# How do I calculate the Fermi Energy of a compound?

HunterDX77M

## 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 EF 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 Ne
$N_e = N_C e^{\frac{-(E_G - E_F )}{k_B T}} \\ N_C = 2(\frac{2\pi m^{*}_{e} k_B T}{h^2})^{3/2}$

I believe EG 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 enery is exactly at the center of the energy gap." Does that mean I take EF to be 0.33 eV / 2? If so, I guess the rest of the problem is just plug and chug.

## Answers and Replies

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.