Ettingshausen Effect in GaAs/AlGaAs Superlattices

Abstract

We present a theoretical investigation of the Ettingshausen effect — the generation of a transverse temperature gradient under the action of an applied electric current — in GaAs/AlGaAs superlattices subjected to combined dc–ac electric fields and an external magnetic field. Using the Boltzmann transport equation (BTE) in the constant relaxation-time approximation, explicit expressions for the longitudinal and transverse Ettingshausen coefficients are derived in terms of the miniband width, chemical potential, magnetic field strength, and thermal conductivity. Analytical asymptotics reveal that at high temperatures, both coefficients saturate to finite plateaus, while at low temperatures, they exhibit strong non-monotonic behaviour and possible sign reversals depending on the superlattice parameter values. Numerical analysis demonstrates that increasing the miniband width enhances the low-temperature response, higher chemical potentials suppress and may invert the effect, and stronger magnetic fields or larger thermal conductivities reduce the net magnitude. These results show that the Ettingshausen effect in superlattices is highly tunable through band structure and external controls, suggesting opportunities for thermomagnetic cooling, field sensing, and nanoscale energy conversion applications.