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I am trying to find the amount of electrons in a conduction band in Si (Silicon), all I've got is a graph similar to this one:

enter image description here

I've tried to integrate like this: $$ N = \int_{1}^{\infty} \frac{1}{1+\exp(E-E_f)} \cdot D(E)\text d E$$

However, I have a hard time finding what $D(E)$ is supposed to be. If i put is as: $D(E) = C \cdot \sqrt{E}$, where $C = \text{const.}$ The integral becomes unsolvable.

I appreciate any help!

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    $\begingroup$ Isn't $D(E)$ just the function plotted in your graph? $\endgroup$
    – probably_someone
    Commented May 25, 2020 at 15:07
  • $\begingroup$ Yes, but in order to solve the integral, I need an expression for it. $\endgroup$
    – geby
    Commented May 25, 2020 at 15:09
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    $\begingroup$ Ok, so digitize the graph, then. For example: datathief.org $\endgroup$
    – probably_someone
    Commented May 25, 2020 at 15:11
  • $\begingroup$ What is the temperature? What is the chemical potential? How can you take something like $\exp(E-E_f)$ where $E$ is a dimensionfull energy (I assume that this is what it is)? $\endgroup$
    – user245141
    Commented May 25, 2020 at 16:27
  • $\begingroup$ Try calculating the effective density of states kx.lumerical.com/t/calculating-the-effective-density-of-states/… at 300K you should get a number around 3e19/cm^3 $\endgroup$
    – boyfarrell
    Commented May 25, 2020 at 19:41

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