Thermoelectric figure of merit in transverse magnetic field under adiabatic and isothermal conditions

Abstract The influence of the magnetic field on the thermoelectric figure of merit in semiconducting materials is studied theoretically. One of the important issues is the urgency to distinguish the various conditions under which the magneto-thermoelectric effects can be observed. Isothermal effects take place when there is no temperature gradient in the direction perpendicular to the plane containing the magnetic field and applied temperature gradient. Adiabatic effects occur when there is no heat current in the same transverse direction while a temperature gradient arises due to the Righi-Leduc effect. In this paper we examine how the application of an external magnetic field can vary the figure of merit ZT under isothermal and adiabatic conditions and establish relations among them for both longitudinal and transverse Nernst-Ettingshausen effects. Analytical expressions for the figures of merit are obtained in semiconductors with both non-degenerate and strongly degenerate statistics of charge carriers, in limiting cases of weak and classically strong magnetic fields.