Semiconductors: Find maximum Operating temp.

  1. 1. The problem statement, all variables and given/known data
    "A GaAs device is doped with a donor concentration of 3x10^15 cm^-3.For the device to operate properly, the intrinsic carrier concentration must remain less than 5% of the total electron concentration. What is the maximum temperature that the device can operate?"

    2. Relevant equations
    ND=3 x 1015 cm-3

    n0*p0 = ni2

    ni=0.05n0 or 20ni=n0

    ni=sqrt(NCNV)*exp(Eg / 2kT)

    NC=2(m*dsekT / 2pi(h-bar)2)3/2

    NV=2(m*dshkT / 2pi(h-bar)2)3/2

    ND - NA -n0 + p0 = 0

    k = boltzman's constant

    I think that's all the equations that will be needed?

    3. The attempt at a solution
    Honestly, I've just been rearranging equations and plugging things in up to this point. My teacher said we will need MATLAB to find the final solution, not sure if that really is the case or not. Really, I have no idea where to start. I've just been looking at it for a solid hour and haven't written much down. I will start that now and post updates, I just wanted to get this up and let people look at it I guess.

    Actually, I take some of that back. I substituted and rearranged the last equation I put up there.
    3 x 1015 cm-3 = NA + 20ni - ni/20 = NA - (399/20)*ni

    I'm going to work on this now. Any help/advice/stimulating conversation will be greatly appreciated. Thanks.
    Last edited: Mar 8, 2012
  2. jcsd
  3. How do I know if I can neglect NA? In a lot of the example problems in the book, it always talks about neglecting one thing or another because it small, but I don't see where it says what "small" means, or how you know something is small based on another value.
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