Thermal conductivity calibration for hot wire based dc scanning thermal microscopy

Abstract

Thermal conductivity characterization with nanoscale spatial resolution can be performed by contact probe techniques only. The technique based on a hot anemometer wire probe mounted in an atomic force microscope is now a standard setup. However, no rigorous calibration procedure is provided so far in basic dc mode. While in contact with the sample surface, the electrical current I injected into the probe is controlled so that electrical resistance or the wire temperature is maintained by the Joule effect. The variation in current is assumed to be linearly related to the heat flux lost towards the sample and traditional calibration is carried out by relating the thermal conductivity of a set of samples to the measured current I. We provide analytical and numerical thermal modeling of the tip and sample to estimate the key heat transfer in a conductivity calibration procedure. A simple calibration expression is established that provides thermal conductivity as a function of the probe current or voltage measured. Finally, experimental data allow us to determine the unknown quantities of the parametric form obtained, i.e., the mean tip-sample contact radius and conductance.

Nanoscale heat transfer at contact between a hot tip and a substrate

“…In those conditions, the range of radius values is 1.5-3.3μm (90%) and 4 -5.4μm (50%). A value of 1μm for b was obtained in previous works [7] from experimental data when the tip temperature is higher than 100°C. In those conditions, the meniscus disappears and air conduction becomes predominant.…”

“…The temperatures at both ends are set to the ambient because the silver is assimilated to a heat sink. The detailed solving of the thermal problem is proposed in references [7,9]. The expression of the probe-sample conductance G eq including the contact G C and the sample G S contributions writes:…”

“…In our previous papers [7][8][9], we identified the contact radius as being 1 micron when the tip temperature is larger than 100°C and about 200nm when it is lower. We presume that the change in the contact radius produces a change in the modes contributions.…”

Finite Element Analysis of the Material’s Area Affected during a Micro Thermal Analysis Applied to Homogeneous Materials

“…The heat flux q on the top of sample surface due to convection is governed by boundary convection: estimate a circular contact surface with a 80 nm radius and a concentric circular water meniscus surface with an outside radius of 306 nm. As for Lefèvre et al [17][18][19], they have suggested contact radii values ranging from 200 nm to 1 µm depending on temperature and probe geometry.…”

Batch fabricated dual cantilever resistive probe for scanning thermal microscopy

“…By scanning a heated tip across the sample surface a spatial map of the thermal properties of the sample may be mapped out as localized heat transfer between the tip and sample surface changes the tip temperature. Many theoretical and instrumental studies have been devoted to the measurement of temperature and conductivity [4][5][6][7][8][9][10][11][12][13]. However, the results obtained depend strongly on the nature of the tip-surface contact, which is poorly defined [3,10].…”