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Fermi Energy in Intrinsic Si, Ge, and GaAs

  1. Nov 4, 2014 #1
    1. The problem statement, all variables and given/known data

    Using the values of the density of states effective masses me* and mh* in table 5.1, find the position of the Fermi energy in intrinsic Si, Ge, and GaAs with respect to the middle of the bandgap (Eg/2).

    Table 5.1 shows the following density of states effective masses me*/me and mh*/me:

    Si: 1.08
    Ge: 0.56
    GaAs: 0.67

    Si: 0.60
    Ge: 0.40
    GaAs: 0.50

    2. Relevant equations

    Fermi energy for an intrinsic semiconductor:

    EFi = Ev + (1/2)Eg - (3/4)kT⋅ln(me*/mh*)

    3. The attempt at a solution

    I believe understand the equation perfectly. The Fermi energy will be about half way between the edges of the valence and conduction bands, and will vary slightly with temperature depending on the - (3/4)kT⋅ln(me*/mh*) term. The problem I am having is determining the values for Ev to use in the equation. I can only think of three possible solutions:

    - I am expected to give the answer in the form of "the Fermi energy for intrinsic Si is X above the valence band (or X below the conduction band)"

    - I really am expected to look up the values for Ev in a table somewhere.

    - I'm supposed to calculate Ev somehow with a different equation (which I am unfamiliar with).

    Can someone please point me in the right direction?
  2. jcsd
  3. Nov 5, 2014 #2
    Looking at the question more closely, I noticed it asks for the Fermi energy "with respect to the middle of the bandgap (Eg/2)." Does this mean that I can just ignore the Ev + (1/2)Eg - (3/4)kT part of the equation? I think this is the solution.
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