Title: Accurate determination of thermoelectric figure of merit using ac Harman method with a four-probe configuration

Abstract: The ac Harman method has been used for the direct estimation of dimensionless thermoelectric figure of merit (zT) through ac/dc resistance measurements. However, accurate zT estimation with a four-probe configuration is difficult owing to the occurrence of a thermal phase-delay in the heat flow with a low frequency current. This study reports an exact solution for zT estimation by solving the heat conduction equation. The analysis can explain the reverse heat flow, which is the main source of the error in the four-probe configuration, and the experimentally obtained behavior of the frequency dependence of zT of (Bi,Sb)$_2$Te$_3$. Approximately 20 % of the error is caused by a thermal phase-delay, unless an appropriate current frequency and voltage-terminal position are chosen. Thus, an accurate zT evaluation using a four-probe configuration at any voltage terminal position is achieved. These findings can lead to interesting thermoelectric metrology and could serve as a powerful tool to search for promising thermoelectric materials.