## 2 Materials and Methods
### Traceability in the SMM Mode  
In contrast to microwave-guided measurements, including a metallic waveguide, coaxial, on-wafer propagating structures for which the traceability has been established for decades, the normalization of SMM technology, including the experimental set-up and the measurement configuration and calibration standards, are still an issue. Whereas SMM technology has been identified as a unique solution to provide a microwave and millimeter-wave characterization at the submicron scale, there is an urgent need to harmonize the best practices at the international level. In particular, we identified the main bottlenecks to be tackled for offering quantitative and traceable SMM measurements. Firstly, whereas AFM can operate in air to provide a topography image of the sample under test, water meniscus in the vicinity of the apex tip of the probe contributes to the overall complex impedance at the apex tip, especially because water has a high dielectric constant and loss tangent in the microwave range. Moreover, the shape of the water meniscus is usually unknown; therefore, only approximations of the water meniscus can usually be derived by 3D electromagnetic modeling and are not easily discriminated from other parasitic capacitances involved in the measurement. Operating in a vacuum presents the advantage to allow the elimination of the water meniscus by heating the sample, simplifying the electrical modeling. Secondly, a second advantage of operating in an SEM is the possibility to directly image the probe in contact with the sample, even during the scanning operation. Indeed, probe microscopy tools, especially in the contact mode, are methods that may damage the sample or the tip apex with impacts on the electrical measurement, especially in the case of RF electrical measurements using sub-100 nm platinum/iridium wire as a sensing element. Finally, it is well accepted in the SMM community that spatial resolution is mainly governed by the apex tip geometry [36]. In particular, to surpass the diffraction limit imposed by the half-wavelength of radiation, waveguide structures with dimensions far below the wavelength of excitation exhibit evanescent electrical fields in the vicinity of the apex tip. Nevertheless, the collimation of the electrical fields is frequency dependent. Therefore, operating at a higher frequency improves the distribution of the electrical fields and the lateral resolution and, incidentally, the signal-to-noise ratio (SNR). To verify this assumption, electromagnetic simulations using a high-frequency structure simulator (HFSS) were performed at three test frequencies (1, 10 and 30 GHz) by designing an RMN probe and plotting the distribution of the electrical fields (the magnetic field here being negligible), as shown in Figure 2.  
As expected, the lateral resolution, i.e., the footprint of the electrical field distribution at the probe apex, decreases for higher frequencies. It has to be mentioned that the depth resolution is of course lower. These results are in favor of operating in the millimeter-wave regime. Nevertheless, as the transmission losses increase with frequency, especially in the RF cables and transitions from the input of the VNA to the AFM/SMM tip, there is a compromise between the lateral resolution and SNR. As an illustration, we present in Figure 3 the measured return loss measured up to 50 GHz of the probe. For frequencies greater than 35 GHz, the standing wave ratio is more pronounced, leading to a mixing of the amplitude and phase-shift of the complex reflection coefficient at the probe apex. It has to be mentioned that the measured response can be enhanced by considering the optimization of the mounting and soldering of the AFM/SMM probe on the PCB substrate, both done manually. In the following, we consider measurements performed at the test frequency of 30 GHz. Figure 3: Measured return loss of the AFM/SMM probe (including the modified RMN® cantilever, the PCB and the coaxial-to-PCB transition) in the input coaxial plane.