Design and Nonlinear Analysis of a Novel MEMS-Based Resonator for Biomedical Applications
الموضوعات : مهندسی هوشمند برق
Farbod Setoudeh
1
(Department of Electrical Engineering, Arak University of Technology, Arak, Iran)
Mohsen Ghadami
2
(Department of Electrical Engineering, Islamic Azad University, Arak Branch, Iran)
الکلمات المفتاحية: MEMS, Biomedical applications, Microresonators, Switching time, Material type, Temperatu,
ملخص المقالة :
Complementary metal oxide semiconductor (CMOS) based microelectromechanical systems (MEMS) resonators are the main component of modern integrated systems that are designed and fabricated using CMOS composite layers. The design of these resonators, which are actuated electrostatically, is strongly dependent on the ambient temperature and the used materials. Important factors, such as structural features, actuator type, and the used materials should be considered in the design of micro resonators because they strongly affect the quality factor, power consumption and operating frequency of these devices. However, in designing micro resonators, electrostatic actuators are preferred over other actuator types due to their lower manufacturing cost, lower losses, and higher controllability. In this paper, first, some micro resonators are designed and their structures are then investigated. The micro resonators are mechanically analyzed to optimize their dimensions. A bias voltage of 0.1 V is applied to the micro resonators to investigate their feasibility for implantable biomedical applications. The switching time for a Zinc (Zn) movable plate is equal to 0.5 µs. In this paper, the role of device dimensions, Young’s modulus, switching time, material type, bridge displacement, and voltage (which is an important challenge in electrostatic resonators since it is usually high), as well as the effects of temperature on displacement are investigated.
149 International Journal of Smart Electrical Engineering, Vol.9, No.4, Fall 2020 ISSN: 2251-9246
EISSN: 2345-6221
pp. 143:148 |
Design and nonlinear analysis of a novel MEMS-based resonator for biomedical applications
Farbod Setoudeh1, Mohsen Ghadami2
1 Faculty of Electrical Engineering, Arak University of Technology
2 Department of Electrical Engineering, Islamic Azad University, Arak Branch, Iran
Abstract
Complementary metal oxide semiconductor (CMOS) based microelectromechanical systems (MEMS) resonators are the main component of modern integrated systems that are designed and fabricated using CMOS composite layers. The design of these resonators, which are actuated electrostatically, is strongly dependent on the ambient temperature and the used materials. Important factors, such as structural features, actuator type, and the used materials should be considered in the design of micro resonators because they strongly affect the quality factor, power consumption and operating frequency of these devices. However, in designing micro resonators, electrostatic actuators are preferred over other actuator types due to their lower manufacturing cost, lower losses, and higher controllability. In this paper, first, some micro resonators are designed and their structures are then investigated. The micro resonators are mechanically analyzed to optimize their dimensions. A bias voltage of 0.1 V is applied to the micro resonators to investigate their feasibility for implantable biomedical applications. The switching time for a Zinc (Zn) movable plate is equal to 0.5 µs. In this paper, the role of device dimensions, Young’s modulus, switching time, material type, bridge displacement, and voltage (which is an important challenge in electrostatic resonators since it is usually high), as well as the effects of temperature on displacement are investigated.
Keywords: MEMS, Microresonators , Switching time, Biomedical applications, Material type, Temperature
Article history: Received 29-Jan-2020; Revised 19-Feb-2021; Accepted 02-Mar-2021.
© 2020 IAUCTB-IJSEE Science. All rights reserved
1. Introduction
Nowadays, microelectromechanical (MEMS) resonators and and nanoelectromechanical (NEMS) resonators are widely used in different measurement applications, such as chemical sensors [1], magnetic field sensors [2], and inertia sensors (wearable motion sensing systems for measuring the biomechanics of human movement) [3-5]. Furthermore, microelectromechanical systems resonators have been studied and used in oscillators and filters for RF communication applications [6-9]. MEMS/NEMS resonators can be applied in different structures such as, single-ended/double-ended clamped structures, hemispherical shells, micro disk, drum, ring, fork, surface acoustic wave Bulk, acoustic wave, and other original resonant structure [5]. These resonators are excellent alternative to quartz resonators, and their quality factor, Q, can be improved to reach to that of quartz resonators [10, 11]. MEMS resonators based on silicon piezoelectric thin film (TPoS) have a high Q-factor coefficient to provide satisfactory results in their applications such as filters and sensors [12]. MEMS resonators have lower power consumption, longer life time, higher durability and stability, as well as smaller size and simpler design [13-15] compared to other resonators. The use of MEMS devices in different temperature ranges has been investigated in [16-24]. In these references, the stability of the materials at high temperatures is discussed in detail. Most of MEMS devices are made of silicon, which has normal mechanical properties below 600° C [25-27]. Selecting the right material in the structure of MEMS devices requires special care, as addressed in several studies [28-31]. The miniaturization of MEMS devices cannot be studied by ordinary mathematics, particularly in micrometer or nanometer scales [32-35]. Therefore, the evaluation of mechanical properties and measurement at small scale are of great importance. One of the most important parameters that characterizes the overall stability of MEMS devices is the quality factor (Q). In [36], the effect of temperature on the quality factor of microresonators is investigated. Since MEMS devices have complex geometry and are used in a wide range of applications under different temperature conditions, highly accurate and reliable technologies are required for manufacturing them. In [37], RF-MEMs resonators with multi-frequency adjustable generations are proposed for radio frequency applications. The integration of complementary metal oxide semiconductor (CMOS) and MEMS provides a superior technology that enables miniaturization and performance improvement [38]. In CMOS-MEMS devices, the support beam and suspended plate are made of composite layers (e.g., aluminum and silicon dioxide layers). These layers are sensitive to temperature, and therefore, the overall variability in Young's modulus of CMOS layers and the temperature dependence of quality factor are thoroughly investigated in this reference. Resonators with different actuators are usually high-voltage [39], environmentally unfriendly, high-cost, and affected by temperature variations [21]. Therefore, we propose a special design with appropriate dimensions using different materials to overcome such problems to a large extent. In this paper, it is aimed to obtain the maximum displacement at the lowest possible voltage (and thus electrostatic force), compared to previous designs, which use piezoelectric, electromagnetic [13], and other types of actuators. Furthermore, it is attempted to achieve a design that operates perfectly at different temperatures with no effect on temperature-displacement characteristics so that the most ideal switching speed (time-displacement) is achieved. Accordingly, COMSOL software is used to perform simulations and the results are discussed in detail.
2. Construction and Topology of the Microresonator Structure for Biomedical Applications
The basic structure of an electrostatic actuator and the electrostatic force between its parallel plates are shown in Fig. 1. According to this figure, when a voltage is applied between the top movable electrode (metal bridge) and the bottom fixed electrode, the metal bridge deflects downwards due to the electrostatic force. To approximate the electrostatic force, the metal bridge and the fixed plate are modeled as a parallel-plate capacitor. The capacitance 
can be calculated using Eq. (1) [24].
(1)
where A is the area of the parallel plates of the capacitor, d is the air gap between the plates, and ε0 is the permeability of free space (ε=8.854*10-12 F/m). Oscillation in this resonator has electrostatic nature due to the applied voltage Vi, which causes a force of attraction between the fixed and movable plates of the actuator as shown in Fig. (1).
Fig. 1. Simple electrostatic actuator and electrostatic force between the parallel plates.
Figure 2 shows the schematic of a basic electrostatic actuator model. In this model, electrodes are assumed to be perfect. Moreover, it is assumed that the capacitor operates in vacuum environment to ensure zero external mechanical force on the top plate. The beam is of length 
, width 
, thickness 
, and is separated from a fixed ground plane by an initial airgap thickness 
.
Fig. 2. Simple electrostatic actuator.
Equation (1) can be rewritten as Eq. 2.
(2)
where 
and
denote the widths of the metal bridge (top plate) and the bottom electrode, respectively; g is the air gap between the plates, and V is the applied voltage. The potential energy stored in the capacitor resulting from the bias voltage V can be calculated using Eq. 3.
(3)
In Eq. 4, the electrostatic attraction force 
is obtained by differentiating the potential energy stored in the capacitor with respect to the position of the movable plate.
(4)
Electrostatic force is exerted uniformly on the metal bridge and the metal bridge reacts mechanically to this force. This mechanical response can be modeled by a spring. In this case, the deflection of the metal bridge (
) is used to determine the mechanical elastic force (
) as follows:
(5)
where 
is the spring constant, which is assumed to be linear. Thus, the electrostatic force opposes the linear spring restoring force (due to the stiffness of the bridge). Therefore, by substituting Eq. 4 into Eq. 5, the applied voltage magnitude can be calculated in terms of the displacement of the metal bridge; that is,
(6)
With increasing applied voltage, the electrostatic force on the metal bridge increases. When the electrostatic force is greater than the restoring force, the metal bridge becomes unstable and suddenly collapses. This occurs when the metal bridge is displaced by two-thirds of the air gap. If the voltage increases above the pull-in voltage, the electrostatic force causes the top movable and bottom fixed plates to snap together and the capacitor is short-circuited. Pull-in voltage is the maximum operating voltage of the actuator.
(7)
where 
indicates the permittivity of free space, 
represents the initial airgap, and The spring is specified by an effective stiffness, 
. The effective stiffness 
is calculated by [40, 41]:
(8)
where is the thickness of the bridge and 
is the Young's modulus (depending on the type and mechanical properties of materials), is the beam length, 
and 
indicate the effective residual stress and the
tension axial force which is expressed, respectively, 
, and 
.
The effective stiffness is used to show voltage-displacement ratio.
The pull-in distance can be calculated as follows:
(9)
Moreover, the pull-in gap can be calculated as follows:
(10)
This device requires very low voltage (about subthreshold voltage) and has suitable dimensions, so it can be used in medical equipment (such as implantable cardiac pacemakers) without requiring an external voltage supply and only using the electric field produced inside the body. Moreover, MEMS devices can operate in the temperature range 200~400
K with an insignificant effect on the displacement of the bridge. Therefore, besides medical applications (hearing aids, heart rate swing, heart battery, etc.), MEMS devices can be used in mountaineering equipment, mobile antenna technology, and especially in integrated circuits. Other advantages of MEMS devices are very high switching speed (time-displacement characteristics) and the ideal electrostatic force of the design, which provide an optimal quality factor. Therefore, it is expected that using MEMS resonators in microsensors and microactuators becomes increasingly popular. In this paper, the aim is to create oscillation by applying an appropriate electrostatic force at the lowest possible voltage while considering the effects of temperature on the displacement of the movable plate.
3. New Design of Square Microresonator
In this section, a basic microresonator model is introduced and important factors such as the applied voltage and displacement are discussed. Then, different microresonator structures are examined to improve the performance. The overall schematic of the electrostatic microresonator is shown in Fig. 3. According to this figure, the microresonator consists of a fixed and a movable plate. These plates are made of Al with thicknesses of, respectively, 2 and 1.5 µm, and an air gap of 2.5 µm between the plates. The material of the bulk and the substrate of the microresonator are silicon and silicon dioxide, respectively.
Fig. 3. Overall schematic of the electrostatic microresonator.
In the finite element method, geometric approximations are used to reduce the size of the model as well as the simulation time. Therefore, the details, which are not shown in Fig. 4, are used in the software as the boundary conditions. The geometrically approximated three-dimensional model of the proposed structure is shown in Fig. 4.
Fig. 4. 3D model of the proposed structure.
In Eq. 8, 
, and (denoting, respectively, the thickness of the bridge, Young's modulus, and the length of the beam) can be used to obtain the voltage-displacement ratio. According to Eq. 8, a reduction in or reduces the value of 
, while an increase in , reduces the value of. Therefore, the main structure of this device is current and effects of external magnetic field on the resonator). The Young’s modulus, heat transfer coefficient of this metals are represent in Table 1.
2. Table 1. The Young’s modulus, heat transfer coefficient of four metals (Al, Au, Ag, and Zn)
Characteristic | AL | AU | AG | ZN | CU |
Young’s modulus | 10 | 11 | 12 | 16 | 17 |
Heat transfer | 250 | 310 | 429 | 116 | 401 |
5. Simulation Results
For the primary design in Fig. 5, the displacement distribution on the microresonator with Al components is shown in Fig. 6 at a bias voltage of 80 V. According to this figure, a maximum 
displacement of 2.299 μm occurs at the center of the bridge.
Fig. 5. Displacement versus voltage variations at the center of the microresonator.
Fig. 6. Displacement distribution on the microresonator at a bias of 80 V.
This design requires high voltage, so some modifications are made to optimize it. For this purpose, the design structure is shown in Fig. 7. In First, the lengths of the resonator beams are increased, as shown in Fig. 7.
Fig. 7. The proposed structure of resonator with Increasing in the length of beams resonator.
The displacement of the bridge versus voltage variation is shown in Fig. 8. According to this figure, the maximum displacement occurs at 10 V.
Fig. 8. Displacement versus voltage at the center of the microresonator with longer beams.
The displacement distribution on the microresonator at 10 V bias voltage is shown in Fig. 9. A maximum displacement of 0.006 
occurs at the center.
In the input layer, the water droplets, relative humidity and temperature difference are used as the inputs for estimating. According to the input variables number, 3 layers is the neurons number in the input layer.In this paper, the prediction of leakage current is purpose so, only the leakage current amount is assumed as the output and there is only one neuron in the output layer. The output layer transfer function is selected as the purelin function, that is, the linear transfer function. The hidden layer setting is essential for BP neural network. There is no standard technique to define the neurons number in the hidden layer.
Fig. 9. Displacement distribution on the microresonator with longer beams at 10 V bias voltage.
Figure 10 shows the displacement versus time. This figure shows a switching speed of about 2 
for the resonator.
Fig. 10. Time analysis curve.
The Electrostatic force of the proposed microresonator with longer beams is shown in Fig. 11.
Fig. 11. Electrostatic force of a microresonator with longer beams.
As shown in figures 8-11, better results are obtained for narrower and longer beams, while the applied voltage still needs to be reduced. Therefore, we open a set of holes in the bridge in order to reduce the air damping. However, these holes are not sufficient to achieve the ideal results. In the following, we apply this method to a Zn plate with a thickness of 0.5 μm.
Other simulations are performed to evaluate the effects of the air gap height and the thickness of the bridge. As these two parameters decrease, the displacement due to the applied voltage increases. According to the investigation for designing the resonator in Fig. 7, the following points should be considered:
• For narrower and longer beams, the resonator efficiency (displacement due to the applied voltage) increases. However, the beams cannot be narrowed too much due to fabrication limitations.
• The material of the bridge affects the efficiency of the resonator.
• By reducing the air gap size and bridge thickness, the efficiency of the actuator can be increased. However, this reduction is restricted by fabrication limitations.
As mentioned, the structure, beam dimensions, and bridge material can be changed to achieve the best efficiency of the resonator. Therefore, the structure shown in Fig. 12 is designed and simulated.
Fig. 12. BP neural network prediction model
The curve of the bridge displacement in terms of voltage variations are shown in Fig. 13. According to this figure, the maximum displacement occurs at 10 V.
Fig. 13. Displacement versus voltage of the Al microresonator.
The displacement distribution on the microresonator at a bias voltage of 10 V is shown in Fig. 14. The maximum displacement is 14 µm at the center.
Fig. 14. Displacement distribution at a bias voltage of 10 V.
Electrostatic force analysis is shown in Fig. 15.
Fig. 15. Electrostatic force analysis of the microresonator with Al plate.
According to the results, the designed structure is more efficient than the previous designs. In the following, we optimize the designed structure. In this section, the optimized microresonator is introduced and effective parameters in this design such as the applied voltage, displacement and switching speed are evaluated.
The optimized microresonator in Fig. 12 is first implemented using Al for the fixed and movable plates. The thicknesses of the movable and fixed plates are 1 and 1.5 µm, respectively, and the air gap is 2.5 µm. The beams of this microresonator are stiff (has spring-like behavior), so the efficiency of the microresonator increases.
The displacement of the bridge versus voltage is shown in Fig. 16. According to this figure, the maximum displacement occurs at 10 V.
Fig. 16. Displacement versus voltage in the optimized microresonator.
The displacement distribution on the microresonator at a bias voltage of 10 V is shown in Fig. 17 with a maximum displacement of 14 µm at the center.
Fig. 17. Displacement distribution at a bias voltage of 10 V.
Similar results are obtained for an Al plate of 0.5 μm thickness, as shown in Figs. 18 and 19.
Fig. 18. Displacement versus time in the optimized Al microresonator of 0.5 μm thickness.
Fig. 19. Electrostatic force analysis of the optimized Al microresonator of 0.5 μm thickness.
To achieve the optimal efficiency of the resonator, we perform simulations with different plate materials (here, the results for Ag, Zn, and Au are presented). Moreover, different thicknesses are examined to obtain the optimal design. According to the simulation results, the resonator made of Zn plate has the highest efficiency. The simulation results for different metals are given in Table 2.
Table 2. Simulation results for different metals.
Electrostatic force for optimized state ×10-7 | Displacement at 0.1 V (μm) | Displacement at 10 V (μm) |
Bridge thickness (μm)
| Metal type |
9.91 | -- | 0.1 | 2 | Al |
20 | 0.1 | 6 | 2 | Al |
0.2 | Around 0.2 | 13 | 1 | Al |
0.02 | Around 1 | 35 | 0.5 | Al |
0.2 | 0.1 | 11 | 1 | Ag |
0.00249 | 8 | 80 | 0.5 | Ag |
0.2 | -- | 100 | 1 | Au |
22.9 | -- | 32 | 0.5 | Au |
20 | Around 1 | 8000 | 1 | Zn |
0.00249 | 8 | -- | 0.5 | Zn |
0.000001 | 4 | --- | 0.5 | Zn plate with holes |
According to Table 5, a thickness of 0.5 μm and a very low voltage of 0.1 V results in a very large displacement. Moreover, at this thickness, it seems that the metal material has insignificant effect on displacement (the same results are obtained for both Ag and Zn). Reduction in thickness can lead to some limitations, such as lower mechanical strength and difficulty in fabrication process. However, the response of the resonator during the application of voltage is more important. As shown in Figs. 4-17, 31, and 34, in contrast to other thickness values, a thickness of 0.5 μm results in a descending trend in the displacement versus time curve. Accordingly, the maximum displacement occurs initially, and then, despite the voltage is still applied, the displacement decreases. This instantaneous pulse can be an interesting subject to be studied.
The original gap between the movable and fixed plates is about 2.5 µm, and a displacement of two thirds of this gap (i.e., about 1.7 µm) is required for the pull-in phenomenon. It seems that a 1 µm thick bridge made of Zn is a good option. This plate shows very stronger response to the application of 0.1 V bias with a displacement of more than 1 µm compared to Ag, Au, and Al. Moreover, this plate generates a suitable pulse and can be fabricated in a much more feasible process. Some holes can be opened in the central square plate (movable plate) to optimize the performance of the structure. The presence of the holes considerably reduces the weight of the plate, increases the displacement, reduces air damping, and cools the structure. However, the presence of a large number of holes reduces the strength of the plate and generates electric fields in the direction opposite to its motion. Therefore, the number of holes can be determined so that to achieve an optimal structure with the appropriate sensitivity and displacement by introducing a trade-off between these two parameters.
6. Effect of temperature on displacement
The effect of temperature on displacement are shown in Figs. (20-23). The effect of temperature on displacement is simulated and the results shows higher efficiency of Zn compared to other metals. According to Fig. (23), in the temperature range 200-400 K, Zn shows the minimum temperature-dependent displacement variation. This device can be used in a wide range of applications, such as mountaineering, military equipment, mobile phone antennas, and integrated circuits.
Fig. 20. Displacement-temperature curve of Al resonator.
Fig. 21. Displacement-temperature curve of Ag resonator.
Fig. 22. Displacement-temperature curve of Au resonator.
Fig. 23. Displacement-temperature curve of Zn resonator.
7. Conclusion
Simulation results show ideal and similar performance of metal plates made of Ag and Zn in MEMS devices. However, for a Zn plate with a thickness of 0.5 μm, the displacement-time curve exhibits a different trend compared to other results (Fig. 3-9-1). The simulation results in Fig. (3-9-4) shows that the maximum displacement occurs at the initial moment. This behavior can be exploited by microsensors that require high initial speeds and instantaneous pulses. Plates made of Zn with a thickness of 1 µm and Ag with a thickness of 0.5 µm can be used in ideal resonators because of their appropriate properties in terms of Vi-displacement-ratio, electrostatic force, switching speed, and time-
displacement-ratio. These resonators can be used in medical applications (cardiac pacemakers) that need no external voltage source and use only the body-driven subthreshold voltage. Additionally, other important advantages of the proposed design are its low cost, environmentally friendliness, and relatively easy manufacturing process as well as the availability and non-magnetic property of the used metals.
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