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Calculating Fermi Level

  1. Apr 22, 2008 #1
    1. The problem statement, all variables and given/known data
    (a)If a silicon crystal is doped with 10^15 cm−3 phosphorus atoms, find out the electron
    concentrations and hole concentrations in the silicon at room temperature. Find
    out the Fermi level.
    (b)Repeat at temperature = 0K

    2. Relevant equations
    n*p=ni^2
    n=2(2pi(n*)kT)^(3/2)exp-[(Ec-Ef)/(kT)] where (n*) = electron effective mass


    3. The attempt at a solution
    I have calculated the hole concentration p = 10^15 per cm^3
    and the electron concentration n = 1.96*10^5 electrons per cm^3

    but I am not sure where to begin for calculating the fermi level. I don't know what to plug in for Ec the conduction band edge energy. For part (b) I am also unable to find ni, the intrinsic carrier concentration of silicon at T = 0K. Any suggestions or insight would be appreciated, thanks in advance.
     
  2. jcsd
  3. Apr 24, 2008 #2
    Ef=[(Ec+Ev)/2]+((KT/2))ln(Nc/Nv):if n=p=ni

    and i think that you can use Eqs:
    Ef==KT*ln{[(1/4)*[e^(Ed/KT)]*([(1+(8Nd/Nc)e^(deltaEd/KT))^(1/2)]-1)}
     
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