Deconvolution of heat sources for application in thermoelectric micro four-point probe measurements

Abstract

Joule heating is a primary phenomenon responsible for increasing temperature in electronic devices, and consequently, decreasing the lifetime and performance of electronic devices. However, this unwanted Joule heating can itself be used as a local source of heat to map the temperature-dependent material properties. Recently, micro four-point probe (M4PP) showed a promising potential for characterizing the temperature coefficient of resistance (TCR) and the Seebeck coefficient using Joule heating resulting from the measurement current. Here, we use M4PP to estimate the micrometer scale, relative temperature profile resulting from a single heat source. We introduce a triplet of four-point voltages measured at the second harmonic frequency, to deconvolute the thermoelectric voltage from the three individual heat sources involved. This paper tests and documents the validity of the proposed scheme in the 1–40 μm range on highly doped single crystal Si at 300 K, supporting predominantly Fourier heat transport at these scales. The method of deconvolution of heat sources reduces the complexity in evaluation of length- and time-dependent measurements, specifically used in the characterization of thermoelectric properties. The proposed method may also facilitate a more profound understanding of heat transport on the mesoscopic scale.