## 5 Discussion  
These results are very instructive and lay the background for future microwave nanometrology. Indeed, SMM techniques have become a mature technology in both academic and industrial laboratories. National metrology institutes have considerably contributed to enhancing SMM technology. In this effort, we analyzed the experimental results presented in this work, and we draw conclusions for future works in the following.  
* The theoretical capacitances do not consider fringing field effects. Future works will include analytical and electromagnetic simulations to derive more realistic values of capacitance values. In addition, the coupling effect from neighboring capacitors will be studied to yield the optimization of the disposition of the capacitors.
* Electrical drift of the microwave instrumentation is inevitable. Although its impact is reduced for capacitances greater than 300 aF, there is an urgent need to introduce solutions to achieve stable measurements for capacitance as low as 1 aF. To tackle this issue, the microwave path must be reduced to the minimum. The research direction should be directed towards the implementation of the microwave instrumentation closest to the probe. In particular, we omitted capacitances below 300 aF as the longitudinal drift (along the \(y\)-axis) is not compatible with accurate extraction of the electrical parameters. To complicate, the reference kit is used with the smallest capacitors on the top and on the back of the scanning area. It is highly recommended to design reference kits by taking into consideration the electrical drift. In other words, the scanning area and in particular the scanning time must be reduced as necessary to yield consistent quantitative data.
* The calibration reference kit in this study is based on microsized capacitors. Decreasing the size of the microcapacitors is still an issue to address nanoscale characterization. Indeed, the apex tip must be reduced to accommodate smaller footprints. In this effort, we considered a relatively small apex radius of 70 nm. The size can be further reduced as an apex size below 20 nm is commercially available. Operating inside a SEM is beneficial to limit the scanning area when fragile sub-20 nm apex sizes are considered. Ongoing works related to the free-space calibration procedure that exploits the stand-off between the tip apex and the material surface is also a possible alternative. The instrumentation proposed offers the unique possibility to image the apex geometry and to record simultaneously the microwave signals. Indeed, the apex geometry is the main factor that governs the theoretical derivation of the coupling capacitance.  
Conceptualization, K.H., D.T.; methodology, P.P., D.T., C.L., D.D., S.E., C.B., G.D. and K.H.; software, P.P., D.T., C.L., D.D., S.E., C.B., G.D. and K.H.; validation, P.P., D.T., C.L., D.D., S.E., C.B., G.D. and K.H.; formal analysis, P.P., D.D. and K.H.; data curation, P.P., D.D. and K.H.; writing--original draft preparation, P.P., D.D. and K.H.; writing--review and editing, P.P., D.D. and K.H.; supervision, D.T. and K.H.; project administration, K.H.; funding acquisition, D.T., G.D. and K.H. All authors have read and agreed to the published version of the manuscript.  
This work has received funding from the European Union Horizon H2020 Programme (H2020-NMBP07-2017) under grant agreement n\({}^{\circ}\)761036 MMA. This work used the facilities within the EQPX ExCELSiOR funded by the National Research Agency (ANR).  
The data presented in this study are available on request from the corresponding author.