Transverse Nernst–Ettingshausen effect in the two–dimensional electron gas of a doubly periodic semiconductor superlattice

The surface density of charge current in two-dimensional double-periodic $n$-type semiconductor superlattices is calcu- lated in the one-electron approximation in an external magnetic field in the presence of a temperature gradient. The magnetic field was assumed to be constant, uniform, applied perpendicular to the plane of the electron gas. The joint solution of the Schrödinger equation and the kinetic Boltzmann equation showed that the dependence of the transverse surface density of the current on temperature and module temperature gradient are significantly non-linear in nature, areas with negative differential conductivity occur. The dependence of the relaxation time on the quasi-momentum of the electron is taken into account in the model phenomenologically through the dispersion law of carriers in magnetic subbands.