Relation between electronic band structure and Fermi energy

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SUMMARY

The discussion centers on the relationship between electronic band structure, density of states (DOS), and Fermi energy in solid-state physics. It establishes that the Fermi level is determined by integrating the DOS up to the energy level corresponding to the electronic density, expressed mathematically as ##\int_{-\infty}^E DOS(E')dE'=n##. Furthermore, it highlights that the DOS is inversely proportional to the slope of the energy versus wave vector (k) dispersion, indicating a direct correlation between these concepts. Understanding these relationships is crucial for analyzing electronic properties in materials.

PREREQUISITES
  • Understanding of electronic band structure and its representation as energy versus wave vector (k).
  • Knowledge of density of states (DOS) and its significance in solid-state physics.
  • Familiarity with Fermi energy and its role in determining electronic properties.
  • Basic mathematical skills for integrating functions and interpreting physical equations.
NEXT STEPS
  • Study the mathematical derivation of the relationship between density of states and Fermi energy.
  • Explore advanced electronic band structure calculation methods, such as Density Functional Theory (DFT).
  • Investigate the implications of varying DOS on the electronic properties of different materials.
  • Learn about the effects of temperature on Fermi energy and electronic dispersion.
USEFUL FOR

Physicists, materials scientists, and students studying solid-state physics who are interested in the electronic properties of materials and their dependence on band structure and Fermi energy.

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I have some qualitative questions about the relation between band structure, density of states, and Fermi energy (or Fermi level).

1) Say you have a given electronic band structure (energy as a function of k) obtained by any method. How do you relate this to the Fermi energy (or Fermi level) ?

2) I assume something with density of states is involved (is it?). If it is, what is the relation between density of states, electronic dispersion, and Fermi energy (or level)?
 
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From a band structrure calculation you also get the DOS as a function of energy. If the electronic density is n, then ##\int_{-\infty}^E DOS(E')dE'=n## fixes the Fermi level E. The DOS is proportional to the inverse slope of E vs k, i.e. dispersion.
 

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