The effect of the band edges on the Seebeck coefficient

The classical thermopower formulae generally applied for the calculation of the Seebeck coefficient S are argued to be incomplete. S can be separated into two different contributions, a scattering term, S(0), and a thermodynamic term, Delta S, representing the additional change of the electrochemical potential mu with temperature T caused by 'non-scattering' effects, for instance, the band edge shift with T. On the basis of this separation into S(0) and Delta S, it is shown that shifts of the band edges with T lead to an additional contribution to the classical thermopower formulae. This separation provides the basis for an interpretation of positive thermopowers measured for many metals. Positive thermopower is expected if the energy of the conduction band edge increases with T and if this effect overcompensates for the influence of the energy dependent conductivity, sigma(E). Using experimental thermopower data, the band edge shifts are determined for a series of liquid normal metals.