Calibration of conductance channels and heat flux sharing in scanning thermal microscopy combining resistive thermal probes and pyroelectric sensors

The goal of this work is to establish the heat flux sharing among different heat exchange channels in scanning thermal microscopy (SThM), basing on experimental data. To this end, dc or modulated excitation with 3-omega detection at the third harmonic is applied to two types of resistive (Wollaston-, WThP and nanofabricated-, NThP) thermal probes. The main difference between the WThP and the NThP is the absence of a thermal coupling zone between the active zone and the heat sink in the WThP. Probe responsivities in dc or ac regime are defined, which depend only on total thermal conductance of probe-sample system. It is shown that in SThM it is not possible to discriminate between heat fluxes leaking across the air to the ambient and to the sample. Because of their interdependence, only their sum can be determined with the ThP alone. Replacing the sample by a pyroelectric heat flux sensor (PES), its 2-omega signal yields the ratio of the flux received through the contact to that received through the air. Eventually, the complete heat flux sharing among different channels is determined, for the studied high conductivity sample. For both probes, about 60 % of the dissipated power leaks through the cantilever to the probe holder. The heat flux through the contact represents 19.5 % for the WThP and 11.4 % for the NThP. The remaining heat flux is lost to the ambient or to the sample via the air. The corresponding thermal conductance values are determined in successive steps in vacuum (V), in air (A), out of contact (N) and in contact (C) using thermal quadrupole representations. The procedure requires only the calibration of the ThP and not that of the PES. For thermal conductivity measurements, the reference configuration (N) offers superior dynamic range to (A) one.