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Fraction of unoccupied electron states

  1. Aug 29, 2013 #1
    1. The problem statement, all variables and given/known data

    2) For an intrinsic (undoped) semiconductor at room temperature with the Fermi energy in the center of the 1 eV band gap, find the fraction of unoccupied electron states at the top of the valence band and the fraction of occupied states at the bottom of the conduction band.



    2. Relevant equations

    I am looking for a push in the right direction for this problem. I have never encountered this before and we do not have a book as this is a lab class and I had to miss the lecture because my son was sick and had to stay home from school.

    I found an equation for the Fermi Energy which is: E_F=E_{N/2}-E_0=(hbar^2 pi^2)/(2 m L^2) (N/2)^2


    3. The attempt at a solution

    I am not sure how to use the Fermi energy to find the occupied and unoccupied fraction of electron states.

    Ok found some more information. The Fermi function is described by:

    f(E)=1/(e^[(E-E_f)/kT]+1)

    where E_f is the Fermi energy. This equation is supposed to give you the probability that electrons will exist above the Fermi level at a given temperature. I just don't know which values to use for E and E_f. Any suggestions?

    I think I figured it out using the population of conduction band equation I found:

    N_cb = AT^(3/2)e^(-E_gap/(2kT))

    going with this to find the fraction. Sound good to anyone? Ended up getting 2.09x10^-5 as the fraction of unoccupied electron states in the valence band and occupied states in the conduction.
     
    Last edited: Aug 29, 2013
  2. jcsd
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