  Theoretical descriptions of the Seebeck coefficient in terms of the
differential electrical conductivity given by Cutler and Mott is the foundation
of later works in terms of transmission function from the thermoelectric
transport theory. On the other hand, recent studies in the literature have
shown the relation between the Seebeck coefficient and chemical potential of
electrons. In this work, this relation is rigorously derived from fundamental
thermodynamics, and an formalism for the parameter-free calculation of the
Seebeck coefficient based on the electronic density-of-states from
first-principles calculations is presented. Numerical results are given using
the n-type La3-xTe4 thermoelectric material as the prototype. With the rigid
band approximation, the calculated temperature dependences of the Seebeck
coefficients of La3-xTe4 as a function of carrier concentration show excellent
agreements with experimental data.
