How do I calculate the Fermi Energy of a compound?

[member 422733]

Homework Statement

1) This question has to do with pure InAs, with a bandgap 0.33 eV, electron mass 0.02, hole mass 0.41.
(a) Evaluate the number of electrons/m³ int he conduction band at 300K. For this purpose you can assume the Fermi Energy is exactly at the center of the energy gap.

Homework Equations

If the Fermi energy E_F is located at least kT away from the conduction or valence band edge, the probablility of occupation of the electron state is adequately given by
$f(E) = e^{\frac{-(E - E_F )}{k_B T}}$

The number of electrons is given below as N_e
$N_e = N_C e^{\frac{-(E_G - E_F )}{k_B T}} \\<br /> N_C = 2(\frac{2\pi m^{*}_{e} k_B T}{h^2})^{3/2}$

I believe E_G is the band gap energy. h is Planck's Constant.

The Attempt at a Solution

The part where I am stumped is where it says that the "Fermi energy is exactly at the center of the energy gap." Does that mean I take E_F to be 0.33 eV / 2? If so, I guess the rest of the problem is just plug and chug.

 

[Munawar84]

The Fermi energy is a concept in quantum mechanics usually referring to the energy difference between the highest and lowest occupied single-particle states in a quantum system of non-interacting fermions at absolute zero temperature. In a Fermi gas, the lowest occupied state is taken to have zero kinetic energy, whereas in a metal, the lowest occupied state is typically taken to mean the bottom of the conduction band.