# Imaging the Permittivity of Thin Film Materials by Using Scanning Capacitance Microscopy
## 3 Results  
This section may be divided by subheadings. It should provide a concise and precise description of the experimental results, their interpretation, as well as the experimental conclusions that can be drawn. First, in order to determine the parameters (the tip radius \(R\) and the cone half angle \(\theta\)) of the tip, the capacitance gradient \(\frac{\mathrm{d}\mathrm{C}_{\mathrm{meas}}^{metal}}{\mathrm{d}z}\) vs. setting height \(z\) curve for metal ground was measured. The tip was set to touch the metal ground and then was lifted to a proper height \(z\) automatically. The measured capacitance gradient \(\frac{\mathrm{d}\mathrm{C}_{\mathrm{meas}}^{metal}}{\mathrm{d}z}\) vs. setting height \(z\) between the tip and the metal ground was shown in Figure 1. Fitted with Equation (17) by using Origin 2021, the tip radius \(R=R_{0}=16.6\) nm, cone half angle \(\theta=\theta_{0}=20^{\circ}\), and the constant \(k_{stray}^{metal}=0.039\) aF/nm could be obtained. Packaging specification of the probe was tip radius \(R\leq 10\) nm and cone half angle \(\theta\leq 22^{\circ}\). Since the probe was used for some time and may be blunt, the tip radius \(R_{0}=16.6\) nm, and cone half angle \(\theta_{0}=20^{\circ}\) were reasonable. The monocrystalline silicon substrate partly coated with MoO\({}_{3}\) film was grounded. A point of Si substrate area was chosen, and its measured capacitance gradient \(\frac{\mathrm{d}\mathrm{C}_{\mathrm{stray}}^{ground}}{\mathrm{d}z}\) vs. setting height \(z\) between tip and Si ground was shown in Figure 2. Fitted with \(R_{0}=16.6\) nm, \(\theta_{0}=20^{\circ}\) and Equation (18), the constant \(k_{stray}^{ground}=0.043\) aF/nm could be obtained. The value of \(k_{stray}^{dieletric}\) approximately was 0.043 aF/nm, and it was larger than that of \(k_{stray}^{metal}\). Double scanning technology was performed on the sample. A procedure of 1 Order (line-by-line subtraction of the first order approximating curve) was selected, the detection signal was corrected for the tilt contribution. In the second scanning, the tip is lifted to a height \(z^{\prime}=10\) nm. The topography image and SCM image of the sample was shown in Figure 3a,b, respectively. The different area was marked in Figure 3a. Figure 1: The measured capacitance gradient \(\frac{\mathrm{d}\mathrm{C}_{\mathrm{stray}}^{metal}}{\mathrm{d}z}\) vs. setting height \(z\) and its fitted curve. From Figure 3a, the profiles for \(y=56.6\)\(\upmu\)m and \(y=72.3\)\(\upmu\)m (mark in Figure 3a) were exported as shown in Figure 4a,b, respectively. Compared with Figure 3, it could be seen from Figure 4a that the fall from 17 nm to 4 nm at \(x\approx 45\)\(\upmu\)m corresponded to the change from MoO\({}_{3}\) film-doped NaCl to MoO\({}_{3}\) film. It meant that the film of MoO\({}_{3}\)-doped NaCl was 13 nm thicker than that of MoO\({}_{3}\). Compared with Figure 3, it could be seen from Figure 4b that the rise of 70 nm at \(x\approx 52\)\(\upmu\)m corresponded to the change from monocrystalline Si substrate to MoO\({}_{3}\) film. Then, the average thickness \(\overline{h}\) of the film could be set as 70 nm. From the topography image of the film, the rise and fall of every point could be regarded as the thickness change \(\Delta h\). The thickness \(h\) of the film at every point could be set as \(h=\overline{h}+\Delta h=70\) nm + \(\Delta h\). The thickness profile for \(y=56.6\)\(\upmu\)m was shown in Figure 5a. Additionally, the SCM profile for \(y=56.6\)\(\upmu\)m from Figure 5 was shown in Figure 5b. Figure 4: The height profiles for (**a**) \(y=56.6\)\(\upmu\)m and (**b**) \(y=72.3\)\(\upmu\)m of the topography image. Figure 3: (**a**) the topography image of the sample and (**b**) the SCM image with \(z^{\prime}=10\) nm. It could be seen from Figure 5a that there was a fall from 75 nm to 62 nm at \(x\approx 45\) um. The drop corresponded to the change from MoO\({}_{3}\) film-doped NaCl to MoO\({}_{3}\) film.