Quantitative temperature distribution measurements by non-contact scanning thermal microscopy using Wollaston probes under ambient conditions.

Temperature measurement using Scanning Thermal Microscopy (SThM) usually involves heat transfer across the mechanical contact and liquid meniscus between the thermometer probe and the sample. Variations in contact conditions due to capillary effects at sample-probe contact and wear and tear of the probe and sample interfere with the accurate determination of the sample surface temperature. This paper presents a method for quantitative temperature sensing using SThM in noncontact mode. In this technique, the thermal probe is scanned above the sample at a distance comparable with the mean free path of ambient gas molecules. A Three-Dimensional Finite Element Model (3DFEM) that includes the details of the heat transfer between the sample and the probe in the diffusive and transition heat conduction regimes was found to accurately simulate the temperature profiles measured using a Wollaston thermal probe setup. In order to simplify the data reduction for the local sample temperature, analytical models were developed for noncontact measurements using Wollaston probes. Two calibration strategies (active calibration and passive calibration) for the sample-probe thermal exchange parameters are presented. Both calibration methods use sample-probe thermal exchange resistance correlations developed using the 3DFEM to accurately capture effects due to sample-probe gap geometry and the thermal exchange radii in the diffusive and transition regimes. The analytical data reduction methods were validated by experiments and 3DFEM simulations using microscale heaters deposited on glass and on dielectric films on silicon substrates. Experimental and predicted temperature profiles were independent of the probe-sample clearance in the range of 100-200 nm, where the sample-probe thermal exchange resistance is practically constant. The difference between the SThM determined and actual average microheater temperature rise was between 0.1% and 0.5% when using active calibration on samples with known thermal properties and between ∼1.6% and 3.5% when using passive calibration, which yields robust sample-probe thermal exchange parameters that can be used also on samples with unknown thermal properties.