Determination of thermoelectric properties from micro four-point probe measurements

Micro four-point probing is a branch of electrical metrology where electrical (and electromagnetic) properties of charge carriers such as conductance, mobility, and tunneling magnetoresistance can be accurately and precisely determined at the μm scale and below. Here, we propose and demonstrate a novel application of micro four-point probe (M4PP) aimed at quantifying the thermoelectric properties of a sample. Specifically, we show that for an AC current passing through a bulk material at a low angular frequency ω, the voltage drop across the sensing electrodes at 2ω is to first order proportional to the ratio (α/κ) of its Seebeck coefficient (α) to its thermal conductivity (κ). Verified by numerical simulations, our analytic theory is then put into practice on a suite of p- and n-type bulk semiconductors (Si, Ge, and BiTe). The M4PP estimates of the Seebeck coefficient in these materials are characterized both by high accuracy and precision, suggesting a novel in-situ metrology of thermoelectric properties at the µm scale.