1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Fermi Dirac probabilty/density confusion

  1. Oct 6, 2012 #1
    -Admin, If possible, please delete the similar looking question posted in the introductory physics category

    I'm having trouble understanding the concept of the Fermi Dirac probability. What I understand so far, its based upon two variables, cubic length and energy level. In addition, I understand that



    and that


    I end up having trouble when trying to integrate this. Using a textbook example of intrinsic silicon at T=300 Kelvin, (solving for the density of carriers in the conduction band) it mentions the answer as [itex]N(E)=1.102*1010 cm-3 [/itex].

    If I recall correctly:
    [itex]\int\sqrt{x}=\frac{2}{3}*(x)(3/2)[/itex] Since the Energy variable is being integrated, I approach this problem in this fashion

    [itex]N(E)=\frac{1}{1+e\frac{E-EF}{kT}*(\frac{2}{3}*(ΔE)(3/2))[/itex] (within the textbook the limits are Ec and Ec+1ev)

    Since I already know the Boltzmann constant, the temperature, the Energy gap (1.12eV) and the Fermi Energy (given as Energy/2), I'm able to plug in most of the values. What is troubling me is when I preform the math, I end up with a value of 2.073*1012cm-3 and not 1.102*1010

    the values I'm using for e is (Ec)-(Ec-Eg/2), and (300k)*(Boltzmann constant) resulting in

    I do convert the delta E into Joules

    what I don't understand is, why am getting the wrong answer? The textbook doesn't fully explain nor is the professor approachable
    1. The problem statement, all variables and given/known data

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. Oct 7, 2012 #2

    rude man

    User Avatar
    Homework Helper
    Gold Member

    For some reason I'm not getting your itex decoded.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook