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Fermi-Dirac Distribution

  1. Oct 13, 2015 #1
    In the graphs that I see around the internet I see that the energy axis starts at 0 eV and it goes up. So the electrons have positive energies.

    But in the electronic band structure, the electrons have negative energies. And if they go to infinity, then their energy becomes 0.

    So, what is happening?
  2. jcsd
  3. Oct 13, 2015 #2


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    Energy is relative! Maybe the positive energy is the "binding energy" representation, meaning that is the energy needed to liberate the electrons. There can be other possibilities. Without you showing the sources, we can only guess.

    Note that you have encountered something like this already in basic kinematics problems in intro physics. I can designate potential energy to be zero on the ground and having it positive going up, or I can designate some high up points as having zero potential energy and anything below it as having negative potential energy.

    The most important lesson here is to look at the CONTEXT. Understand what is being presented, rather than memorizing what it should be like.

  4. Oct 13, 2015 #3
    It would be better to read about it in a book, so you get the full context of the graphs.

    In introductory solid state usually the first time you see the F-D distribution is when applied to the free electron gas model. This is like a classical ideal gas but following the quantum statistics rather than classical Boltzmann statistics. So, like in ideal gas, in this model the argument of the FD function is just KE and so always positive.
  5. Oct 14, 2015 #4
    Could you recommend a good book? I am looking for a book that introduces the structure of the atom in a quantum way. And preferably free and on the internet.
  6. Oct 16, 2015 #5
    Hi RaduAndrei,

    The two books which I like for the introduction of Fermi-Dirac statistics in relation to semiconductor devices are "Solid State Electronic Devices" by Streetman and "Semiconductor Physics and Devices" by Neamen.
  7. Oct 16, 2015 #6
    Very nice books. Thanks.
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