge represents Homo? And the conduction band edge is a lumo?
Best Regards

[Petr Khomyakov]

This is more chemistry terminology assuming a  discrete energy spectrum given by atomic or molecular orbitals, whereas in solid state we are talking about a continuous energy spectrum with an energy gap and possible discrete levels (e.g., when there are localized states due to defects or dopants). I guess bottom of CB and top of VB could sort of be seeing as LUMO and HOMO, respectively, provided that the Fermi level is in the gap, which would be the case for intrinsic semiconductors and insulators.

[Wisam1222]

Dear Petr Khomyakov
Thanks for your response

If we consider that the bottom of CB and top of VB couldbe seeing as LUMO and HOMO, respectively, then when applying the equation below to calculate the Fermi level energy, we find that the Fermi energy is not in the middle of the gap between Homo and Lumo.
EFermi=(1/2)*(EHOMO+ELUMO)
This is contrary to the equation to calculate the Fermi level energy, what is the explanation for that?

[Petr Khomyakov]

For a given electron temperature and fixed total number of electrons N_electrons, the Fermi level/energy E_F are actually given by a different equation, N_electrons = Integral DOS(E) f_FD(E-E_F) dE, where f_FD is Fermi-Dirac distribution, https://en.wikipedia.org/wiki/Fermi_level. It does not need to be  always in the middle of the gap.