be intrinsic in which case the bands conduct in parallel, and so the measured values will be This results in a crossover behaviour, as shown in the figure. The highest Seebeck coefficient is obtained when the semiconductor is lightly doped, however a high Seebeck coefficient is not necessarily useful on its own. For thermoelectric power devices (coolers, generators) it is more important to maximize the thermoelectric power factor , or the thermoelectric figure of merit, and the optimum generally occurs at high doping levels. Phonon drag Phonons are not always in local thermal equilibrium; they move against the thermal gradient. They lose momentum by interacting with electrons (or other carriers) and imperfections in the crystal. If the phonon-electron interaction is predominant, the phonons will tend to push the electrons to one end of the material, hence losing momentum and contributing to the thermoelectric field. This contribution is most important in the temperature region where phonon-electron scattering is predominant. This happens for where is the Debye temperature. At lower temperatures there are fewer phonons available for drag, and at higher temperatures they tend to lose momentum in phonon-phonon scattering instead of phonon-electron scattering. At lower temperatures, material boundaries also play an increasing role as the phonons can travel significant distances. Practically speaking, phonon drag is an important effect in semiconductors near room temperature (even though well above ), that is comparable in magnitude to the carrier-diffusion effect described in the previous section. This region of the thermopower-versus-temperature function is highly variable under a magnetic field. Relationship with entropy The Seebeck coefficient of a material corresponds thermodynamically to the amount of entropy "dragged along" by the flow of charge inside a material; it is in some sense the entropy per unit charge in the material. References Thermoelectricity