Chemical Potential and Fermi Energy

The chemical potential at OK is the same as the Fermi energy which we obtained in Chapter 2 by summing over the states in the electron in a box problem. The Fermi energy is a constant for a given material. 

Sommerfeld obtained a series solution for Equation 15.29 which provides a good approximation of the chemical potential for Tp 3 T, 

When material 1 with workfunction j i and Fermi level Epi is brought into contact with material 2 with work-function 02 and Fermi level Ep2, the vacuum levels line up and electrons flow from the material with the higher Fermi level (chemical potential) to the lower Fermi level (chemical potential) until equilibrium is reached and the Fermi levels in the two materials are the same. 

All particles can be classified into two categories, bosons and fermions. Bosons include protons, neutrons, most atoms, and molecules. They have integral units of spin and have no restriction on the number of particles that can occupy a quantum state. They obey B-E statistics and the B-E distribution function is given by Equation 15.13, 

In the classical limit, A becomes small so that the —1 in the denominator can be neglected and the distribution reduces to the M-B distribution given by 

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