Features measurement analysis of pull-in voltage for embedded MEMS

ABSTRACT


INTRODUCTION
Embedded micro-electro mechanical systems have become a daily necessity.Through the years, these manufactured devices have decreased in size and increased in efficiency.Micro electro mechanical systems (MEMS) technology has generated a significant amount of interest in the government and business sectors [1].This interest is happening due to the potential performance and cost advantages with micro-scale devices embedded in a portable system and can be manufactured at low cost.As we know, the term MEMS is the combination of two different systems that is mechanical and electrical systems such as MEMS actuators and MEMS sensors including MEMS switches and MEMS accelerometers [2]- [4].Furthermore, MEMS switches embed the advantages of mechanical and semiconductor properties in a small size.This property of the MEMS switch can be applied to radio frequencies (RF), hence the name RF-MEMS switch [5].For example, RF-MEMS filters and resonators are intended for applications such as duplex filters, RX&TX band filters, global positioning system (GPS) filters, VCOs, reconfigurable antennas and reference oscillators [6]- [8].The other application field is RF-MEMS switches, which are very interesting for multi-system phones and with IoT [9], [10].
Electrostatically actuated MEMS switches can operate in an extremely power saving mode, they do not generate distortion of the signal.These categories are important in the present embedded market.For the switching function at RF frequency, the RF-MEMS switches offer better performance, such as low insertion ISSN: 2089-4864  Features measurement analysis of pull-in voltage for embedded MEMS (Hajar Baghdadi) 147 loss, high isolation, high bandwidth, and less noise, than standards PIN diode and field effect transistor (FET) switches [11].Thus, compared to the traditional switches, MEMS switches have several significant advantages for wireless communications and radio frequency technologies [12], [13].However, they still not reliable and their wide spread commercialization has been limited so far due to some design and operational reasons.The main reasons for that are reliability and yield, as well as, high actuation voltage, large switching time, large size, and packaging [14].Currently, many research groups around the world are working on new solutions to surmount these problems.In fact, to overcome these challenges, a number of techniques have utilized such as push-pull or meander was fabricated to surpass the problem of switching speed [15].As well, to decrease the switch actuation voltage, a variety of techniques are employed, including decreasing the spring constant [16], [17], utilizing piezoelectric actuation [18], [19] and other structures [20], [21].
High actuation voltage is one of the most important challenges.A critical aspect of the behaviour of MEMS switch is that the deformation will reduce the distance between the two conductors.This behaviour leads to the phenomenon of pull-in.The increasing of voltage bias will increasingly deform the structure to a point where the deformation will become unstable, then the deformation will increase without the application of any bias until the point of contact between the conductors.Because the distance between the conductors has been dramatically reduced, the applied bias voltage is greater than that required to maintain the contact, so a substantial reduction in the bias voltage is required to allow the mechanical restoring force to again move the structure.This behaviour is the basis for the design of many MEMS because the pull-in voltage is one of the most important parameters of MEMS design [22].
In this paper, a detailed analysis is done to obtain pull-in voltage and optimize the behaviour of the MEMS switch.The pull-in problem of beams cannot be solved analytically as nonlinearity is not taken into account.For this, numerical techniques using finite element analysis (FEA) are adopted.Our contribution is to propose an optimized model that consolidates a compromise between a small area and a reasonable pull-in voltage.For this purpose, we study the MEMS behaviour as a function of some geometrical and mechanical parameters such as length, width, thickness, gap, and Young modulus.Then, we work on these parameters using FEA software called "COMSOL multiphysics" in such a way to decrease the actuation voltage.

RESEARCH METHOD 2.1. Principe working of cantilever MEMS switch
Switching is necessary in many applications, both low and high frequency.MEMS switches use mechanical movement to achieve an open or closed circuit in the radio frequency transmission lines.MEMS switch classification depends on the type of geometry, the contact type, the type of configuration, and the type of actuation.In this work, we will design a cantilever MEMS switch with an ohmic contact series configuration.The mechanical motion is achieved using electrostatic actuation for the reason that it is easily integrable, we don't need a specific material but only a voltage source and a metal plate.This type is the simplest to implement for good performance and is the most one that currently mobilizes the research in this field [23], [24].Its principle is the most convenient for the fabrication that can be compatible with typical RF technologies.
A cantilever is a beam anchored at only one end and free to move at the other end (see Figure .1).In this typical MEMS device, a bias voltage is imposed between two conductors.This causes charge migration that produces an attractive electrostatic force between the two conductors.This force will lead to a mechanical deformation of the cantilever.Normally, this is the principle working that is exploited to achieve the closing of a switch (also to change the position of a mirror).In this case of micromechanical actuators, intermolecular forces such as Casimir and van der Waals forces have been neglected [25].However, Casimir and van der Waals forces can play an important role in nanobeam actuators.In our work published in 2020 [26], we considered these two effects.
To model the system for dynamic analysis, we use a computationally efficient method.we obtain the grouped parameters of the system and solve it as a parallel-plate capacitor constrained by a spring.By lumped the mechanical elements, the system can be approximated into a single degree of freedom system whose governing as (1).
Where m is the mass, and z is the displacement of the movable plate.Under the applied voltage V between the two plates, we simulate the cantilever MEMS switch.The metal cantilever ensures the closing or opening of a transmission line.When a potential difference is applied between the electrode and the cantilever, an electrostatic force   tends to bring the two conductors closer together.From a certain electrostatic force which corresponds to a voltage called pull-in Voltage Vpull, the cantilever sticks on the conductor.
The electrostatic force generated by the applied voltage, as (2).
where V: the applied voltage, A: Air of cantilever, z: the displacement, g0: the initial gap, and εo: permittivity of free space.The application of an electrical voltage between two electrodes also generates a mechanical force   in the opposite direction to the electrostatic force.The corresponding stiffness is k.The force   is proportional to z, as (3).
By substituting the formulas of the forces in (1), we will have (4).
In order to realize the deformation of MEMS switches, the mechanical behaviour of switch can be modelled using a linear spring constant, k(N/m) and it is given by ( 5), where M= Young's Modulus, w=width of cantilever, t = thickness of cantilever and l = length of cantilever [27].At equilibrium, we have: If the electrostatic force is increased by increasing the applied voltage and if that force is greater than the elastic restoring force, the equilibrium is lost and the cantilever will bend and finally makes contact with the fixed ground plate.This phenomenon is known as pull-in.Therefore, we calculate the actuation voltage   at equilibrium and find as (6).
depends on the geometrical parameters of the cantilever as well as on the mechanical parameters such as the k-parameter, which in turn depends on Young's modulus M. In order to determine the pull-in voltage of the MEMS cantilever, a FEA software is adopted.The impact of the geometrical and mechanical parameters on the   will be studied in the following sections.
The moving element deforms up to the point of instability.This point can be expressed by a certain distance which is calculated: Under static equilibrium,   has equal magnitude but opposite direction as the  3) in the previous equation, we will have (7).
Pull-in phenomena will occur when the derivative of voltage with respect to displacement z is zero.
And the instantaneous g depends on displacement z: So, the previous equation can be derived, which yields the following equation: Relationship between the z-displacement, the instantaneous gap and the initial gap Thus, the pull-in displacement is (see Figure 2): The position of   : The pull-in displacement is determined by the initial gap.In terms of beam instantaneous gap, it corresponds to 2 3 ⁄ of the initial gap  0 .

COMSOL modeling
The model of the cantilever is made using COMSOL multiphysics software (see Figure 3).COMSOL was chosen as it allows us to simulate several physical phenomena (coupled or uncoupled) in the same simulation environment.In this work, COMSOL was helpful to model the evolution of the MEMS switches.this tool offered us an interface to make a 3D mechanical drawing of the different parts, namely the cantilever and the ground plane.Also, it allowed us to apply electrical constraints such as the activation voltage to measure the displacement of the cantilever, the resistance or the capacitance.As we mentioned, the behaviour of the cantilever is influenced by its length, width, thickness and the diverse properties of the material utilized to fabricate the structure.The geometric design, as well as the material used to construct the cantilever, affects the applied voltage and in general the stiffness of the cantilever.The analysis is performed on the structure with the parameters indicated in the Table 1.

Impact of mechanical parameters on pull-in voltage
In order to see the impact of the mechanical aspect on   , we keep the same geometry defined in the previous section and we compare different materials defined by their Young's modulus M. In this simulation, aluminium, copper, gold, platinum, nickel and molybdenum metals have been used as the materials of cantilever MEMS switches.
We start by simulating aluminium cantilever (M=70 GPa) and describing the results shown in figures.Hence, all other materials simulations results will be presented in a summary table.As previously mentioned, we maintain the same dimensions presented in Table 1 and we simulate the z-displacement of the cantilever at the limit of symmetry.Figure 5 shows the shape of the cantilever deformation for each applied voltage.

Figure 5. Shape of cantilever displacement for different applied voltages
As we presented, we made our geometry with a gap  0 = −6 , as soon as the cantilever is bent to one third of initial distance −2, automatically it is considered as in a low state.Thus, the pull-in voltage will be calculated at this pull-in position   = −2.The pull-in voltage for a device can be determined by identifying the greatest voltage bias that can be supported before pull-in happens.
Viewing the figure, the voltage is plotted against z in which beam bends.At a voltage close to 21 V, we can reach the   = −2 and hence the low state.The exact value of the voltage can be determined from Figure 6.
We simulate the displacement of the endpoint of the cantilever as it belongs to the contact surface and has the maximum constraints.We obtain the function shown in Figure 6.It presents the z-displacement as a function of the applied voltage.The value of the voltage corresponding to zpull is equal to 20.3 V. Therefore, to activate our cantilever mems, we have to apply a voltage Vpull which is about 20.3 V.In this work, we take the initial gap  0 = −6µ.Therefore, as we demonstrated in the above section, the pull-in position:   = −2µ .We conclude that the pull-in voltage using aluminium cantilever is   = 20.3.This simulation is just for aluminum.Now, we will present a summary table to display the simulation results for other materials.

Results Tabulation:
In the Table 2, we can see the calculated and simulated results of the proposed model.For a comparative study, we determined the pull-in voltage formula by substituting the value of   into (6).Then, we calculated the values shown in Table 4. Here, we maintain the same geometry and compare different materials described by their Young's modulus M. Therefore, we can identify the impact of mechanical aspect on   .Indeed, we deduct from Table 4 that as Young's modulus increases, the Vpull also increases.Now, we will draw a figure of the results in order to see the law that links the mechanical parameter and the actuation voltage and to see the gap between the two curves of the calculated and simulated   .In Figure 7, both curves have the same trend and the same overall behaviour.Moreover, there is a gap between the calculated and simulated   voltages but this gap does not call into question our simulation.From the obtained results, we can see that aluminium and gold correspond to the lowest value of the   voltages.In addition, as mentioned, the simulated Pull-in voltages are in good agreement with the literature values, which confirms the model validity.Aluminium and gold are the most ideal materials for the cantilever.However, for technological reasons, it is more desirable to use aluminium.Firstly, from a technological point of view it is easy to integrate.Secondly, it is less expensive.On the other hand, Gold is more expensive and its manufacturing process is more complex as it does not adhere easily to such a layer.Aluminium also has problems as it oxidises easily.Moreover, both aluminium and gold can't resist the temperature.In the present work, we will choose aluminium as a material for cantilever MEMS switches.

Impact of geometrical parameters on pull-in voltage
Now, to see the impact of the geometric aspect on   , we will always take aluminium as the cantilever material and vary the dimensions of the geometry (See Figure 8).The effect of the length l of the cantilever on the pull-in voltage has been studied and based on the simulation results presented in Table 3.It is found that the cantilever length has an inverse relationship with the pull-in voltage   .Indeed, we can see, from (6) in section 1, a coherence between the theorical and experimental results.The length is inversely proportional to the spring constant and the spring constant is directly proportional to Vpull.Therefore, the increase in length decreases the spring constant and, consequently, the Vpull decreases.
From Table 4, we can see that a small change in thickness plays a major role in the variation of   .The decrease in thickness decreases the spring constant and, consequently, the Vpull decreases.Indeed, from ( 5) and ( 6), the spring constant k is directly proportional to the thickness the cube and the   is also proportional to the square root of k.These formulas confirm the results of the table.From Table 5, the width W of the cantilever is having no much effect on modifying the   .Indeed, by substituting the formula of k into the formula of   (5) and (6), and the air A by its detailed formula.Table 6 shows the impact of gap on pull-in voltage.We can see that the width will be reduced.Thus,   does not depend on the width.This shows the validity of our results.
The   voltage can also be reduced by decreasing the air gap.This relationship can be confirmed based on (6).It can be concluded that any variation of the geometrical parameters such as length, width, thickness and gap, or the mechanical parameters including Young's Modulus, may result in a significant change of the pull-in voltage.
From the results, to optimize the MEMS switch performances, we need a typical compromise between small area and acceptable pull-in voltage.It can be seen that the best actuation voltage occurs with the geometrical parameters of MEMS cantilever, 400 μm in length and 1.5 μm in thickness.For RF applications, it is recommended to use a large gap of 6 μm to prevent radio frequency interferences.Thus, we work on mechanical and geometrical parameters of a cantilever in such a way to decrease the actuation voltage and improve the power consumption.In addition, low pull-in voltage makes the MEMS cantilever susceptible to self-actuation at high RF power levels.Regarding the used material in manufacturing process for RF applications, aluminium and gold are the most ideal materials to minimize   .In the present work, we have worked with aluminium, but in future work, we will adopt gold and elaborate a complete comparison between aluminium and gold cantilever by acting on other technological parameters.Thus, depending on our application, we can modify these parameters in order to obtain the optimized switch model.
The works [28]- [31] are selected for comparison due to the reason that all the switches have cantilever configuration, and they are simulated in order to study their behaviour characteristics, for which the difference between them in the dimensions of the beams is considered.The work [28]- [31] uses very small dimensions that do not meet the needs of our specifications.Typical dimensions of designed switch beam lengths are ranging from 200 to 400 μm, thickness ranging from 1.5 to 3 μm, width ranging from 10 to 40 μm, and gap ranging from 4 to 10 μm.These dimensions are relatively large and are suitable for easy and fast manufacturing.Moreover, by adopting these dimensions, we will avoid the problems of RF interference.Due to these reasons, our model is best suited to manufacturing contraints.

CONCLUSIONS
The keen embedded MEMS are one of the rapidly developing technologies in the present embedded market.For this reason, developers and designers have encountered several problems in the modeling of embedded MEMS.In this paper, A COMSOL-based finite element analysis was used to investigate the structure deflection.We analyzed the impact of mechanical and geometrical parameters on the pull-in voltage of the cantilever.The first study of the impact of the mechanical aspect on   allowed us to define the material we will use, while the second study of the impact of the geometrical aspect on Vpull allowed us to determine the values of the geometrical parameters that minimize   .
In future work, we compare this work by choosing the aluminium cantilever with the gold cantilever by acting on other technological parameters.Also, we correlate all the parameters to find the optimal model that minimises   as much as possible and gives the best functioning.The results obtained from this work would allow us to refine and develop improved RF MEMS switches for a wide range of applications.

Figure 3 .
Figure 3. Model of cantilever in COMSOL software

Figure 4 .
Figure 4.The z-displacement of the cantilever when applied voltage equals to Vpull

Figure 6 .
Figure 6.Displacement as a function of the applied voltage.

Figure 7 .
Figure 7. Calculated pull-in voltage vs simulated pull-in voltage Int J Reconfigurable & Embedded Syst ISSN: 2089-4864  Features measurement analysis of pull-in voltage for embedded MEMS (Hajar Baghdadi) 153

Figure 8 .
Figure 8. COMSOL model described by its geometric parameters

Table 2 .
Young's modulus and pull-in voltage of the different cantilever materials

Table 4 .
Impact of thickness on pull-in voltage

Table 5 .
Impact of width on pull-in voltage

Table 6 .
Impact of gap on pull-in voltage