Fermi Dirac (FD) and Maxwell Boltzmann (MB)

[Corneo]

I have a homework problem that asks me to interpret the two curves for when the Fermi level (Ef) is 0.25 eV. I ploted the two graphs and both of them look nothing alike when E < Ef. But both plots predict a probability of essentially zero when E > Ef. I was wondering why is there such a large difference in the beginning? Is it because the MB predicts that almost all the electrons will in the lowest state, while FD takes into account of the Pauli Exclusion principle? It seems that both plots are essentially the same when E is the conduction band energy level.

 

[StatusX]

The difference depends largely on the temperature, and you haven't mentioned what temperature you're considering. If the temperature is much larger than the Fermi temperature, E_F/k_B (in your case about 3000 K), then quantum mechanical effects, like the exclusion principle, aren't important, and the curves are essentially the same. When the temperature is lower than the Fermi temperature, then the quantum effects are important because most of an electron's energy will be due to the exclusion principle. That is, it has the energy it does because all lower energy levels are occupied, not because of the temperature, which is the only classical source of energy.

 

[Corneo]

I forgot the mention that the temperature I am considering is 300 K. So I guess Quantum Mechanics must be taken into consideration.