Solid State Chemistry Question Regarding Fermi Energy

[SchrodingersMu]

Hi there,

I am new to electron theory, and have a question regarding fermi energy. The book I am reading plots the Fermi energy distribuiton function vs Energy for T=0 ( upper right graph in pcture) and for T not equal to zero. The book says that, when T does not equal zero, the decrease in the fermi energy distribution function "smears out."(Figure in lower left.) The book does not say much more than this, so I am wondering why the increase in temperature causes the fermi energy distribution function to change less rapidly. Is it because we have higher temperatures which, in turn, give the electrons higher kinetic energies and thus the ability to occupy higher energy levels?

Thank you in advance!

 

[DrClaude]

I am new to electron theory, and have a question regarding fermi energy. The book I am reading plots the Fermi energy distribuiton function vs Energy for T=0 ( upper right graph in pcture) and for T not equal to zero.

Just to be clear, that is the Fermi distribution, which gives the average number of particle per state, as a function of the energy of that state.

The book says that, when T does not equal zero, the decrease in the fermi energy distribution function "smears out."(Figure in lower left.) The book does not say much more than this, so I am wondering why the increase in temperature causes the fermi energy distribution function to change less rapidly. Is it because we have higher temperatures which, in turn, give the electrons higher kinetic energies and thus the ability to occupy higher energy levels?

Yes. At T = 0 K, N electrons will fill the N lowest energy states (including spin degeneracy) as the Pauli principle forbids two fermions to occupy the same state. All higher energy states are unoccupied. For T > 0 K, the additional thermal energy leads to excitations of the electrons to higher energy states.