# Homework Help: Fermi Dirac probabilty/density confusion

1. Oct 6, 2012

### cybhunter

-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

$fF(E)=\frac{4\pi*(2*m*n)(3/2)}{h3}\sqrt{E}$

$g(E)=\frac{1}{1+e\frac{E-EF}{kT}}$

and that

$N(E)=\intfF(E)*g(E)dE$

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 $N(E)=1.102*1010 cm-3$.

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

$N(E)=\frac{1}{1+e\frac{E-EF}{kT}*(\frac{2}{3}*(ΔE)(3/2))$ (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
$e\frac{0.56eV}{0.0259eV}$

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. Oct 7, 2012

### rude man

For some reason I'm not getting your itex decoded.