Nonlocal and memory effects in nanoscaled thermoelectric layers

Abstract

In this paper, we address the problem of heat and electric charge transport in a thermoelectric nanoscaled layer when an electric current is applied. The analysis is based on constitutive equations of the Maxwell-Cattaneo type describing the time evolution of dissipative flows with transport and thermoelectric coefficients depending on the width of the layer. This introduces memory and nonlocal effects and consequently a wave-like behaviour of system's temperature. We study the effects of the application of an electric current in two cases, namely, a constant current and a pulsed current. The time evolution of the system and the stationary state are determined. Besides the well known supercooling effect obtained when the electric pulse is applied, our results show the existence of a similar effect during the transient due to the wave-like behaviour of the temperature. The thermal figure of merit (TFM) is calculated at the minimum temperature reached during the supercooling, both in the transient and the pulsed regime. The maximum value of TFM in the transient reaches 114 improving the value of long length scale devices by a factor of 100. When the electric pulse is applied, TFM is improved by a factor of 20 over long length scale devices. We use the spectral methods of solution which assure a well representation of wave behaviour of heat and electric charge in short time scales given their spectral convergence.