The thermal model of a nanofabricated thermal probe (NTP) used in scanning thermal microscopy is proposed. It is based on consideration of the heat exchange channels between electrically heated probe, a sample, and their surroundings, in transient and harmonic regimes. Three zones in the probe-sample system were distinguished and modeled by using electrical analogies of heat flow through a chain of quadrupoles built from thermal resistances and thermal capacitances. The analytical transfer functions for two- and three-cell quadrupoles are derived. A reduced thermal quadrupole with merged RC elements allows for thermo-electrical modeling of the complex architecture of a NTP, with a minimum of independent parameters (two resistance ratios and two time constants). The validity of the model is examined by comparing computed values of discrete RC elements with results of finite element simulations and with experimental data. It is proved that the model consisting of two or three-cell quadrupole is sufficient for accurate interpretation of experimental results. The bandwidth of the NTP is limited to 10 kHz. The performance in dc regime can be simply obtained in the limit of zero frequency. One concludes that the low NTP sensitivity to sample thermal conductivity is due, much like in dc regime, to significant heat by-pass by conduction through the cantilever, and to the presence of probe-sample contact resistance in series with the sample.
Bodzenta, J., Chirtoc, M., & Juszczyk, J. (2014). Reduced thermal quadrupole heat transport modeling in harmonic and transient regime scanning thermal microscopy using nanofabricated thermal probes. Journal of Applied Physics, 116(5), 054501.