# Temperature Effects in Packaged RF MEMS Switches with Optimized Gold Electroplating Process
## 4 Measurements and Discussion  
### Temperature Effect on Mechanical Performance  
Firstly, in order to facilitate continuous and automatic testing of the pull-in voltage and lifetime of the switch, an automatic testing system was designed. The testing platform includes FPGA modules, high-speed 8-bit AD/DA modules, amplification and resistance reading circuits, and control and display end. The connections between each module are shown in Figure 8. The testing system uses the FPGA module to control the DAC to generate periodic signals with adjustable frequency and waveform. Then, the signal is amplified by the amplification circuit to control the on/off state of the switch. At the same time, the resistance reading circuit collects the series resistance of the switch and transmits it to the FPGA module through ADC. The FPGA can generate sawtooth waves or square waves, which are used for pull-in voltage measurement or lifetime testing, respectively. During the pull-in voltage measurement phase, the amplification circuit outputs sawtooth waves. When the switch is pulled in, the values of the DAC and ADC at the moment correspond to the pull-in voltage and on-state resistance of the switch, respectively. During the lifetime testing phase, the amplification circuit outputs square waves. When the on-state resistance suddenly increases or remains unchanged at low resistance, it indicates that the switch has failed. In order to investigate the effect of temperature on the performance, the temperature chest of Cascade SUMMIT-12000B is used to control the temperature environment of the packaged switch. Figure 6: Profile scans of the released electroplated gold beam. The inset displays the released gold beam and profile scanning path. Figure 7: (**a**) SEM image of the fabricated switch. (**b**) SEM image of the switch with a hermetic package. At room temperature, the pull-in voltage range of the fabricated switches is measured to be 45-60 V, and the on-state resistance R\({}_{\text{on}}\) is between 1.5 and 2.5 ohms. Then, the temperature effect on pull-in voltage is tested, and the test results are shown in Figure 9. The testing interval for each temperature point is 1 h to ensure the stability of the temperature environment and switch status. When testing at a certain temperature point, the testing system continuously generates five sawtooth waves, and the average value of the five measured pull-in voltages is obtained. It can be seen that in the range of 25 to 75 \({}^{\circ}\)C, the switching voltage decreases nearly linearly with temperature. In order to analyze how temperature variation affects the pull-in voltage, the theoretical formula of the pull-in voltage \(V_{p}\) of the switch is given as [1]  
\[V_{p}=\sqrt{\frac{8 kg_{0}{}^{3}}{27\epsilon_{0}A}} \tag{1}\]  
in which \(k\) is the elastic coefficient of the movable beam, \(g_{0}\) is the gap between the movable beam and the bias electrode, and \(A\) is the overlapping area between the movable beam and the bias electrode. In the above equation, the parameters that may vary with temperature include the elastic coefficient \(k\), gap \(g_{0}\), and area \(A\). Among them, in the range of 25 to 75 \({}^{\circ}\)C, the change in area A can be ignored. The variation in gap \(g_{0}\) is related to the deformation  
Figure 8: An automatic testing system for pull-in voltage and lifetime test of the switch. Figure 9: Temperature effect on the pull-in voltage of the packaged switches. of the movable beam. According to the profile scan results in Figure 6, the deformation of the movable beam in the range of 25 to 75 \({}^{\circ}\)C can be ignored. The elastic coefficient k is determined by the geometric dimensions and Young's modulus of the movable beam. Among them, the variation in geometric dimensions with temperature can be ignored. Therefore, the temperature effect of Young's modulus of electroplated gold materials is the main reason for the variation of the switch pull-in voltage with temperature [22].