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Cdg8676

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## Homework Statement

2) For an intrinsic (undoped) semiconductor at room temperature with the Fermi energy in the center of the 1 eV band gap, find the fraction of unoccupied electron states at the top of the valence band and the fraction of occupied states at the bottom of the conduction band.

## Homework Equations

I am looking for a push in the right direction for this problem. I have never encountered this before and we do not have a book as this is a lab class and I had to miss the lecture because my son was sick and had to stay home from school.

I found an equation for the Fermi Energy which is: E_F=E_{N/2}-E_0=(hbar^2 pi^2)/(2 m L^2) (N/2)^2

## The Attempt at a Solution

I am not sure how to use the Fermi energy to find the occupied and unoccupied fraction of electron states.

Ok found some more information. The Fermi function is described by:

f(E)=1/(e^[(E-E_f)/kT]+1)

where E_f is the Fermi energy. This equation is supposed to give you the probability that electrons will exist above the Fermi level at a given temperature. I just don't know which values to use for E and E_f. Any suggestions?

I think I figured it out using the population of conduction band equation I found:

N_cb = AT^(3/2)e^(-E_gap/(2kT))

going with this to find the fraction. Sound good to anyone? Ended up getting 2.09x10^-5 as the fraction of unoccupied electron states in the valence band and occupied states in the conduction.

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