3.1. Electromechanical performance analysis without holes
When there are no holes in switch designed, obtained displacement is \(2.04\times {10}^{-6}\) µm for the applied actuation voltage is 10 volts.
3.2. Electromechanical performance analysis with holes
When there are holes in the design of the switch, then the displacement obtained is \(2.03\times {10}^{-6}\) µm for the applied voltage of 10V, which is less than the displacement obtained when there are no holes. From which it is understood that holes play a major role in improving the performance of the switch. As the number of holes increases up to a limited number, pull in voltage decreases and the switching time is also decreased. Due to the presence of square holes in the switch structure, damping effect is also reduced [4]. Above theory is observed from the figures So the further simulations and observations are carried out on the switch with holes for better performance results.
3.2.1. Pull in voltage
When the electric field is exerted on the electrode, the electrostatic force is exerted upon the beam. The applied electric field is what the working of the cantilever predominantly dependent on. The spring constant is given by the equation
\(k=\frac{w\epsilon {t}^{3}}{{l}^{3}}\) (1) Where,
K is Spring Constant
l is Length of the beam
W is Beam Width
t is Thickness of the Beam
E is Young's modulus
Pull in voltage is given by the equation,
\({v}_{p}\)=\(\sqrt{\frac{8k{{g}_{o}}^{3}}{27{\epsilon }_{o}A}}\) (2)
Here the actuation voltage is V. A is the area between beam and electrode. The spring constant is K. As the voltage which is applied increases uniformly, the electrostatic force that is developed on the membrane will be increased which will tend to pull down the beam towards the electrode. This eventually decreases the gap that is present in between the beam and the electrode. When the original gap between the beam and the electrode fixed is reduced to two-third then that voltage is called the pull-in voltage [13].
A. Metal change
Effect of change in the material of the switch among gold aluminum, copper, and chromium on the performance of the switch is analyzed while keeping the dielectric material as silicon nitride. It is observed from the displacement vs. voltage graph obtained in COMSOL software that aluminum is having the best performance in the terms of displacement.
B. Dielectric material change
When the material used for the dielectric of the switch among generally used materials like silicon nitride, aluminum nitride, Hafnium dioxide, silicon dioxide, it is observed that the silicon nitride is giving optimum performance from the graph below, when the metal is fixed to aluminum.
C. Beam thickness change
When the thickness of the beam is varied among 0.5 µm,1 µm,1.5µm,2µm by keeping the metal as aluminum and dielectric as silicon nitride, it is observed that as the thickness of the beam is 0.5 µm, the displacement is low which gives the best performance.
D. Beam Width Change
When the width of the beam is varied between 100 µm,60 µm and 80 µm, it is observed from the graph by keeping the metal as aluminum and dielectric as silicon nitride, it is observed that as the beam width is 100 µm, the displacement is low which gives the best performance.
E. Dielectric Thickness Change
When the thickness of the dielectric is varied in between 0.1 µm ,0.3µm and 0.5 µm, it is observed from the figure that how the displacement is varied when a voltage of 10v is applied.
It is observed that as the dielectric thickness is 0.1µm, the displacement is low which gives the best performance when compared to 0.5 µm and 0.3 µm values, from which it can be concluded that the thickness of dilelectric is inversely proportional to the displacement[15] .
3.2.2. Up state (Cu) and Down state (Cd) Capacitance.
The structure is in UP state when the actuation voltage is not applied to the membrane. the capacitance of the shunt switch putting the device in OFF state. As the voltage for actuation is applied, the structures membrane starts moving downwards towards the electrode. This capacitance is called the downstate capacitance which allows the RF signal to pass, putting the device in ON state. By decreasing the upstate capacitance and increasing the downstate capacitance, RF MEMS switch performance can be improved [14]. The capacitance variation depends mainly on material chosen for dielectric. In this simulation, silicon nitride is considered.
The equation for upstate capacitance of the membranes
\({c}_{u}\)=\(\frac{\left({\epsilon }_{^\circ }A\right)}{\left({g}_{^\circ }+\frac{{t}_{d}}{{\epsilon }_{r}}\right)}\) (3)
Where,
\({\varepsilon _0}\) - the permittivity of the free space,
\({\varepsilon _r}\) - the relative permittivity of the electrode material
A - the overlapping Area between electrodes,
g0 - the gap between the electrodes and beam
td - the dielectric layer thickness electrodes
The equation for downstate capacitance of the membranes
$${C_d}=\frac{{\left( {{\varepsilon _0}{\text{ }}{\varepsilon _r}{\text{ }}A} \right)}}{{{t_d}}}$$
4
The capacitance ratio which is referred as Cd/Cu tells about the device's capacitance sensitivity [6]. In this case the obtained capacitance ratio is 76.25. Hence, the results of capacitance of shunt membrane need to be in the range of upstate and downstate capacitance.
The shunt membrane is simulated by applying electro- mechanics physics using COMSOL tool.
3.2.3. Switching Time Analysis
For opening and closing any connection a switch is used. For fast processing speeds in electronic devices, the reduction in switching time is essential. It is the time required to achieve the touching of bottom electrode and beam structure. Switching time depends on source voltage, pull-in voltage and resonant frequency [9].
\(\left[9\right]\) \({T_s}=\frac{{3.67{V_p}}}{{{\omega _0}{\text{ }}{V_s}}}\) (5)
Where,
Vs is the input source voltage,
Vp is the pull – in voltage,
ω0 is the resonant frequency,
The spring constant and effective mass of the membrane, is determine the resonant frequency
$${\omega _0}=\sqrt {\frac{k}{m}}$$
6
The switching response of the shunt membrane is 0.54 µs. The performance of the device increases when the switching time is minimized.