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Question regarding FD distribution and doped SC

  1. Sep 28, 2006 #1
    Consider an n-doped semiconductor. I am trying to figure out at which temperature half of all the donors will be ionized, given energies of donor level and band gap.

    I was thinking that, because the chance is 50% that the donors be populated, the Fermi level must lie exactly on the donor level energy, [tex]E_d[/tex]. I was thinking that if we integrate the FD from the conduction band edge to infinity and set this integral equal to one half:

    [tex]\int_{E_c}^{\infty} \frac{1}{e^{(\epsilon - \mu)/kT} + 1} d\epsilon = \frac{1}{2}[/tex]

    Obviously, this is the wrong way about to solve this problem, since i get the temperature 8570K(Using [tex]E_d = E_C - 0.025, E_g = 1.12[/tex] as example values (in eV). I am not very used to working with the FD distribution as you see, and i would need some input.

    Another way to go about this problem i guess, is multiplying the FD distribution with the density of states and integrate, setting the integral equal to N_d/2, where N_d is the number of donor atoms.

    Thanks
     
    Last edited: Sep 28, 2006
  2. jcsd
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