A quantitative thermal conductivity measurement technique, the method, is applied in a scanning thermal microscope (SThM) with a resistive probe for the determination of thermal properties with a high spatial resolution in the nanometre range. With this set-up the quantitative thermal conductivity of materials can be determined with a deviation of less than 2%. Using gold as the reference material, the local thermal conductivities of silver and a CVD diamond film have been measured with a spatial resolution of approximately 30 nm.

We present a new method to extract resistivity and doping concentration of semiconductor materials from Scanning Microwave Microscopy (SMM) S11 reflection measurements. Using a three error parameters de-embedding workflow, the S11 raw data are converted into calibrated capacitance and resistance images where no calibration sample is required. The SMM capacitance and resistance values were measured at 18 GHz and ranged from 0 to 100 aF and from 0 to 1 MΩ, respectively. A tip-sample analytical model that includes tip radius, microwave penetration skin depth, and semiconductor depletion layer width has been applied to extract resistivity and doping concentration from the calibrated SMM resistance. The method has been tested on two doped silicon samples and in both cases the resistivity and doping concentration are in quantitative agreement with the data-sheet values over a range of 10(-3)Ω cm to 10(1)Ω cm, and 10(14) atoms per cm(3) to 10(20) atoms per cm(3), respectively. The measured dopant density values, with related uncertainties, are [1.1 ± 0.6] × 10(18) atoms per cm(3), [2.2 ± 0.4] × 10(17) atoms per cm(3), [4.5 ± 0.2] × 10(16) atoms per cm(3), [4.5 ± 1.3] × 10(15) atoms per cm(3), [4.5 ± 1.7] × 10(14) atoms per cm(3). The method does not require sample treatment like cleavage and cross-sectioning, and high contact imaging forces are not necessary, thus it is easily applicable to various semiconductor and materials science investigations.

A new three-dimensional finite element method model of the conventional resistive thermal probe, usually employed within scanning thermal microscopy (SThM) has been developed. As a result, the line heat source characteristic of the bent thermal sensitive filament seems to permit the explanation of the experimental results within a certain frequency range. The verification of this line heat source characteristic of the thermal probe finally leads to the introduction of a general near-field condition of SThM, which considers the spatial and temporal characteristic of the heat source. Here, the contact area between the probe and the sample is not considered as the source but rather as the aperture between the heat source and the sample. In addition, the combination of this kind of thermal probe with the so-called 3ω-method has been justified for the quantitative determination of the local thermal conductivity. Moreover, the applicable sample thermal conductivity range has been expanded significantly by considering the varying heat flow into the sample within the conditional equation.

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