Interpretation of electronic bands in a solid

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SUMMARY

The discussion focuses on the interpretation of electronic band structures in solids, specifically addressing the E(k) diagram. The lowest band corresponds to the 1s2 molecular orbital, while the upper band corresponds to 2s2 2p6. The symbol "Γ" indicates a specific symmetry direction in k-space, which is common across band diagrams. The Fermi level analysis reveals that at absolute zero (0K), the first four bands are fully occupied, and at slightly elevated temperatures, the occupancy changes, indicating partial filling in subsequent bands. It is clarified that germanium (Ge) is a semiconductor, not a semimetal.

PREREQUISITES
  • Understanding of electronic band theory
  • Familiarity with E(k) diagrams
  • Knowledge of Fermi levels and their significance
  • Basic concepts of k-space and symmetry directions
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  • Research the implications of band gaps in semiconductors versus semimetals
  • Study the role of temperature on electronic band occupancy
  • Explore the significance of symmetry points in k-space for different materials
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Keru
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Homework Statement


The exercise asks many questions about the following E(k) diagram, but I'm more interested in understanding some basic things about it, from which I'm sure i'll be able to find the answers I'm requested.

bands.png

1) What do the bands actually correspond to? Is the lowest band corresponding to 1s2 molecular orbital, the upper to 2s2 2p6 and so on?
2) I have several diagrams and all of them contain a "Γ", what is the meaning of that 'k' apparently common to every band diagram?
3) Looking at the Fermi level, would this statements be true?
3.1) At 0K the first 4 bands would be full, and the rest empty.
3.2) At a little higher temperature (let's say 0,1eV more for the Fermi level), the first three bands would be full, while the next two partially filled.
4) If 1) was correct, by looking at the intersection of Fermi level and Γ, the graphic could only correspond to the semimetals Ge or As, right?

Thanks in advantage for any help.
 

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This site has some good explanations. Basically, the Γ corresponds to a specific symmetry direction in k-space. One comment on your point 4) - Ge is a semiconductor, not a semimetal.

EDIT - I meant to say a particular symmetry direction.
 
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