Frequency domain analysis of 3ω-scanning thermal microscope probe—Application to tip/surface thermal interface measurements in vacuum environment

Abstract

Material thermal properties characterization at nanoscales remains a challenge even if progresses were done in developing specific characterization techniques like the Scanning Thermal Microscopy (SThM). In the present work, we propose a detailed procedure based on the combined use of a SThM probe characterization and its Finite Element Modelling (FEM) to recover inoperando 3 measurements achieved under high vacuum. This approach is based on a two-step methodology: (i) a fine description of the probe's electrical and frequency behaviors in "out of contact" mode to determine intrinsic parameters of the SThM tip, (b) a minimization of the free parameter of our model, i.e. the contact thermal resistance, by comparing 3 measurements to our simulations of the probe operating "in contact mode". Such an approach allows us to accurately measure thermal interface resistances of the probe as a function of the strength applied between the tip and the surface for three different materials (silicon, silica and gold). In addition, FEM modeling provides insights about the 3-SThM technique sensitivity, as a function of probe/sample interface resistance to measure material thermal conductivity, paving the way to quantitative SThM measurements.

Quantitative Characterization of Local Thermal Properties in Thermoelectric Ceramics Using “Jumping‐Mode” Scanning Thermal Microscopy

“…[52] Apparently, with the boundary resistance dominating, we have to include in the analysis of the maps the possible variation of the boundary resistance b th R between materials. Indeed, Small Methods 2023, 7,2201516 the data of Table 1 become consistent with expectations if we introduce into the analysis the material-dependent interface thermal resistance i th ρ . For that, we set k ZrO2 = 6.5 W m −1 K −1 with a contact-sample thermal radius of r = 50 nm as was determined multiple times for the KNT probes [26,27,32] (keeping in mind that this size can change as a result of the sampleprobe interaction in the course of the probe usage) and evaluate the difference between bs th R for the inclusion and matrix, 1 for the DC ZnAlOZrO map, we find that the data can be explained by a larger i th ρ for zirconia inclusions with a difference i th ρ ∆ = (3.1 ± 1.6) × 10 −8 K m 2 W −1 relative to the ZnO matrix (which yields an about order of magnitude larger variation of the contact resistance than due to the spreading resistance of the materials).…”

“…The KNT resistive probes are widely used for SThM, and different aspects of their static and dynamic behavior have been addressed in a number of reports with experimental and numerical methods. [4,7,12,21,[25][26][27][28] The measurements can be quantitative, [2][3][4] and the typical approach to quantification of the sample thermal properties can be illustrated with a simplified lumped-element equivalent electrical circuit shown in Figure 2b. We conduct experiments in a vacuum at a pressure of about 10 −3 Torr, when the heat transfer between the probe and environment by air can be neglected.…”

“…Other calibration protocols were proposed; some of them need complicated calibration samples, multi-step procedures, or include numerical simulations. [7,27,[34][35][36] In this work, we developed and implemented a different approach based on the determination of the probe tip apex temperature as a function of the probe current. All calibration measurements are performed in the same setup as the SThM experiments.…”

“…The measurements can be performed in quasistatic (heating by a DC, Direct Current) [ 5 ] and dynamic (heating by an AC, Alternating Current) modes. [ 4,6,7 ]…”

“…The measurements can be performed in quasistatic (heating by a DC, Direct Current) [5] and dynamic (heating by an AC, Alternating Current) modes. [4,6,7] Despite many efforts to quantitatively map thermal conductivity, realistic quantitative SThM has been shown mostly for topographically very smooth materials, such as thin-film hafnium oxide, [8] graphene-based nanomaterials, [5,9] van der Waals 2D materials, [10] self-assembled monolayers, [11] etc., while there is a lack of studies in conventional bulk materials. One of the reasons is probe durability, [12] which significantly limits the range of the materials that can be studied by scanning in the contact mode.…”