Modeling of transient thermoelectric transport in Harman method for films and nanowires

Harman method is a technique with great potential for rapidly scanning the figure-of-merit (zT) of emerging nanostructured thermoelectric materials. In the AC variant of this method zT is determined from the ratio of the electrical resistance measured across a thermoelectric material subjected to a sinusoidal current at high and low frequencies. The low frequency resistance incorporates both ohmic and Peltier responses, while at high frequencies the Peltier component vanishes. This work employs finite element modeling of the transient thermoelectric transport equations in thermoelectric thin films and nanowires to determine the frequency regime for a measurable temperature and voltage response to an applied alternating current. The lower bound for the high frequency requirement was found to depend on nanostructures' geometry (i.e. thin film thickness or nanowire diameter) and thermal properties. It is shown that reducing the thickness of the films or the diameter of the nanowires increases the lower bound for the high frequency regime, often imposing challenging conditions for the measurement of zT. Although heat losses from the sample surface due to natural convection have little effect on measured zT, the electrical contact resistance between the thermoelectric material and the contact electrodes can be the source for large errors. These aspects should be taken into account when performing experiments to characterize zT using the Harman method.