The motion of comb-drive actuators and parallel actuators is controlled by the equilibrium of the electrostatic force and spring force of the suspension system. During lateral motion or parallel actuation, the attractive force between two comb electrodes is mainly due to the fringing fields because the small fingers are thick compared with their width and length (Lau et al., 2010). Because the distance between the comb fingers is constant, capacitance changes linearly regarding the area of the plates that overlap during such movement. Meanwhile, transverse movement of the plates maintains the overlapping area and changes the size of the gap between the comb fingers (see Fig. 12.1) (Sun et al., 2002). Keeping the direction of motion (in both cases) along the x-axis, the electrostatic forces are:

where n is the number of comb pairs; t_e is the thickness of the plate; g is the gap spacing; ε is the permittivity of the medium; A is the overlapping area of each finger pair; x₁ and x₂ are the initial gap spacings; x is the changes in gap spacing; and V is the voltage.

This is a function of the spring stiffness in the y-direction K_y, the spring stiffness in the x-direction K_x, the length of overlap L₀, and the gap spacing g between the fixed and movable electrodes. Different methods for increasing the stable displacement have been reported, including changing the spring constants of the system by altering the maximum setting of the suspension system (Fig. 12.2(a)), reducing the negative spring constant (Fig. 12.2(b)) and shifting the minimum setting of the negative spring constant (Fig. 12.2(c)) (Hou et al., 2006). The mechanical design of the suspension system is therefore crucial for large displacement comb-drive actuators. From Eqs. (12.4)–(12.6), it can be observed that the driving force does not change with motion, so for compliance in the x-direction, linear spring stiffness K_x is desirable, while a high stiffness ratio K_y/K_x is required to avoid pull-in instability and to increase displacement.

This configuration works in a similar way to the transverse mode comb actuators, except that it has only one pair of plates instead of a large array. It also suffers from pull-in instability and displacement of one-third of the gap spacing. The solutions to these problems are the same as the solutions to problems in parallel-plate comb actuators. Parallel-plate actuators are often employed to move a micromirror or three-axis stage vertically while horizontal movements are actuated by comb drives (Srinivasan et al., 2010; Liu et al., 2007). Curved electrode actuators have been proposed for use in situations where the gap is small near the anchored edge of the electrode and gradually increases along the electrode to obtain larger displacement than conventional parallel-plate actuators (Legtenberg et al., 1996; Shao et al., 2010). An insulator layer (Legtenberg et al., 1996) or bumper (stopper) (Shao et al., 2010) is formed along the curved electrodes (see Fig. 12.8(a) and (b)). To overcome limitation on gap spacing because of the commercial Poly Multi-User-MEMS-Process (PolyMUMPs), an L-shaped spring for electrostatic actuated deformable micromirrors (see Fig. 12.8(c)) (Hu et al., 2010), which increases the deflection, has been proposed. Also, slit and grating actuators, which have an opening on the movable plate and fixed electrodes gratings below the slits, reduce pull-in stability, can extend travel range, and lower actuation voltage (see Fig. 12.8(d)) (Lee, 2007).

SDAs (Honarmandi et al., 2010; Li et al., 2002) comprise an L-shaped plate and bushing and support arms that are connected to a spring box. By applying a bipolar pulse voltage, the plate is attracted toward the substrate during the positive cycle. However, the end of the plate, which is attached to the bushing, cannot be pulled down and is therefore tilted, sliding forward because of the warping of the plate. When the voltage goes to the negative cycle, strain energy in the plate will pull the actuator forward as a one-increment step. This type of actuator is capable of generating high forces (>200 μN), large displacement (∼100 μm), and nanometer positioning resolutions (∼10 nm). Its speed can range from 70 to 250 μm/s, depending on the amplitude and frequency of the input signal. However, minimum driving voltages of 60 V may be required and can go as high as 290 V (Li et al., 2002). Also, the upward–downward and impact motion that is caused by warping may not be suitable for gripping and precision nanoassembly operations. SDAs are highly sensitive to plate length and applied voltage. A larger step size can be obtained by increasing the bushing height or the applied voltage. Driving voltages change linearly with the bushing height and exhibit an inverse relationship with the plate length (see Fig. 12.9) (Honarmandi et al., 2010).

Recent innovations with new microactuator designs to either improve the actuator's displacement, output force, or lower the driving voltage include the fishbone-shaped comb-drive microactuator and two-end fixed beam driven by both vertical and horizontal forces. The slant comb fingers of a fishbone-shaped microactuator can produce stronger electrostatic fringing forces than ordinary straight comb fingers because the sharp edges of the fishbone-shaped comb-drive has highly concentrated electric field as shown in Fig. 12.10(a) (Megat Hasnan et al., 2014).

Also dubbed “the Guckel” (Guckel et al., 1992), this electrothermal actuator configuration is an electrically closed loop that resembles a “U” shape. It generally consists of a “hot” arm and a “cold” arm that usually has a flexure in the in-plane U-beam as shown in Fig. 12.12(a). The hot arm has a higher temperature than the cold arm because it has a narrower conductive path, which increases the resistivity and current density. In-plane deflection toward the cold arm is achieved by the differential thermal expansion of the arms, giving it one operation mode (“open” or “closed”). The flexure is a thin structure positioned between the cold arm and the anchor that amplifies the deflection. When a current is passed through the narrow and wide arms in parallel, as shown in Fig. 12.12(b), the structure will deflect toward the narrower arm because the wider arm has a lower resistance, hence drawing more current and becoming hotter than the narrow arm. Another configuration is the long–short beam, which bends toward the shorter arm because the longer beam elongates more than the short beam when heated as shown in Fig. 12.12(c). By adding an extra buckling arm, which exploits the buckling effect as shown in Fig. 12.12(d), higher actuation can be achieved.

The V-beam design features an array of bars that are attached symmetrically to either side of a movable central shuttle. The beams are designed with a prebend angle, α, that predefines the buckling direction. Joule heating causes the beams to expand and pushes the shuttle in the direction of the opposite side to angle, α (Fig. 12.15(a)). Within thermal buckling limits, longer beams can extend the travel range of the shuttle. More beam pairs produce more out-force. Chevron actuators also provide flexibility by controlling the peak temperature and gripping force by increasing the beam's cross-sectional area. Similar to U-beam, displacement of the V-beam actuator can be improved by varying the cross-sectional area by contouring the hot arms along the actuator's length, which provides more uniform temperature distribution along the length. Peak temperature and power consumption are therefore reduced. Also, contouring reduces thermal errors, thereby increasing the accuracy of the actuator that is required for nanopositioning applications (Li and Uttamchandani, 2004; Chen and Culpepper, 2006). Because of the processes that take place during fabrication, a parasitic angle, θ, is usually formed between the beams and the horizontal plane, as shown in Fig. 12.15(b). Vertical motion of chevron actuators can be enhanced by increasing this angle (Varona et al., 2009). Fig. 12.15(c) shows another bent-beam actuator with only one beam connecting the anchors at both ends and without a shuttle (Zhang et al., 2006). It could be challenging to fabricate small features with smooth sidewall surfaces of the slanted beams of V-shaped actuators. An alternative is to use the Z-shaped beam as shown in Fig. 12.15(d) (Guan and Zhu, 2010).

In electrothermal bimorph actuators, mechanical motion is achieved by the differential expansion of two or more different materials, with a large variation in the coefficient of thermal expansion. Materials with a higher thermal expansion coefficient, such as platinum or gold, usually comprise the top layer (Aioubi et al., 2004). Bimorphs are initially curled up because of the intrinsic stress that is generated in the structural layers during fabrication, but they flatten when voltage is applied (Wu and Xie, 2008; Aioubi et al., 2004). Bimorph thermal actuators are advantageous because of their simplicity in fabrication, large array integration, large actuation range, and low voltage operation, which makes them suitable for parallel processing and large throughput applications. However, such multilayer structures will suffer from delamination and the top layer will be damaged at elevated temperatures (Chen et al., 2003), although bimorphs of titanium tungsten (Ti–W) and silicon nitride (SiN) have been shown to be capable of sustaining large deflection without delamination (Fig. 12.16) (Boutchich et al., 2008). Many materials can be exploited as electrothermal bimorph. For example, vanadium dioxide has been reported to be suitable if high-speed actuation is required where the actuator reaches its steady state in around 8.3 ms and the performance can be further enhanced to just 3.3 ms by applying an extra layer of single-wall carbon nanotube (Wang et al., 2015). Shape-memory alloy materials have been recently used as electrothermal microactuators because of their attractive features such as high work density, large actuation force, resistance to corrosion, and compatible with standard MEMS process (AbuZaiter et al., 2016; Kabla et al., 2016). A bimorph made of super-aligned carbon nanotube sheets (SACNS) and polydimethylsiloxane (PDMS) composites was demonstrated to be able to reach 9.5 mm at 98°C (with a displacement coefficient of 44 μm/[100 μm × °C]). This bimorph is highly reliable and has a long working life because no delamination was found in it. However, the power consumption can be quite high (Chen et al., 2011). Displacement amplification can be carried out by cascading bimorphs (Wu and Xie, 2008; Geisberger and Sarkar, 2006), which is similar to the segmented meander zipper actuator. Also, rotary and linear actuators have been designed based on this principle (see Fig. 12.17) (Geisberger and Sarkar, 2006).

Possessed of unique characteristics (Lau et al., 2008; Nguyen et al., 2004), the SU-8 polymer is attractive as an electrothermal actuator that offers low handling forces, large displacement, and low operating voltages. Therefore, the SU-8 polymer is suitable for the handling and manipulation of micro- or nanoscale and biological applications (Nguyen et al., 2004; Duc et al., 2008). However, their low heat conductivity leads to a slower thermal response (Lau et al., 2008; Duc et al., 2008). Lau et al. presented a concept of embedding silicon structures topped with aluminum track within the SU-8 epoxy with a 30% silicon to 70% SU-8 ratio. This improves the properties of the actuator, such as Young's modulus, thermal stress, and work density (by more than 2.5 times), thermal expansion (by 5% more), and response time (by 20%) (Lau et al., 2010). The aluminum film track is used to enable Joule heating by allowing a current to pass through it and subsequently heat up the silicon skeleton underneath. Another configuration fills the gap between the silicon comb fingers with the polymer. Confinement of the polymer inside the high-aspect ratio silicon structure leads to higher displacement, higher stiffness, and less out-of-plane motion (Duc et al., 2008). Lau et al. have also employed this design in rotary micropositioner in hard disk drives recently (Lau et al., 2016).

Combinations of the aforementioned actuators in an appropriate configuration lead to the design of electrothermal compliant mechanisms (ETCs). In ETCs, elastic deformation due to thermal expansion provides the actuation force to the revolute joints hinges and flexures and amplifies the motion. There have been demonstrations of various ETC mechanisms that use a combination of U-beam actuators to achieve lateral translation and expansion (Moulton and Ananthasuresh, 2001) (see Fig. 12.18(a)). Parallel configuration is used in 3-DOF planar micromanipulators. Tsai et al. (2005) proposed 28 different feasible configurations to transform the conventional rigid links kinematic macromechanism into ETC mechanisms. Combination of U-beam and V-beam has also been proposed by Margarita et al. (2016). Compliant designs have been developed by topology optimization (Huang and Lan, 2006; Sardan et al., 2008), which use a finite element-based method with a multiparameter optimization algorithm for the optimal material distribution within a fixed domain. Compared with a pair of three-beam designs (Andersen et al., 2009) (Fig. 12.14(c)) without topology optimization, a topology-optimized electrothermal actuator (see Fig. 12.18(b)) (Sardan et al., 2008) is able to provide a higher gripping force and lower end-effector temperature within the same geometric domain as the double–U-beam microactuator. The end-effector was measured to be at 229°C and deflection was up to 1 μm with a gripping force of 18–20 μN.

Like their electrostatic counterpart, piezoelectric microactuators are often deployed in high-speed applications because of their rapid response time (see Fig. 12.20) (Ivan et al., 2009) and low-power requirement (Oldham et al., 2008). Large forces (i.e., hundreds of micronewtons) are demonstrated even in simple designs such as a thin film (Oldham et al., 2008) or a beam (Kommepalli et al., 2009) with an excitation voltage of 20 V. Although conventional piezoelectric microactuators produce displacement of only 35 nm to 1.5 μm (Morita et al., 2002; Tsuchiya and Davies, 1998; Wang et al., 2002) with a high actuation voltage (from 50 V to several hundred volts) and have a large lateral dimension (Wiederkehr et al., 2008) or footprint (usually measured in mm²), a considerable number of improvements have been reported. Those findings showed that piezoelectric microactuators are quite versatile: small-step piezoelectric microactuators can be employed in fine-positioning applications, whereas large displacement microactuators can be integrated into devices such as micromirrors.

A piezoelectric cantilever is usually composed of at least one layer of piezoelectric film and one layer of a passive substrate such as a nickel alloy, titanium, or silicon, which operates in an out-of-plane motion. An unimorph structure consists of only one layer of piezoelectric film, usually on the top, whereas bimorph structures are made of two layers of piezoelectric materials that sandwich the center shim. Sometimes, the piezoelectric film is deposited in the center of cantilever, coated with passive substrates and electrodes. The characteristics of piezoelectric materials make them good candidates for many applications, such as driving micromirrors and atomic force microscopy (Rogers et al., 2004). Also, there have been reports of an oscillating PZT thick film (thickness of 1–50 μm) (Maeda et al., 2004) on a nozzle that changed an outlet pressure and increased a fluid flow rate (Wiederkehr et al., 2008). As previously mentioned, small displacement and fabrication incompatibility are major setbacks for piezoelectric actuators. Researchers have sought to create designs that will avoid these problems. Deposition of a gold layer on either end of the PZT beam changes the overall system neutral axis, thus enhancing the displacement in one direction. A 500 μm long and 100 μm wide actuator with 50% gold covered on its top surface (25% of the actuator covered on either end) was reported to be able to apply 7 mN force at almost 1 μm displacement and displacements near 5 μm against a 25 μm opposing force at 20 V (Oldham et al., 2008). Using a similar approach and concept, a set of four 920 μm × 70 μm compound bend-up/bend-down unimorph microactuators, which were used to drive a vertical stage, have been shown to achieve displacement as high as 120 μm (see Fig. 12.21) (Qiu et al., 2010). Similar to its electrostatic and electrothermal counterparts, several beams can be cascaded to achieve high displacement. A micromirror based on Wu et al. design (actuated by three cascaded electrothermal bimorphs) (Wu and Xie, 2008) has been built using piezoelectric thin film (<1 μm) (Maeda et al., 2004) unimorph actuators. Applying 3.5 V_pp moved the micromirror 32 μm vertically (Zhu et al., 2011). With four symmetric PZT unimorph connected in a serpentine pattern as reported by Choi et al., 430 μm of out-of-plane displacement is achieved with excitation voltage of 15 V (Jongsoo et al., 2014). Other approaches included adding other mechanics (e.g., introducing an aluminum flexure that connects both ends of the piezoelectric cantilever). When voltage is applied, the piezoelectric cantilever will deform and compress the aluminum cap so that it buckles outward, giving more displacement (Kommepalli et al., 2009). A hybrid thermopiezoelectric microactuator has also been proposed to extend the displacement. An unimorph composed of PZT and copper is connected to the top of a Peltier module, also known as a “thermoelectric cooler,” to give greater variation in the temperature between the two materials, hence increasing the deflection (Rakotondrabe and Ivan, 2010). CMOS-compatible fabrication methods and alternative piezoelectric materials have also been proposed. Instead of PZT, AlN has been reported to be a post-CMOS compatible piezoelectric material because aluminum and nitride are common materials in IC fabrication (Doll et al., 2010). However, AlN has a poor piezoelectric constant, giving ∼15 nm of displacement at 5 V (Doll et al., 2010), making it more suitable for nanoscale applications. Andrei et al. showed that displacement can be extended by using a thicker AlN layer with nonstandard CMOS metals, such as chromium (Cr), as electrodes and a higher excitation voltage (Andrei et al., 2008). Pretreatment of the surface of silicon substrate by an inverse sputter etching process prior to AlN film deposition is found to increase the piezoelectric constant of AlN by about 20% (Schneider et al., 2015).

Membrane-type piezoelectric actuators can be either thin or thick piezoelectric film or bulk piezoelectric actuators (50–1 mm) (Maeda et al., 2004) such as stacks or bimorph piezo discs or films, which have one of their wide area sides completely anchored to either a bulk substrate or a passive membrane. Adhesive epoxy is used to glue these piezoelectric diaphragms to the substrates. Membrane-type actuators are used for applications such as micropumps (Li and Chen, 2003) (see Fig. 12.22(a)), microvalves (Doll et al., 2007), micromotors (Mashimo and Toyama, 2010), and hard disk drive head positioning (Hu et al., 2016) (see Fig. 12.22(b)). Their displacements are relatively small at less than 1 μm (Li and Chen, 2003; Mashimo and Toyama, 2010). IDT electrodes can be used to manipulate the operation of piezoelectric film. Using a stack of piezoelectric diaphragms with IDT electrodes can increase the deflection of a membrane-type actuator (Jing and Luo, 2005) (see Fig. 12.22(c)). IDT electrodes aligned in 45 degrees on a bulk piezoelectric beam lead to torsional operational mode of the cantilever (Grinberg et al., 2016). The IDT diaphragms, which are 800 μm in diameter and 2.8 μm thick, are reported to generate around 7.0 μm center deflection. Displacement improvement on single layer of piezoelectric membrane can be achieved using specifically designed electrode patterns to control in-plane stress level on the idle part of PZT (see Fig. 12.22(d)) (Ma et al., 2015). Other mechanisms can be added to convert the large force exerted by the PZT into higher displacement via a micro-compliant amplifier, as achieved by Huang and Lan (2006). Bolzmacher et al. used a silicon membrane leverage unit to amplify the piezoelectric actuator displacement. The piezoelectric bulk actuator is placed in a slot at the center of the unit and covered by membrane slices. When voltage is applied, the piezoelectric actuator will push the membrane slice upward, where the tip will reach its highest position (see Fig. 12.22(e)) (Bolzmacher et al., 2010).

Compliant mechanisms are monolithic structures that utilize their flexible structures to transmit motion or force from an actuator (Ouyang et al., 2008). For example, a micro-compliant made of SU-8 (Fig. 12.23) with an average amplifier factor of 6.9 has successfully produced ∼15.2 μm and 730 μN at 20 V from a piezoelectric actuator (Huang and Lan, 2006). Large forces from the piezoelectric actuator have been converted into a greater displacement.