Experimental analysis of a low controlling voltage tri-electrode MEMS electrostatic actuator for array applications

A tri-electrode electrostatic actuator with one moving microelectromechanical systems (MEMS) electrode and two stationary electrodes (tri-electrode actuator topology) is experimentally tested in this article. The stationary controlling (intermediate) electrode is perforated and below the moving MEMS electrode, and the common electrode is further below. Numerical simulations were performed to discover the most optimum tri-electrode design parameters to enable the best performance improvement compared to a conventional two electrode electrostatic actuator. A silicon-based moving MEMS electrode was designed with a relatively linear spring constant, and the controlling intermediate and primary stationary electrodes were fabricated on either side of a quartz substrate instead of free space to simplify their fabrication. The measurement results showed that the tri-electrode topology can control the displacement of the MEMS with a lower controlling voltage and with extended controllable range before pull-in instability, compared to the conventional actuator. Simulations and measurements showed the controlling voltage was decreased by 2.6 times smaller than the conventional actuator topology using a bipolar driven intermediate electrode, and the controllable deflection range before pull-in was elevated by 33%. This tri-electrode topology offers benefits for applications in need of arrays of electrostatic actuators such as deformable mirrors.


Introduction
Adaptive optics (AO) technology has seen a considerable advance in the last few decades and is being employed in various fields, including but not limited to astronomy, microscopy, and vision science [1][2][3][4][5][6]. AO systems utilize a segmented mirror or a deformable mirror (DM) to correct an aberrated wavefront such as due to atmospheric turbulence [7][8][9][10][11][12][13][14]. DMs, as one of the main parts of an AO system, consists of two parts of a flexible reflective layer (mirror face sheet) and an array of actuators deforming the flexible surface located on the back of the reflective layer. There are various types of DMs technology, but the MEMS designs are more popular due to their potential for batch production and compact size [15][16][17][18]. Many MEMS actuators have been employed in manufacturing DMs [19][20][21][22], with the electrostatic actuator being one of the most popular due to its low steady-state power consumption and compact design. However, DMs with electrostatic actuators face pull-in instability [23], which limits the actuator deflection range, and leading to DMs being applied for lower stroke applications resulting weaker astronomical performance [17]. Increasing the initial gap spacing between the actuator's electrodes can help increase the deflection range, but the drawback is the need for a higher controlling voltage. Thus, deflection range and the controlling voltage of an electrostatic actuator are the two parameters that are necessary to be improved for enabling DMs with higher performance.
Aside from DMs, an electrostatic actuator with higher performance is advantageous for other types of applications such as high isolation MEMS switches and micro pumps. The potential for lower controlling voltage is specifically more advantageous when there is a need for arrays of actuators. For example, supplying hundreds or thousands of actuators with 100 V or more is very challenging since each single actuator requires a separate high voltage amplifier. There have been numbers of solutions for lowering the voltage; however, they are not specifically designed for arrays of actuators.
Several solutions have been reported to overcome the pullin instability. Pre-stress structures were utilized to reduce the controlling voltage and increase the deflection range. Chiou and Lin [24] used a pre-stress comb-drive actuator to solve the pull-in instability. The actuator does not have the pull-in instability problem, and it has a longer displacement range and low voltage. However, the actuator's initial lift highly depends on the residual stress and manufacturing steps, so a possible minor change in the material thickness can alter the designed lift. Furthermore, post-heat treatment is always needed to elevate the lift to a desired value. In [25], Chu et al also used the residual stress to bend up a radio frequency MEMS switch and control the gap between electrodes by gradient stresses. The switching voltage is small due to the controlled small gap between electrodes. However, the actuator's characteristics highly depend on the residual stress and fabrication steps characteristics. Using nonlinear springs is another way to extend the actuator deflection range. In [26], nonlinear springs increased the travel range by reducing the positive feedback. However, nonlinear springs can have the problem of increasing the controlling voltage. Offset electrode designs [27][28][29][30] are another common reported method to improve the deflection range. The offset electrode configuration also reduces the pull-in instability. However, the overall size of the MEMS is larger due to the adjacent electrodes. Atik et al introduced an electrostatically actuated MEMS micro-valve for flow manipulation in microfluidics. The moving electrode was a circular diaphragm opening and closing the fluid channel. One issue of this design is for having better leakage behavior, a thicker diaphragm is needed and as a result, a higher controlling voltage is required. This can be a serious problem as the regular pull-in voltage was as high as the average of 221 V [31]. Admassu et al built a parallel plate electrostatic microactuator with three spring-like x-beam configurations. Different springs were examined in each configuration, and it was shown that the serpentine spring is more flexible which results in a lower control voltage. However, for that configuration with serpentine springs, the required voltage is 128 V for only 9.89 µm of displacement [32]. Banerjee et al presented a low-cost and compact electrostatically actuated DM with an aperture size of 10 mm. Standard micro-machining techniques were used to build the device to reduce the fabrication cost. The maximum stroke of the DM is as high as 15 µm. However, a relatively high voltage of 375 V is needed [16].
In [33,34], a novel tri-electrode topology was introduced to reduce the controlling voltage and increase the deflection range. In this topology, two stacked electrodes are used, forming a compact structure. The intermediate electrode is perforated, allowing a low voltage on this electrode to modulate the lower (primary) electrode's background electric field provided by a fixed voltage.
This paper presents experimental testing of a tri-electrode low voltage and large stroke electrostatic actuator. A siliconbased MEMS moving electrode is designed to implement the actuator topology. The MEMS electrode is supported by four serpentine springs and is placed over the perforated controlling intermediate electrode. The primary electrode is located under the intermediate electrode providing the background electrostatic force to be modulated by the controlling intermediate electrode. The primary electrode and intermediate electrode are separated by a quartz substrate to facilitate fabrication. First, the design, the parametric analysis, and simulations for the specific actuator and tri-electrode topology are presented. Finite element method (FEM) analyses are used to study the actuator performance and extract the resulted electrostatic forces applied by the controlling voltage. In sections 3 and 4, fabrication and experimental measurements are presented.

Design and parametric analysis
The conventional electrostatic actuators consist of one stationary electrode and one MEMS moving electrode, as shown in figure 1. There have been various designs for the moving platform and spring structure, however, a straightforward configuration can be a flat rigid silicon-based platform supported by micro-springs [35]. Due to the pull-in effect, the conventional electrostatic actuator snaps down after traveling one-third of the initial gap. This means that in order to increase the control range, a larger initial gap is required, which results in a larger controlling voltage.

Tri-electrode topology
The tri-electrode topology was already introduced and studied in [33] using FEM and restoring spring force method (RSFM). All the design parameters were investigated, and their influence on the actuator performance was reported. As shown in figure 2, there are two underlying stationary electrodes in the tri-electrode configuration compared to the conventional topology, which has only one stationary electrode. The perforated intermediate electrode controls the MEMS moving electrode. The bottom primary electrode sits further from the moving MEMS electrode. It provides a fixed background electric field to boost the attractive electrostatic force and compensate the smaller effective area of the intermediate electrode. Together these two electrodes, allow the perforated intermediate electrode to enable similar deflections as the conventional topology, but with a lower controlling voltage (V I ). In addition, the tri-electrode topology can provide a longer displacement before snap-down occurs, larger than the one-third of the initial gap of the convention actuator situation.
The design parameters to be considered in the tri-electrode actuator are the perforation size (W E ) and spacing (W S ) of the intermediate electrode, the separation of the MEMS moving electrode from the intermediate electrode (D 1 ), the separation of the intermediate electrode to the underlying primary electrode (D 2 ), and the fixed voltage on the bottom primary electrode (V P ). The tri-electrode performance varies depending on these various design parameters [33]. Figure 3 contrasts the performance of a conventional actuator, with an arbitrary tri-electrode system for the situation with design parameters W S = 2.5 D 1 , W E = 0.83 D 1 , D 2 = 1.67 D 1 , and V P = 4.37 V snap-down . For the conventional actuator, snap-down occurs at X snap-down = 1/3 D 1 and at a voltage V snap-down . The red crosses show the snap-down point where the actuator becomes unstable. In order to contrast the performance of the tri-electrode compared to the conventional topology, the response curves in figure 3 are normalized with the conventional topology response curve characteristics.
As can be seen for this particular design, the tri-electrode controlling voltage (V I ) is smaller than the conventional controlling voltage (V snap-down ) by a factor of 1.25 for achieving the same deflection possible for the conventional actuators (X snap-down ). It should be mentioned that to enable this superior decrease in the needed controlling voltage V I on the intermediate electrode, compared to the conventional actuator, the tri-electrode's bottom primary electrode is biased to a fixed voltage greater than that of V snap-down (V P = 4.37 V snap-down ).
In the case of actuator array applications, the disadvantage of having one common larger voltage V P on the bottom primary electrode is outweighed by the benefit of each individual actuator needing a smaller individual controlling voltage V I . As shown in figure 2, there are two gaps between the trielectrode electrodes to consider, one between the intermediate electrode and MEMS (D 1 ), and the other between the intermediate and the primary electrodes (D 2 ). According to [33], which only considered air gap in the region between the fixed electrodes, the ratio of the D 2 to D 1 should always be larger than 1 to have a considerable reduction in controlling voltage. It was previously shown that the controlling voltage tends to increase with increasing relative permittivity of the spacer material between intermediate and primary electrodes. However, this can be mitigated by increasing using a thicker spacer material and so giving a larger D 2 /D 1 ratio. Therefore, while air might be the best spacer material (ε r = 1) in terms of voltage reduction, the additional challenges in fabrication due to having a hollow space between the electrodes may make a solid material preferable.
In order to simplify the fabrication of the experimental demonstrator, a solid quartz substrate was used between the intermediate and primary electrodes. To compensate for the possible loss in voltage reduction performance, a larger D 2 /D 1 ratio was used. The performance as a function of W S to W E ratio was explored, to determine the lowest controlling voltage and largest deflection range enhancement before snap-down. Numerical simulations were performed to find the optimized design as described in the following section.
The schematic of the tri-electrode layers is shown in figure 4. The actuator consists of two parts which were attached together post fabrication. The layers were placed upon each other and anchored in place for experimental testing.

Tri-electrode design parameters and simulation
The designed tri-electrode is depicted in figure 5, and its parameter values are summarized in table 1. The parameters are extracted from the FEM simulations [33] and are basically according to the performance of the tri-electrode actuator. The designed parameter's values are decided based on the available materials, power supplies, and microfabrication limitations. The MEMS electrode is a large 6.7 × 6.7 mm 2 . The   ), and primary electrode voltage (V P ) that provided the best device performance. The simulations were performed in 2D mode for a unit-cell to reduce the time and increase the accuracy of the calculations. This also helped to enable smaller mesh sizes in the FEM simulations to provide smaller tolerance errors, while reducing computation time.
The unit cell is displayed in figure 5, along with the meshing, potential, and electric field distribution between electrodes.
Three modes are defined for the tri-electrode operation based on the power supply used to control the actuator. Unipolar mode is when a power supply with the same polarity (positive or negative) is used to supply the intermediate and primary electrodes. For the unipolar mode in this paper, the controlling voltage is positive. Bipolar mode is when a bipolar power supply is used, and the controlling voltage varies from negative to positive. For both these modes of operation, in order to show the voltage reduction, a figure of merit (FOM) was defined for the deflection per unit controlling voltage, and contrasted this to that of a conventional actuator: where X snap-down is the maximum deflection of the conventional actuator before snap-down, V snap-down is the voltage at which this occurs, FOM S defines the figure of merit for the conventional actuator (displacement vs. voltage), ∆d u is the displacement in unipolar mode to give the movement of X snap-down , ∆d b is the displacement in bipolar mode to give the movement of X snap-down , FOM u defines the figure of merit for the unipolar mode of operation occurring at voltage ∆V u , FOM b defines the figure of merit for the bipolar mode of operation occurring at voltage ∆V b . All three modes along with the conventional topology are illustrated in figure 6. The displacement (y-axis) is common for the conventional, unipolar, and bipolar modes. The required controlling voltage (x-axis) is shown with the width of the green region. As can be seen, the width of the green region is smaller from conventional for the unipolar and bipolar modes, which illustrates the smaller required controlling voltage in unipolar and bipolar with respect to conventional. The green region that the controlling voltage is entirely positive in unipolar mode, and that the bipolar power supply has equal positive and negative controlling voltage. The maximum displacement mode shows a higher controllable displacement possible, and it has nonequal negative to positive voltage range. In the maximum displacement mode, a bipolar power supply is used, but the deflection is the maximum range the actuator can travel before snap-down. This mode shows the enhancement in the controllable deflection range that is possible with the tri-electrode topology, while the other two modes show the control voltage reduction.
The voltage and deflection range of all three modes are illustrated in figure 7 for the actuator defined in table 1. The contrasting conventional actuator parameters (A, D 1 and k) are as the same values as for the tri-electrode. The FOM S of the conventional topology at the full snap-down displacement of X snap-down is calculated to be FOM S = 1.3 µm/V. For unipolar operation, simulations show that the same X snap-down displacement is possible with FOM u = 1.4 FOM S , which means the unipolar controlling voltage is 40% smaller than for the conventional actuator for the same displacement. For bipolar operation, the same X snap-down displacement is possible with FOM b = 2.6 FOM S , illustrating its 2.6 times smaller required controlling voltage. The tri-electrode device performance is very dependent on the primary electrode voltage. For the results of figure 7, the primary electrode voltage was V Pu = 109 V for the unipolar mode, V Pb = 140 V for the bipolar mode, and V Pmax = 80 V for the maximum displacement mode. These voltage values are the ones for which the best performance was found. In order to determine these voltages, the study of figure 8 was done, which shows the largest deflection possible before snapdown for the unipolar, bipolar, and maximum displacement modes, as a function of V P .

Experimental testing
The experimental demonstrator consists of two parts. The upper part is the single crystal silicon MEMS moving electrode, and the lower part is the quartz material with the aluminum intermediate and primary electrodes coated on either side. The thickness of the quartz is then the spacing D 2 . The  two fabricated parts are then placed upon each other to form the entire tri-electrode actuator. Figure 9 shows the fabrication steps of the MEMS moving electrode. The moving electrode is formed from a 300 µm double-sided polished single crystal silicon wafer with <100> crystal orientation.

MEMS fabrication process
First, the wafer was cleaned using piranha etch with a combination of 1100 ml H 2 SO 4 and 300 ml H 2 O 2 for 10 min. Then the silicon wafer was cut into pieces using a wafer saw  and put in a high-temperature oxidation furnace for 24 h at 1100 • C. The wet thermal oxide was grown on both sides of the samples with a thickness of 2.5 µm ( figure 9(a)). The oxide is the mask layer for the following back etch step to thin the silicon wafer to the required thickness. In the next step, both sides of the sample were coated with positive HPR 504 photoresists, and the backside was patterned using photolithography. Following this, the backside thermal oxide was etched and patterned using (10:1) buffered oxide etchant (BOE) to expose the silicon area for thinning ( figure 9(b)). Next, the silicon was etched in 30% KOH etchant at 80 • C with magnetic stirring of 255 rpm (figure 9(c)). The KOH etching step is performed in several steps to control the etched thickness precisely and uniformly. The silicon cavity formed by KOH etch is considered as the D 1 gap spacing for the tri-electrode. After removing the remaining oxide, 300 nm aluminum was deposited using sputtering on the frontside of the sample and patterned using photolithography ( figure 9(d)). In the next step, the aluminum was etched using aluminum wet etch at 60 • C (figure 9(e)). The aluminum layer will serve as an electrode and etch protecting mask layer for the following plasma etch step. The MEMS electrode was then released with plasma etch using fluorinebased reactive ion etching (RIE) ( figure 9(f)). The anisotropy of the plasma etch was determined mainly by the flow of SF 6 and O 2 gases [37]. The recipe of the RIE utilized for silicon etch is summarized in table 2. Figure 10 shows the fabricated MEMS electrode. Figure 11 shows the fabrication steps of the stationary electrodes. A 490 µm single-sided polished quartz wafer was  cleaned using acetone and isopropyl alcohol. The thickness of the quartz sample is equal to the D 2 gap size designed in the trielectrode topology. After cutting the wafer using a wafer saw, both sample sides were coated with 300 nm aluminum using sputtering ( figure 11(a)). The aluminum was coated with a positive HPR 504 photoresist and patterned using an aluminum etchant to form the intermediate and primary electrodes on the two opposite sides of the quartz samples ( figure 11(b)). Next, hexamethyldisiloxane coating was carried out for 5 min at 150 • C to improve the adhesion of the quartz samples upon which 3 µm SU-8 is spin coated on the sample and patterned using photolithography (figures 11(c) and (d)). The SU-8 is used as a thin electrically insulating spacer to isolate the MEMS electrode part and the intermediate electrode.

Stationary electrodes fabrication process
The quartz samples are ready to be attached to the siliconbased moving MEMS electrodes. Figure 12 shows the stationary electrodes after fabrication.

Measurement results
The setup utilized for the tri-electrode test experiment is shown in figure 13. Three Agilent power supplies with different voltage ranges were employed to drive the intermediate and primary electrodes. Two were used to enable the bipolar intermediate electrode voltage (V I ), and the third was for the primary electrode voltage (V P ). Olympus (BX51) and Keyence (VHX-7100) microscopes were utilized to measure the movement of the MEMS electrode. After attaching the two parts, the gap spacing between the moving MEMS electrode and the intermediate electrode (D 1 ) was measured to be 140 ± 5 µm. Figure 14 shows the assembled device as measured by the Keyence microscope.
The tri-electrode response curve was first measured with no voltage applied to the primary electrode. In this case, the tri-electrode performs as a conventional actuator (figure 15(a)) but with a less effective stationary electrode area ( figure 15(b)) due to perforation. For comparing the results with the conventional topology, the measurements were plotted along with the simulation of the conventional and perforated conventional, shown in figure 16. As was expected, the snap-down voltage for the perforated conventional actuator is larger compared to the conventional topology. Figures 16-18 contrast the simulated performance to the experimentally tested performance of the fabricated conventional and tri-electrode actuators. Each figure has two curves,  with the red star solid line showing the simulation values, and the black cross points showing the measurement results. As simulated using FEM analysis for best performance, the unipolar mode was tested with V Pu = 109 V. The controlling voltage (V I ) was swept from 0 to 26.6 V. Figure 17(a) shows the measured displacements. It can be seen that the measurement and simulation results are in close agreement. In a similar fashion, the bipolar operation mode was tested by sweeping the controlling voltage from −25 to 14.5 V, with primary voltage V Pb = 140 V. The measured results for the bipolar mode are depicted in figure 17(b). Again, close agreement between measured and simulation results is seen. Comparing both the unipolar and bipolar modes with the conventional response curve, it can be seen that the controlling voltage is smaller for the same deflection range for both.
In unipolar operation ( figure 17(a)) the controlling voltage of 25.8 V gives the same displacement as the conventional actuator with 35.2 V. For the bipolar operation, only ±13.35 V was needed. The reduction of controlling voltage magnitude is apparent in both modes, and the calculated FOM is almost equal to FOM u = 1.4 FOM S and FOM b = 2.6 FOM S . The maximum controllable displacement mode was then explored. The case for an intermediate electrode with W S = 300 µm and D 1 = 140 µm is illustrated in figure 18(a). It can be seen that ∆d max = 59 µm (for V P = 80 V), which is almost 26% higher than the conventional snap-down displacement of X snap-down = 47 µm. Since the maximum displacement is also a function of the gap spacing of the intermediate electrode (W S ), another gap spacing was explored. A second intermediate electrode was fabricated with a larger gap spacing of W S = 450 µm, to show the impact of W S on the tri-electrode maximum deflection range. This device had a slightly higher D 1 = 155 µm. The result shown in figure 18(b), has ∆d max = 69 µm (for V P = 120 V), which is 33% higher than the conventional snap-down displacement of approximately X snap-down = 52 µm for this larger D 1 gap spacing. Therefore, the intermediate electrode gap spacing (W S ) has not only a significant impact on controlling voltage reduction, but it can also be selected such to provide the actuator with a higher maximum controllable displacement possible before snap-down.
Comparing the experimental results with other recent electrostatically actuated applications is challenging, due to the fact that device performance is specific to particular MEMS design configurations. Nonetheless, some examples are given below to illustrate how the tri-electrode configuration can enable lower controlling voltages. For example, we can see in figure 17(a) that in the unipolar mode, the tested tri-actuator travels around 50 µm with only 0-26.6 V of controlling voltage. By contrast, in [31] an average of 0-221 V is required for closing and opening a microfluidic channel with a depth of not more than 9.1 µm. In [32], a controlling voltage of 0-128 V was used to control the electrostatic actuator with serpentine springs for a range of 9.89 µm. In [16], an electrostatically DM was deflected 15 µm with around 0-375 V. Therefore, we see that the tri-electrode offers a controlling lower voltage. In addition, considering the bipolar mode, the actuator can be controlled with a smaller bipolar power supply for the same displacement range.

Conclusions
In this work, experimental testing of a tri-electrode electrostatic actuator was undertaken to demonstrate its lower controlling voltage and enhanced deflection, compared to a conventional parallel plate electrostatic actuator. FEM simulations were used to determine optimal designs for performance improvements. Experimental measurements showed close agreement with numerical simulations. Tri-electrode designs demonstrated almost 36% reduction in controlling voltage in the unipolar mode, and 2.6 times reduction in bipolar mode, compared to the conventional topology. A maximum controllable deflection range of 33% higher than the conventional topology was experimentally demonstrated with the appropriate design of tri-electrode topology parameters. It was shown in simulations and experiments that the intermediate electrode gap spacing (W S ) has a significant effect on controlling voltage reduction and the maximum possible deflection range.

Data availability statement
The data that support the findings of this study are available upon reasonable request from the authors.