## 3 Control Strategy and Experiment  
A CCP etching system was used in the experiments conducted in this study. This system could generate high-density plasma and free radicals for dry etching. The bottom electrode was connected to an RF power output to generate plasma for the etching process and to control the acceleration of ions on the wafer surface. The upper electrode was applied with a DC voltage, and the plasma density was controlled by adding the DC voltage (Figure 2). The operating range of the chamber pressure was 10 to 800 mTorr. The pressure was regulated by controlling the gas flow from a gas diffusion plate by using a flow control system. The temperature of the top electrode could be set to a maximum value of approximately 150 \({}^{\circ}\)C. As shown in Figure 3, an ESC was used to fix the wafer during the dry etching process, and an electrode plate with a high DC voltage was used to generate the chucking force. Helium gas was allowed to flow through holes distributed on the surface of the ESC into the back side of the wafer to control the wafer's temperature. A liquid flowing through the ESC cooling path was used for external temperature control to regulate the process temperature. Figure 3: Plasma etching process. (**a**) Wafer in the chamber. (**b**) The pins are pushed down, the plasma is generated, and high voltage is applied to the electrostatic chuck (ESC) to chuck the wafer. (**c**) The wafer etching process is completed, and the ESC is turned off, followed by the plasma flow. (**d**) After the wafer has completed discharging, the pins are pushed up. (**e**) The wafer is removed, and the chamber is cleaned. Figure 2: Diagram of the adopted capacitive coupled plasma dry etching system. The chucking force is a key factor affecting the performance of the ESC. This force is influenced by the voltage applied to the ESC, the properties of the dielectric layer of the ESC, and the geometric structure of the ESC. The Coulomb force of the ESC (i.e., the chucking force) is expressed as follows:  
\[\mathrm{F}=\frac{1}{2}\varepsilon_{0}\mathrm{A}\left(\frac{\mathrm{k}\mathrm{U }}{\mathrm{h}}\right)^{2} \tag{5}\]  
where A is the electrode area, \(\varepsilon_{0}\) is the permittivity of free space, k is the relative permittivity, U is the applied voltage, and h is the distance between the bottom surface of the wafer and the top surface of the ESC [27]. The distance h is equal to the combined thickness of the dielectric layer \(d\) with a relative permittivity of k\({}_{\mathrm{d}}\) and the gas layer g with a relative permittivity of k\({}_{\mathrm{g}}\). The sandwich structure formed by these layers can be considered as a structure containing two capacitors connected in series. By substituting for h in Equation (5), the chucking force can be expressed as follows:  
\[\mathrm{F}=\frac{1}{2}\varepsilon_{0}\mathrm{A}\left(\frac{\mathrm{k}_{ \mathrm{d}}\mathrm{k}_{\mathrm{g}}\mathrm{U}}{\mathrm{k}_{\mathrm{g}}\mathrm{ d}+\mathrm{k}_{\mathrm{d}}\mathrm{g}}\right)^{2} \tag{6}\]  
where k\({}_{\mathrm{g}}\approx 1\) if g \(\gg\) d, which occurs in most cases. By using this approximation, the following equation is derived:  
\[\mathrm{F}=\frac{1}{2}\varepsilon_{0}\mathrm{A}\left(\frac{\mathrm{k}_{ \mathrm{d}}\mathrm{U}}{\mathrm{d}+\mathrm{k}_{\mathrm{d}}\mathrm{g}}\right)^{2} \tag{7}\]  
Equation (7) reveals that the chucking force is directly dependent on the properties of the dielectric material (k\({}_{\mathrm{d}}\)) and the layer thickness (d). Thinner dielectric layers can be used to achieve a higher chucking force. In the conducted experiments, the effects of polluting particle sources and driving forces were investigated. We first opened the chamber with the most wafer particles for maintenance to identify the parts of the chamber in which particle sources caused deposition. Powder was then collected from the by-products in the turbo pump exhaust line, as shown in Figure 4a.