## 4 Metallic MEMS Cantilevers: Nonlinear Dynamics of the Pull-In Behavior
### Simulations on Pull-In and Actuation Time for Different Real Materials
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Ref.** & **Study Type** & **MEMS Type** & \begin{tabular}{c} **MEMS** \\ **Dimensions/\(\mu\)m** \\ \end{tabular} & \begin{tabular}{c} **Moving** \\ **Material** \\ \end{tabular} & \
\begin{tabular}{c} **Closing** \\ **Time/\(\mu\)s** \\ \end{tabular} &
\begin{tabular}{c} **Actation** \\ **Voltage/V** \\ \end{tabular} & **Application** \\ \hline
[22; 23; 24] & Experiment & \begin{tabular}{c} Curled \\ shutter \\ \end{tabular} & \begin{tabular}{c} \(l=450\)–\(2400\), \\ \(b=200\)–\(600\), \(h=0.5\)–\(1\) \\ \end{tabular} & Cu & \begin{tabular}{c} 100 \\ 200 \\ \end{tabular} & \
\begin{tabular}{c} 80 \\ 180 \\ \end{tabular} &
\begin{tabular}{c} Display and \\ smart glass \\ \end{tabular} \\ \hline
[25; 26] & Experiment & Flat mirror & \begin{tabular}{c} \(l=150\), \(b=400\), \\ \(h=0.22\) \\ \end{tabular} & Al-Cr-Al & \begin{tabular}{c} 300 \\ 300 \\ \end{tabular} & \
\begin{tabular}{c} 40 \\ 40 \\ \end{tabular} &
\begin{tabular}{c} Light \\ steering via \\ smart glass \\ \end{tabular} \\ \hline
[33] & Experiment & \begin{tabular}{c} Curled \\ shutter \\ \end{tabular} & \begin{tabular}{c} \(l=600\)–\(1000\), \\ \(h=1.25\)–\(1.6\) \\ \end{tabular} & \begin{tabular}{c} Poly-Cr-Au- \\ poly \\ \end{tabular} & \begin{tabular}{c} 18 \\ 180 \\ \end{tabular} & \
\begin{tabular}{c} 180 \\ 180 \\ \end{tabular} &
\begin{tabular}{c} Eyelid \\ protection of \\ sensors \\ \end{tabular} \\ \hline
[27; 28] & Experiment & \begin{tabular}{c} Curled \\ shutter \\ \end{tabular} & \begin{tabular}{c} \(l=100\)–\(400\), \\ \(h=0.1\) \\ \end{tabular} & \begin{tabular}{c} Si-Cr and \\ other metals \\ \end{tabular} & \begin{tabular}{c} 40 \\ 40 \\ \end{tabular} & \
\begin{tabular}{c} 20 \\ 20 \\ \end{tabular} &
\begin{tabular}{c} Light \\ modulation \\ via smart \\ glass \\ \end{tabular} \\ \hline
[32] & Experiment & \begin{tabular}{c} Curled triangular- \\ gualshutter \\ \end{tabular} & \begin{tabular}{c} \(l=1400\), \\ \(h=0.3+0.35\) \\ \end{tabular} & Al/Mo/SiNx & \begin{tabular}{c} 1000 \\ \end{tabular} & \
\begin{tabular}{c} 30 \\ 30 \\ \end{tabular} &
\begin{tabular}{c} Camera \\ shutter \\ \end{tabular} \\ \hline
[34; 35] & Experiment & \begin{tabular}{c} Curled \\ shutter \\ \end{tabular} & \begin{tabular}{c} \(l=200\), \(b=160\), \\ \(h=0.1\) \\ \end{tabular} & Ti-Au & \
\begin{tabular}{c} 20 \\ 20 \\ \end{tabular} &
\begin{tabular}{c} 20 \\ \end{tabular} & LED displays \\ \hline
[29] & Experiment & \begin{tabular}{c} Curled \\ shutter \\ \end{tabular} & \begin{tabular}{c} \(l=200\), \(b=30\), \\ \(h=0.3\) \\ \end{tabular} & SiO2-Al & \begin{tabular}{c} 3000 \\ 300 \\ \end{tabular} & \begin{tabular}{c} 55 \\ \end{tabular} & \begin{tabular}{c} Light \\ modulation \\ via smart \\ glass \\ \end{tabular} \\ \hline This & Experiment & \begin{tabular}{c} Curled \\ shutter \\ \end{tabular} & \begin{tabular}{c} \(l=40\), \(b=2000\) \\ \(h=0.185\) \\ \end{tabular} & Al-Cr-Al & \begin{tabular}{c} 100 \\ 18 \\ \end{tabular} & \
\begin{tabular}{c} 100 \\ 100 \\ \end{tabular} &
\begin{tabular}{c} Fast \\ mechanical \\ shutter for \\ optics \\ \end{tabular} \\ \hline
[45] & Experiment & \begin{tabular}{c} Cantilever \\ \end{tabular} & \begin{tabular}{c} \(l=140\), \(b=10\)–\(12\), \\ \(h=2.2\) \\ \end{tabular} & SiONx-Au & \begin{tabular}{c} \(10.75\) \\ \(15\) \\ \end{tabular} & \
\begin{tabular}{c} 60 \\ 50 \\ \end{tabular} &
\begin{tabular}{c} RF MEMS \\ switch \\ \end{tabular} \\ \hline
[46] & Experiment & \begin{tabular}{c} Cantilever \\ \end{tabular} & \begin{tabular}{c} \(l=10\),\(000\), \\ \(b=180\), \(h=50\) \\ \end{tabular} & Si & \begin{tabular}{c} 20,\(000\) \\ \end{tabular} & \
\begin{tabular}{c} 0.3 \\ \end{tabular} &
\begin{tabular}{c} Fiber-optical \\ switching \\ device \\ \end{tabular} \\ \hline
[19] & Experiment & \begin{tabular}{c} Cantilever \\ \end{tabular} & \begin{tabular}{c} \(l=650\), \(b=200\), \\ \(h=0.3\) \\ \end{tabular} & Al & \begin{tabular}{c} 60 \\ 32 \\ \end{tabular} & \
\begin{tabular}{c} 32 \\ \end{tabular} &
\begin{tabular}{c} Audible \\ frequency \\ generator \\ \end{tabular} \\ \hline
[30] & Theory & \begin{tabular}{c} Cantilever \\ \end{tabular} & \
\begin{tabular}{c} \(l=200\), \\ \(h=0.1\)–\(0.6\) \\ \end{tabular} & Mo-Ta- SiNx &
\begin{tabular}{c} \(<\)50 \\ \end{tabular} & - & Display \\ \hline
[47] & \begin{tabular}{c} Theory and \\ Experiment \\ \end{tabular} & \begin{tabular}{c} Cantilever \\ \end{tabular} & \begin{tabular}{c} \(l=40\),\(000\), \\ \(b=10\),\(000\), \(h=50\) \\ \end{tabular} & Si & \begin{tabular}{c} 62,\(300\) \\ \end{tabular} & \
\begin{tabular}{c} 85 \\ \end{tabular} &
\begin{tabular}{c} Electrostatic \\ actuator \\ \end{tabular} \\ \hline
[48] & \begin{tabular}{c} Theory and \\ Experiment \\ \end{tabular} & \begin{tabular}{c} Cantilever \\ \end{tabular} & \begin{tabular}{c} \(l=1500\), \\ \(b=12\), \(h=60\) \\ \end{tabular} & Cu-Au & \begin{tabular}{c} 120 \\ \end{tabular} & \
\begin{tabular}{c} 28 \\ \end{tabular} &
\begin{tabular}{c} MEMS \\ lays/switches \\ \end{tabular} \\ \hline
[49] & \begin{tabular}{c} Theory and \\ Experiment \\ \end{tabular} & \begin{tabular}{c} Irregular \\ Cantilever \\ \end{tabular} & \begin{tabular}{c} \(l=67\), \(b=42\), \(h=6\) \\ \end{tabular} & Au & \begin{tabular}{c} 2 \\ \end{tabular} & \
\begin{tabular}{c} 55 \\ \end{tabular} &
\begin{tabular}{c} MEMS \\ electrostatic \\ actuator \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table}