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I have some difficulty in understanding the electronic band structure.I want know that for a 3D crystal,what information can I extract from its complicated band structure,for example the band structure of the SiC(I downloaded this figure from google).And what intuition that I can build for such a complicated band structure?the band structure for SiC

meTchaikovsky
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1 Answers1

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The most useful information you can extract from the band structure for an insulator like SiC involves: (1) the value of the bandgap (the energy difference between the highest occupied band--the valence band--and the lowest unoccupied band--the conduction band); (2) the direct or indirect nature of the band gap (direct if the valence band max occurs at the same k point as the conduction band minimum, and indirect otherwise); and (3) the band dispersion or the slope of the bands involved in the band gap--steeper slopes indicate stronger orbital interactions and faster carrier mobility, on the other hand an ionic crystal will have very flat bands.

compmatsci
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  • I'm sorry that my response came so late...Thank you for your answer! There's two questions ,the first one is that is it right to think that the very flat bands of ionic crystal indicates the electrons of the crystal are well localized? And can I consider the very flat band to be some localized impurity band? The second question is how can I deduce the highest occupied band and the lowest unoccupied band from that band structure? I just see many gaps in the figure,and I just don't know how to find the right one...Thank you so much! – meTchaikovsky Mar 29 '17 at 11:37
  • Yes flat bands indicate localization, low group velocity and ionicity. I'm not sure about the impurity bands but typically band structure calculations are done for pure compounds so you don't see impurities. To figure out the valence and conduction band first locate the fermi level, E=0 in the figure. This is actually the chemical potential of the electrons and tells you how much energy it takes to add or remove electrons to the system. So at E=0 you can consider all bands below it to be filled, and all bands above it to be empty. E.g. Your band gap is the energy between G15 to X1. – compmatsci Mar 29 '17 at 16:27
  • Thanks! But I have a few more questions, the first one is that in that band structure, we only calculate a few directions and find a band gap, but how can we conclude that there's not a even smaller band gap in some other direction, in some other wave vector in the FBZ? And the second one is that I've read some papers about the doped semiconductors and there're some figures of band structures which contains both the bands of the host and the impurity, so are these two kinds of bands calculated separately or simultaneously? – meTchaikovsky Mar 30 '17 at 01:59
  • The first question might merit a separate post, I've also wondered if there is a theorem or something that states that band energies must attain critical values at high symmetry points. I guess for a structure with a defect you could have a flat band associated with the impurity within the band gap, if that's what you're asking--this could be done in the same calculation I imagine but I've personally never done one. If you feel that the above post answers your question please accept it! – compmatsci Mar 30 '17 at 03:19
  • Thanks a lot! I will just take some time to think it over! – meTchaikovsky Mar 30 '17 at 03:25
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    High symmetry points in First Brillouin Zone have crucial information about any possible variation of band gap within the crystal. Rest reciprocal vectors will show some periodicity in the band gap with same variation so it is not necessary to calculate band structure at any random k-points but at high symmetry points. You may try to understand the Bloch's Theorem first :) – UJM Jan 08 '21 at 14:17