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Band Gap Theory

  1. Oct 12, 2015 #1
    I attached a picture.

    In the first figure, we see that the difference between bands is rather large. We see that electrons do not occupy all the energy levels from energy 0 to Fermi energy level. There are forbidden band gaps.

    But in the second figure, I see that the electrons occupy everything from energy 0 to the Fermi energy level (so there are no forbidden band gaps like the first figure shows) So, what is happening?

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    Last edited: Oct 12, 2015
  2. jcsd
  3. Oct 12, 2015 #2
    The diagram on the left is a plot of the Fermi-Dirac distribution at zero K. It is not the band structure. In the band gap the density of levels is zero. The F-D does not have to be zero.
  4. Oct 12, 2015 #3
    On both figures I see the energy axis.

    In the first figure, I see electrons not occupying certain energy levels on this energy axis. In the second figure, I see electrons occupying all energy levels from energy level 0 to Fermi energy level on this energy axis.
  5. Oct 12, 2015 #4


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    Insulators and semiconductors have a fully occupied valence band and an empty conduction band at low temperatures. There is a band-gap, forbidden energies, between them.
    In case of metals, the conduction band is not empty even at 0 K. Half of the states in the conduction band are occupied. The electrons occupy the lowest levels at 0 K. It is shown in the figure on the right.
    Last edited: Oct 12, 2015
  6. Oct 13, 2015 #5
    In metals, at 0K, the conduction band is empty. The band, where the Fermi level resides, is separated into a valence band and a conduction band. The valence band is fully occupied while the conduction band is empty. If the temperature increases, for example room temperature, then the electrons need little energy to go in the conduction band.
    You are confusing the conduction band with the allowed band where the Fermi level resides.

    But I am asking about something else. In the second figure, I don't see band gaps like in the first figure.

    I think I figured it out.

    I think the 0 on the axis is the 0 for the probability, and not the energy.

    Maybe in the figure, we see only the valence and conduction band. We don't see everything. And at 0K, the valence band is fully occupied like the figure shows, while the conduction band is empty.

    I mistaken the 0 to belong to the energy axis.
    Last edited: Oct 13, 2015
  7. Oct 13, 2015 #6


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    Read this.
    The right figure shows the highest band with any electrons in it at 0 K. All states with energy below the Fermi level are filled, all above it are empty. The vertical axis is the energy above the bottom of the band. That is, why no band gap is shown. The figure is not clear, but the red circles might represent the occupied states.
  8. Oct 13, 2015 #7
    The second figure does not represent a band structure at all. It is a plot of the F-D function. You can see F(E) on the x axis.
    these red circle are meaningless. The density of electrons depends both on density of states and the probability to occupy that state. So there is no point to show these electrons there.
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