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Homework Help: Semiconductor Physics - Density of States Calculation Problem?

  1. Sep 20, 2012 #1
    1. The problem statement, all variables and given/known data

    Determine the total number of energy states in silicon from the edge of the conduction band to Ec + kT for T = 300K.

    2. Relevant equations

    N = [itex]\int[/itex]g(E)dE

    3. The attempt at a solution

    I'm pretty sure I know how to do this one. The only problem is, when I get to the step where I have to plug in numbers (i.e. the equation becomes N = (2/3)(4[itex]\pi[/itex](2mn*)(3/2)*(kT)(3/2))/h3), I cannot calculate it!

    Reason: Obviously Planck's Constant cubed is an INCREDIBLY small number, and my calculator takes exception, just rounding to 0. There must be a way around it, or a rearrangement that helps, but I don't know what to do. Any advice? Sorry if my equation is formatted a little strangely.
  2. jcsd
  3. Sep 20, 2012 #2
    Update: Realized I could use Google to calculate such a sum, and got the answer! Now I have a new problem.

    The second part of that question asks for the same thing, but for the holes. It gives the effective hole mass as 5.10*10^-31. T = 298K this time. When I plug in the values, I get about 1.4*10^19 (in states /cm^3; my answer in m^3 is to the 10^25), but that's not correct. I'm quite confused as I believe I've put it in correctly.

    Besides doing the calculation over again, I was wondering if there was a relationship between the electron state density and the hole state density that might allow me to approximate? I know the temperature differs by 2K.
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