Quantifying non-contact tip-sample thermal exchange parameters for accurate scanning thermal microscopy with heated microprobes.

Simplified heat-transfer models are widely employed by heated probe scanning thermal microscopy techniques for determining thermal conductivity of test samples. These parameters have generally been assumed to be independent of sample properties; however, there has been little investigation of this assumption in non-contact mode, and the impact calibration procedures have on sample thermal conductivity results has not been explored. However, there has been little investigation of the commonly used assumption that thermal exchange parameters are sample independent in non-contact mode, or of the impact calibration procedures have on sample thermal conductivity results. This article establishes conditions under which quantitative, localized, non-contact measurements using scanning thermal microscopy with heated microprobes may be most accurately performed. The work employs a three-dimensional finite element (3DFE) model validated using experimental results and no fitting parameters, to determine the dependence of a heated microprobe thermal resistance as a function of sample thermal conductivity at several values of probe-to-sample clearance. The two unknown thermal exchange parameters were determined by fitting the 3DFE simulated probe thermal resistance with the predictions of a simplified probe heat transfer model, for two samples with different thermal conductivities. This calibration procedure known in experiments as the intersection method was simulated for sample thermal conductivities in the range of 0.1-50 W m K and clearance values in the 260-1010 nm range. For a typical Wollaston wire microprobe geometry as simulated here, both the thermal exchange radius and thermal contact resistance were found to increase with the sample thermal conductivity in the low thermal conductivity range while they remained approximately constant for thermal conductivities >1 W m K, with similar trends reported for all clearance values investigated. It is shown that versatile sets of calibration samples for the intersection method should employ either medium range (1 W m K) and (2 W m K) thermal conductivities, or wide range (0.5 W m K) and (50 W m K). The medium range yielded results within 1.5%-20.4% of the expected values of thermal conductivity for specimens with thermal conductivity within 0.1-10 W m K, while the wide range yielded values within 0.5%-19.4% in the same range.