Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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.

    Last edited: Sep 28, 2006
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?