[Zorkon]

So I am having a hard time understanding Band Theory. I hope somebody can help me.
I would like to explain 3 things:
1) The band structure of sodium chlorid in a energy/density of states diagram  (qualitativly)
2) How the band gap of the elements in the fourth group of the periodic table change (From C to Sn)
3) How the wavelength of light in a laser changes when you cool it (liquid nitrogen) or heat it up
I know the answer to all three questions but I can`t explain them.
The explaination should include: Orbital overlap; Interatomic distance; Dispersion of bands; Diffusion of orbitals

[Corribus]

You need to show your work (or thinking) to receive help. This is a forum policy.

[Enthalpy]

And maybe you could bring some data here, because band theory is not accessible to qualitative thinking.

• Good luck make any prediction about a band structure. Have you already seen a real one?
• Who asked this question? The shape of the conduction band changes between C, Si, Ge (I don't know Sn) at identical crystal shape. You can't explain that by atom sizes.
  And what is the allotrope?
• Again a bad question. A laser diode is difficult enough to let lase and nevertheless keep cool that you have little choice for its temperature. Heating it more uses to destroy it immediately. Cooling it strongly is about impossible due to the power density. But if it still lases, the colour is unpredictable. I saw LED change their colour completely in liquid nitrogen, which thermal expansion can't explain.

You (and whoever asked these question) could have a glimpse there
http://www.ioffe.ru/SVA/NSM/Semicond/

[Corribus]

The bandgap of a semiconductor does shrink at higher temperatures, although effect is modest. This is due to the effect of temperature on atomic distances (thermal expansion), which affects the background potential experienced by mobile charge carriers, which affects the exciton size, which affects the bandgap. You get a similar effect when a material is compressed.

https://ecee.colorado.edu/~bart/book/eband5.htm

[Enthalpy]

It does, but the opportunities to observe that are limited, and at a laser (1) Forget heating more, forget attaining the temperature of liquid nitrogen (2) It will be overshadowed by other effects: destruction, end of lasing, other recombinations getting more important, changing effects of doping (3) Already the mean carrier energy in both bands changes faster than the material's gap.

Let's take an example: 10ppm/K expansion, as much on the momentum, hence 20ppm/K on the energy, put signs as you like. For 2eV gap it's 40µV/K drift of the gap. Alone the carriers' thermal energy drifts by 90µV/K. Then, carriers are very far from thermalised in a laser diode, so their mean energy, which defines much the emitted wavelength, depends much on the speed of thermalisation and of recombination.

So while whoever asked the question expects answers like "thermal expansion changes the gap", real life has little to do with it.