Quantum theory of the seebeck coefficient in metals

Based on the idea that different temperatures generate different carrier de nsities and the resulting diffusion causes the thermal emf, a new formula f or the Seebeck coefficient S is obtained: S = (2 ln 2/3)(qn)(-1) epsilon (F )k(B)(N-o/V), where q, n, epsilon (F), N-o and V are respectively charge, c arrier density, Fermi energy, density of states at epsilonF and volume. Ohm ic and Seebeck currents are fundamentally different in nature. This differe nce can cause significantly different transport behaviors. For a multi-carr ier metal the Einstein relation between the conductivity and the diffusion coefficient does not hold in general. Seebeck (S) and Hall (R-H) coefficien ts in noble metals have opposite signs. This is shown to arise from the Fer mi surface having "necks" at the Brillouin boundary.