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Effective density & Intrinsic carrier concentration

  1. May 3, 2007 #1
    1. The problem statement, all variables and given/known data
    Given "n=Nc*e-(Ec-Ef)/KT", prove "n=ni*e(Ef-Efi)/KT"


    2. Relevant equations
    Quasi-Fermi Energies..? Ef is Fermi level (extrinsic) and Efi is Fermi level (intrinsic). Ec is Fermi level (conduction).


    3. The attempt at a solution
    Very honestly, I cannot figure out how to start.....
    I know the value of "Nc", but I don't know how to deal with "ni" to prove the relationship.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. May 4, 2007 #2
    Is there given any relation between Nc and ni ?
    Can you say more about Nc? What is the expression of Nc??
     
  4. May 4, 2007 #3
    Nc=2[(2pi*m*KT)/h^2]^(3/2). (m=m*, effective mass for n)
    ni^2=NcNv*e^-(Ec-Ev)/KT.
    These are the only values I know.......
     
  5. May 6, 2007 #4
    You have Nc and Nv, i guess Nv is something related to the holes, right?
    having Nv=2[(2pi*m*KT)/h^2]^(3/2). (m=m*, effective mass for p)
    and p=Nv*e-(Ef-Ev)/KT. :blushing:

    Consider intrinsic semiconductor case (ie n=p=ni)
    we denote the intrinsic Fermi level as Efi and
    n=Nc*e-(Ec-Ef)/KT
    gives
    ni=Nc*e-(Ec-Efi)/kT

    Then, it can be seen that
    n=ni*e(Ef-Efi)/KT

    Notes: This result can be applied to any non-degenerate semiconductor (ie not just intrinsic/undoped semiconductor)

    Once little thing i want to confirm is that,
    what i learn for Nc is as a form of 2[(m*KT)/2pi*h^2]^(3/2) but not 2[(2pi*m*KT)/h^2]^(3/2).
    Are you using cgs unit system?? I dont know this makes the difference or not....:redface:
     
  6. May 7, 2007 #5
    oh..I see.
    Thank you so much tnho!
     
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