A simplified model to estimate thermal resistance between carbon nanotube and sample in scanning thermal microscopy

Scanning thermal microscopy (SThM) is an attractive technique for nanoscale thermal measurements. Multiwalled carbon nanotubes (MWCNT) can be used to enhance a SThM probe in order to drastically increase spatial resolution while keeping required thermal sensitivity. However, an accurate prediction of the thermal resistance at the interface between the MWCNT-enhanced probe tip and a sample under study is essential for the accurate interpretation of experimental measurements. Unfortunately, there is very little literature on Kapitza interfacial resistance involving carbon nanotubes under SThM configuration. We propose a model for heat conductance through an interface between the MWCNT tip and the sample, which estimates the thermal resistance based on phonon and geometrical properties of the MWCNT and the sample, without neglecting the diamond-like carbon layer covering the MWCNT tip. The model considers acoustic phonons as the main heat carriers and account for their scattering at the interface based on a fundamental quantum mechanical approach. The predicted value of the thermal resistance is then compared with experimental data available in the literature. Theoretical predictions and experimental results are found to be of the same order of magnitude, suggesting a simplified, yet realistic model to approximate thermal resistance between carbon nanotube and sample in SThM, albeit low temperature measurements are needed to achieve a better match between theory and experiment. As a result, several possible avenues are outlined to achieve more accurate predictions and to generalize the model.