Suppose we have the full band structure from tight-binding model for a hexagonal (or square) lattice. If there are only two bands, often in literature one band is called hole-band and the other is the electron-band. How does one actually calculate the electron and hole densities as function of Fermi energy? And what happens if there are more than 2 bands?

  • $\begingroup$ How is it different from any other semiconductor? $\endgroup$
    – Jon Custer
    Commented Apr 12, 2023 at 16:15
  • $\begingroup$ Where did you find the term "hole band"? $\endgroup$
    – freecharly
    Commented Apr 12, 2023 at 20:54

1 Answer 1


Just integrate the Fermi function: \begin{equation*} n_{e(h)}=\int f(E,\pm\mu)D(E)dE \end{equation*}

where $f$ is the Fermi function, $D$ the density of states, and the integral is over the conduction and valence bands for electrons and holes, respectively.

Typically, the electron density is the sum of contributions from all conduction bands and hole density is the sum of contributions from all valence bands, but it is reasonable to suppose only the bands nearest to the Fermi level contribute.


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