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I'm trying to figure out what determines the energy of the bands, either conduction or valence band. Mostly I can read about the bandgap energy, which is mostly just the difference between $ E_C $ and $ E_V $ but there are also more concise expressions like $ E_g(T) = E_g(0) - \frac{ \alpha \cdot T^2 }{T + \beta} $. According to wiki, $ E_g(0) $ is "just" a material constant.

In short words: What determines $ E_V $ and $ E_C $ ?

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Really it depends how deep you want to go! I hopefully will keep it fairly simple. If you consider an atom, the energy levels are determined by the orbital the electron is in, calculated from the Schrodinger wave equation. It is a similar concept for a material, albeit complicated by there being a large number more atoms and the interactions between them. It should be noted here that these energy levels also vary periodically throughout the lattice.

Essentially this means that Ev and Ec are determined by the solution to the electron wavefunction for the highest occupied and lowest unoccupied energy band in the material.

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    $\begingroup$ Thanks, to be a bit more precise: The bands are a solution of the superpositions of (all) electron wavefunctions, or? Not that of a single atom. $\endgroup$
    – Ben
    Commented Jun 18, 2020 at 5:12
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    $\begingroup$ I'm going to use the wikipedia definition, because I think it sums it up quite nicely. The bands come from a single electron in a large, periodic lattice of atoms or molecules - link. $\endgroup$
    – Sam Pering
    Commented Jun 18, 2020 at 6:55
  • $\begingroup$ If you want to go even deeper the commenter above who spoke about particle in a one dimensional lattice is a good start - I'm afraid I'm more of an applied semiconductor physicist, if you wanted to go even deeper I would suggest framing it using a quantum mechanics tag. $\endgroup$
    – Sam Pering
    Commented Jun 18, 2020 at 6:58
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    $\begingroup$ Thanks again, I will move to the article but nevertheless, before that, I'd like to raise a question: This means these bands already emerge even without the presence of any electron. Therefore, it is only a result of the presence of the cores then. I didn't expect that. As an applied semiconductor physicist, I would like to adress another question to you :) Are the bands temperature dependent? So far I only see any temperature dependency for the fermi energy but it's quite likely that I oversee something(?). $\endgroup$
    – Ben
    Commented Jun 18, 2020 at 8:55
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    $\begingroup$ I'm sorry I'm not sure I completely understand - the bands wouldn't be there if there wasn't an electron, as the wavefunction is based on electrons, and the effect of the cores on them. As far as temperature dependence, a change in temperature will change the vibration of the lattice, meaning the bands will change too. $\endgroup$
    – Sam Pering
    Commented Jun 18, 2020 at 9:05

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