Effects of sample topography and thermal features in scanning thermal conductivity microscopy

This article analyses the operation of an atomic force microscope whose cantilever, which is heated at its free end, is used to map topography and thermal features across a sample surface. The analysis takes into account the thermal flow along the cantilever, between the cantilever and sample via air, and through the constriction formed at the tip-sample contact area. The thermal flow through the constriction is analysed in terms of Maxwell and Sharvin components as given by Wexler. Examples using silicon tips and samples with a rectangular grid consisting of (a) silicon and silicon oxide features and (b) silicon oxide steps of 100 nm height, show that long tips are more sensitive to the thermal features of the sample while short once are more sensitive to its topography.