# Analytical Approach in the Development of RF MEMS Switches
## 2 Analytical Approach to the Development of RF MEMS Switches of Electrostatic Type
### Selection of Structural Material of RF MEMS Switch with Capacitive Switching Principle  
Due to the fact that the stiction of the membrane to the pull-down electrode as a consequence of the electric charge of the dielectric film is one of the main problems of the reliability of RF MEMS switches with capacitive switching principle, significant efforts of researchers in this area have been aimed at reducing or completely eliminating this problem. In this regard, the properties of materials play a very important role in preventing stiction. The choice of structural material depends on the hardness, resistance and complexity of the process. The properties of the materials significantly depend on the conditions and deposition technology of the material. For example, the specific resistance of the deposited metal film is almost twice that of the original material. Pure Au provides the lowest contact resistance and is inert to the formation of oxides, but it has been empirically found that the predominant number of failures are associated with pure Au due to the point destruction of the contact area under repeated efforts. Hence, pure Au is not suitable as a structural material of RF MEMS switches that require a long lifespan. Solid metals, such as tungsten or molybdenum, are capable of processing sufficiently high-frequency signal power and do not exhibit any stiction problems. However, they are more sensitive to oxidation and require a relatively high initial contact force. Thus, tungsten and molybdenum are not suitable as structural material. From the obtained results, it was found that the evaporated aluminum is one of the suitable candidates as a contact material [53]. Such materials as gold, aluminum, platinum, molybdenum, copper, and nickel can be used to make an RF MEMS switch with capacitive switching principle [54; 55; 56; 57]. When choosing the appropriate material, we should address three main performance indexes of the RF MEMS switches with capacitive switching principle: pull-down voltage, the level of RF losses, thermal residual stress. The key material properties are Young's modulus, Poisson's ratio, thermal expansion coefficient and thermal conductivity. The pull-down voltage is determined by Equation (1) [1]:  
\[V_{pull\text{-}down}=\sqrt{\frac{8k}{27\epsilon_{0}A}g_{0}^{3}} \tag{1}\]  
where \(k\)--the coefficient of stiffness of elastic suspension elements; \(g_{0}\)--the value of the air gap between the electrodes; \(A\)--the area of electrostatic interaction. The coefficient of stiffness \(k\) depends on the Young's modulus, thermal residual stress and Poisson's ratio of the material of the membrane and the elastic suspension elements. Consequently, the pull-down voltage can be optimized by selecting a material with the corresponding above properties. The second performance index is the RF loss level, which can be reduced by selecting a material with good conductivity. The power dissipated by RF is determined by Equation (2) [56]:  
\[P_{loss}=I^{2}R \tag{2}\]  
where \(I\), \(R\)--the current and the resistance of the membrane. At the RF signal of high-power (from 100 mW and above), the membrane of the switch design experiences self-heating, which leads to a change in the thermal residual stress, which is determined by Equation (3) [56]:  
\[\Delta\sigma=E\Delta\alpha P_{loss}R_{TH} \tag{3}\]  
where \(P_{loss}\)--the level of power dissipated by RF; \(R_{TH}\)--the thermal resistance. Thus, as a result of the analysis, as well as on the basis of material selection diagrams [58], it was found that the most suitable candidate as the main structural material is aluminum after gold and copper. The use of structures with elastic suspension elements in the form of a meander or thin beams allows us to obtain low values of the stiffness coefficient and control voltage, which is often a compromise between reliability and switching speed.