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Intrinsic carrier concentration where did I go wrong?

  1. Nov 16, 2017 #1
    1. The problem statement, all variables and given/known data
    I've looked up the intrinsic carrier concentration of silicon, and what I've got isn't close. The question says given there are ##2\times 10^{22}## electrons per cubic cm in silicon, and the bandgap is ##1.1##eV, what is the free electron concentration at room temperature?

    2. Relevant equations


    3. The attempt at a solution
    My first thought is that since
    ##n_i = \sqrt{N_cN_v} \exp\left(\frac{-E_g}{2kT}\right)##
    Maybe as T tends to infinity all electrons are free electrons so that ##\sqrt{N_cN_v}=n_i##, but then subbing that back in at room temp would mean ##10^{12}## free electrons per cubic cm, so too high, but then that would be assuming the densities of states are constant at different temperatures, and they're not.

    For silicon I can get around this by just looking up ##N_c## and ##N_v##, but I have to repeat the process for diamond and the values aren't available. I do get the right order of magnitude estimate for diamond's carrier concentration just by using the same ##N_c## and ##N_v## as for silicon, presumably that's because they're similar in terms of crystal structure.

    However, my professor assures me that all I should need is the electron concentration and the bandgap. I'd appreciate any help, been stuck on this for a while! :)
     
    Last edited: Nov 16, 2017
  2. jcsd
  3. Nov 21, 2017 #2

    DrDu

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    Science Advisor

    How is the situation at T=0?
     
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