## 3 Results
### Data Analysis  
The raw data are transferred to Gwyddion(r) software for analysis. We cross-check the images from Figure 5 together. Then, each capacitor on the atomic force microscopy image in Figure 5b is referenced according to Figure 6.  
From the topography image given in Figure 6, we can calculate the theoretical capacitances according to Relations (2) to (3). The four circular areas of the metallic electrodes have targeted diameters of 1, 2, 3 and 4 \(\upmu\)m, respectively. The three oxide layers determined from the topography image by considering the 1D profile (indicated in Line 1 in Figure 5b) are, respectively, 87.5, 137.1 and 198.3 nm. The corresponding oxide capacitances have values in the range of 0.14-5.09 fF (\(10^{-15}\) F). It has to be mentioned that MC2 Technologies(r) has developed two reference calibration kits considering doped P-type silicon with substrate resistivity of 1 and 0.01 \(\Omega\).cm, respectively. In contrast with our previous studies  
Figure 5: (**a**) SEM image of the apex tip. (**b**) Measured atomic force microscopy image, (**c**) real part and (**d**) imaginary part images of the complex reflection coefficient \(\Gamma_{\text{M}}\): f = 30 GHz. (Only the parts of the images of interest are represented on a 25 \(\times\) 35 \(\upmu\)m\({}^{2}\) area). Figure 6: Topography image with the named capacitor (for example, H2V1 corresponds to horizontal Position 2 and Vertical Position 1). The red circles denote the capacitors used for calibration. based on the first type of reference capacitance kit, due to the high doping of the silicon substrate, the depletion capacitance is negligible (fifth row of Table 1). Consequently, it is highly recommended to consider highly doped materials for the fabrication of the MOS capacitance kit. Another possibility investigated in [21] is to consider indium tin oxide (ITO) as the metal substrate. From the theoretical capacitance values, the theoretical reflection coefficient \(\Gamma\) of the capacitors is calculated. The capacitors considered lossless (as demonstrated in Section 2) have phase-shifts of \(\Gamma\) in the range \(-0.15\)--\(5.31\) degrees. The calibration process developed in Section 2.3 is applied by considering three oxide capacitances values as the reference loads. From Table 1, we chose H2V2, H2V4 and H3V1 with capacitances 0.56, 2.24 and 5.09 fF to cover a wide range of capacitance values. As the calibrated measurements are very sensitive to the knowledge of the reference loads, we did not consider the smallest capacitances as reference. Using Equation (4), the complex error terms \(e_{00}\), \(e_{01}e_{10}\) and \(e_{11}\) are determined (Table 2). \begin{table}
\begin{tabular}{c c c c c c c c} \hline \multirow{2}{*}{**Capacitor**} & \multirow{2}{*}{**Diameter**} & **Oxide** & **Oxide** & **Depletion** & **Total** & \multirow{2}{*}{**Phase-Shift**} & **Relative Error** \\  & & **Thickness** & **Capacitance** & **Capacitance** & **Capacitance** & **Capacitance** & **(Degrees)** & \(\frac{C_{m}-C_{total}}{C_{0}}\) \\  & & **(nm)** & **(fF)** & **(fF)** & **(fF)** & **(fF)** & **(fF)** & **(fF)** \\ \hline H1V1 & 1 & 198.3 & 0.14 & 9.35 & 0.14  
Whereas in conventional guided measurements, the directivity corresponds to a small incident signal that leaks through the forward path of the coupler and into the receiver of the VNA, the directivity around \(-6.68\) dB corresponds mainly to mismatch effects in the path of the microstrip probe without reflecting off the device under test (DUT). Given the nature of the probe structure for which the end platinum wire of the cantilever is not supported by a TEM propagating mode, around 75% of the incident power is transmitted to the DUT. The reflection tracking around \(-32\) dB indicates transmission losses from the apex tip to the VNA receiver of around 16 dB. From Figure 3, 3 dB transmission losses are attributed to the microwave probe, including the coaxial-to-microstrip transition.