The Fermi distribution function

   f(\epsilon) = 1/((e^(\epsilon-\mu)/k_BT+1)  (1)

has a term \mu. This is called chemical potenntial. This is a function of temperature. Also \mu has to be chosen for the particular problem in such a way that the total number of the particles in the system comes out correctly, i.e. N. At absolute zero \mu = \epsilon_F or Fermi energy. (The Fermi energy \epsilon_F is defined as the energy of the topmost filled level in the ground state.) This is because in the limit T tends to zero the function f(\epsilon) changes discontinuously from the value 1 (filled) to the value 0 (empty) at \epsilon = \epsilon_F = \mu. At all temperatures f(\epsilon) is 1/2 when \epsilon = \mu for then the dinominator of the equation (1) has the value 2.

It is difficult to suggest books unless I know your background. If you are a theoretician or aspire to be a theoretical condensed matter physicist I shall suggest you to read the books by W. Harrison or P. Fulde. But if you are an experimentalist then you should be content to read the elementary text books on solid state physics. There are plenty of them available.

I forgot to give the thermodynamic definition of chemical potential which I assumed you know already. I am now recapitulating this: In the limit of a large system the Helmholtz free energy F approaches a smooth function of N, V and T where N is the total number of particles, V and T are volume and temperatures. The chemical potential is then defined as

      \mu = F(N+1,V,T) - F(N,V,T).