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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

[itex]f_{F}(E)=\frac{4\pi*(2*m^{*}_{n})^{(3/2)}}{h^{3}}\sqrt{E}[/itex]

[itex]g(E)=\frac{1}{1+e^{\frac{E-EF}{kT}}}[/itex]

and that

[itex]N(E)=\intf_{F}(E)*g(E)dE[/itex]

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*10^{10 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 cm-3 the values I'm using for e is (Ec)-(Ec-Eg/2), and (300k)*(Boltzmann constant) resulting in [itex]e\frac{0.56eV}{0.0259eV}[/itex] 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}

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# Homework Help: Fermi Dirac probabilty/density confusion

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