Simple Intrinsic Semiconductor Question

[bartersnarter]

Homework Statement

Can anyone explained to me the factor of 2 in the equation for the intrinsic carrier concentration?

Homework Equations

n_i is proportional to exp(-E_g/2kT)
where n_i is the intrinsic carrier concentration, E_g is the band gap energy, k is Boltzmann's constant, and T is temperature in Kelvins.

The Attempt at a Solution

I understand that there are two charge carriers (a hole in the valence band and a free electron in the conduction band), but I don't understand why it is E_g/2 and not 2E_g.

 

[nasu]

Why would you think that it should be 2Eg?
Have you ever looked-up how the formula for intrinsic concentration is obtained?