## 3 Results
### Data Analysis
Consequently, the transmission losses around 13 dB are attributed to the coaxial cables and transition (vacuum coaxial transition at the air/SEM interface). The input power and the IFBW set to 0 dBm and 50 Hz, respectively, are therefore appropriate for accurate measurements. Ideally, in reflection measurements, all of the signal that is reflected off of the DUT is measured at the VNA receiver. Due to the high impedance of the probe apex in contrast with the 50 \(\Omega\) impedance of the microwave instrumentation (including the microstrip part of the probe, coaxial-to-microstrip transition, coaxial cables and feedthrough, VNA), a large part of the signal reflects off the DUT, and multiple internal reflections occur between the probe apex and the DUT. In particular, the source match value of \(-0.87\) dB indicates that 80% of the microwave power is reflected off the DUT. All of these systematic errors are taken into account by the calibration procedure. By inverting Relationship (5), the calibrated complex reflection coefficient \(\Gamma\) in the reference plane of the apex tip can be determined. We developed a MATLAB\({}^{\circledR}\) program called \"SPAR2Y\" for the determination of the inverse problem, i.e., determination of the quantitative data from the measured complex reflection coefficient (Figure 7). The input variables of the program consist of real and imaginary parts of \(\Gamma_{\text{M,ij}}\), the error terms \(\text{e}_{00}\), \(\text{e}_{11}\), \(\text{e}_{10}\text{e}_{01}\) and the test frequency to derive the data of interest in a text file format. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Calibration Error Terms** & **Amplitude (dB)** & **Phase-Shift (Deg)** \\ \hline Directivity \(\text{e}_{00}\) & \(-6.68\) & \(163.03\) \\ \hline Reflection tracking \(\text{e}_{10}\text{e}_{01}\) & \(-31.67\) & \(-46.55\) \\ \hline Source match \(\text{e}_{11}\) & \(-0.87\) & \(-15.13\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Calibration error terms obtained from the modified SOL calibration procedure. f = 30 GHz. Figure 7: Functional diagram of the MATLAB\({}^{\circledR}\) script developed for quantitative data determination. The input data file *.txt consists of the frequency of operation, measured real and imaginary parts of the complex reflection coefficient \(\Gamma_{\text{M,ij}}\) and complex calibration error terms. The code Spar2Y determines the calibrated complex reflection coefficient \(\Gamma_{\text{ij}}\) at the probe tip and the related complex impedance \(Z_{\text{ij}}\) admittance \(Y_{\text{ij}}\) (including capacitance \(C_{\text{ij}}\)). An output *.txt file is generated. After running the program \"SPAR2Y,\" we present the images of the real part and imaginary part of the admittance \(Y\) obtained after calibration (Figure 8). In addition, we plot a 1D profile along the \(x\)-axis to appreciate the fluctuations. The image of the microwave conductance indicates a value close to 0, demonstrating that the DUT is only reactive. The extracted 1D profile given in Figure 8c indicates the insensitivity of the real part of the admittance along the \(x\)-distance. Figure 8b shows the imaginary part of the admittance that is a direct signature of the capacitance image. Along the 1D profile, the signal fluctuations are very low. Nevertheless, most of the DUTs show heterogeneity in the middle of their respective areas. Investigations were made to identify the origin. In particular, a fine analysis of the topography, microwave and SEM images lead to the conclusion that contamination effects mainly on the middle of the gold patch areas induce a reduction or loss of electrical contact between the apex tip and the gold patch. From the imaginary part image of \(Y\), the capacitance image at 30 GHz is plotted in a 3D format in Figure 9.  
Figure 8: (**a**) Real part and (**b**) imaginary part images of the admittance \(Y\) measured at 30 GHz. (**c**) Extracted 1D profile along the \(x\)-axis (from Line 1 denoted in (**a**,**b**)). From Figure 9, the microwave capacitances are extracted.