Modeling and Design Enhancement of Electrothermal Actuators for Microgripping Applications

Abstract

Microgrippers are miniature tools that have the capability to handle and manipulate micro- and nano-scale objects. The present work demonstrates the potential impact of the incorporation of perforations on a ‘hot and cold arm’ electrothermal actuation mechanism in order to improve the operation of microgrippers in terms of arm opening and operating temperature. By applying a voltage to one arm and setting the other as a ground, the current passes through the electrothermal actuator and induces its displacement along the in-plane direction. The difference in the geometry of the two arms causes one arm to expand more than the other and this results in transverse bending. A computational model was developed using a finite element analysis tool to simulate the response of the thermal actuators with varying geometries and investigate the impact of incorporating perforations on the arms of the thermal actuators to enhance its performance in terms of deflection and operating temperature. The simulation results were compared to their experimental counterparts reported in the literature. A good agreement between the numerical and experimental data was obtained. A novel design of a microgripper, made of perforated electrothermal actuators, was introduced. Its main characteristics, including the tip opening of the gripper arms, the applied voltage, and the stress and temperature distributions, were analyzed using the developed computational model. Different perforation shape and distribution were investigated. The present study demonstrates the capability of perforations to enhance the operation of microgrippers as manifested by the obtained higher tip displacement and lower tip temperature in comparison to conventional microgripper designs made of non-perforated thermal actuators. Furthermore, the highest stress generated on the microgripper elements was found to be much lower than the yield strength of the constituent material, which indicates proper functioning without any mechanical failure.

1. Introduction

Micro-Electro-Mechanical-Systems (MEMS) are devices that are widely used across different industries. MEMS can serve in several engineering applications, including sensing, actuation, and signal conditioning. For instance, MEMS accelerometers can be used for structural health monitoring applications. Khan et al. [1] developed and deployed a data acquisition system equipped with MEMS accelerometers to measure and analyze the vibrations of reinforced concrete beams when subjected to different damage levels. Alembagheri et al. [2] acquired vibration data from MEMS accelerometers to investigate the dynamic response of modular steel frames and the impact of gypsum partition walls on their dynamic characteristics. MEMS strain sensors have also been deployed in the design of crackmeters used for measuring cracks in structures [3,4]. Another use of MEMS technology includes the measurement of envelope air leakage in buildings using a network of MEMS pressure sensors [5]. There are multiple actuation methods that MEMS devices can deploy for operation, such as electrostatic [6,7,8], piezoelectric [9], electromagnetic, and electrothermal [10,11]. Electrostatic and electrothermal actuations are two that are commonly used due to their simple operating principle, high energy density, and compatibility with other electronics. Electrostatic actuation is characterized by a fast response, low power requirement, and well controlled force [12]. However, the associated nonlinearity limits the travel range of the actuated microstructure and can lead to its collapse due to pull-in instability and the failure of the MEMS device. On the other hand, electrothermal actuation relies on the Joule effect by heating a microstructure by means of passing a current through it in order to achieve large deflection of flexible elements, as required in several MEMS applications [13].

There are three main mechanisms of electrothermal actuation, namely the hot/cold arm actuator, the chevron, and the bimorph [10,12,13,14,15]. The operation of the hot/cold arm actuator is based on two arms of different thermal expansions leading to more generation of heat in one arm, which results in the deflection of the supporting microstructure. The chevron actuator also relies on the thermal expansion of the material, but it is only restricted to move in one direction. Lastly, the bimorph actuator is made of two materials with different thermal expansion coefficients that result in one material expanding more than the other and hence deflecting the actuator [13]. The most well-known design for a hot/cold arm actuator is the U-shaped actuator. This actuator has the capability to achieve wider ranges of displacement compared to other actuators [13,14]. In other words, large output forces can be produced by applying relatively low voltages (below 10 V) [13,14]. Electrothermal actuators have been widely deployed for microgripping applications [16,17,18,19,20,21,22,23,24,25,26,27,28].

Microgrippers are expected to finely grab and handle small-sized objects, such as microchips in electronics and cells in the biomedical field, without any damage. They include actuators and gripping arms made of thin silicon or stainless sheets, which are used to produce sufficient strength. Several research studies have reported on the design and performance analysis of microgrippers [16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35]. The design aspects of these microstructures include the kinematic structure [18,24], the material selection [21,24], the actuation mechanism [16], the fabrication process [17,20], and the impact of the surrounding environment on their operation [21,22]. For instance, Vargas-Chable et al. [16] designed an unconventional microgripper comprising hot and cold arms of varying area instead of uniform area. This modification resulted in an increase in the deformation of the arms and lower power requirements for actuation. Jain et al. [29] designed and experimentally tested a microgripper equipped with piezoelectric actuators. Their developed prototype showed a capability to precisely handle and manipulate miniature parts. A PID controller was also implemented in order to achieve the stability of the microgripper operation. Cauchi et al. [17] designed a microgripper based on a hot/cold arm micro-actuator, which is used in biomedical applications. The authors highlighted some of the failures that may occur in microgrippers, such as out-of-plane buckling, residual stresses, and stress concentration. Cauchi et al. [18] also investigated the effect of the material (silicon type) and air gap thickness on the operation of MEMS microgrippers. Some studies available in the literature focused on observing the differences in results obtained from microgrippers by changing the fabrication process, arm widths, air gap thickness, and fabrication process. Gaafar and Zarog [19] designed and analyzed a microgripper that uses comb-drive electrostatic actuation as the driving force. Another electrothermally actuated microgripper design is proposed by Somá et al. [20], in which the tip is designed in a way which facilitates the grip of a bio cell. The main difference between the microgripper proposed in this study and other available microgrippers is the presence of perforations on the surface of the hot arm of the actuator. In MEMS, perforations are mainly implemented in RF MEMS switches to reduce the squeeze film damping and increase the switching speed [36]. The perforations facilitate switches which operate at low actuation voltages and power [37,38]. Several research studies examined the impact of perforations on the dynamic response of structures at different scales [39,40,41]. Almitani et al. [39] conducted a theoretical study using the finite element method to investigate the free vibrations and forced responses of perforated multilayer beam structures. They analyzed the impact of different perforation configurations on their natural frequencies and mode shapes. Kumar and Harsha [41] develop a nonlinear mathematical model to analyze the vibrations of functionally graded piezoelectric plates under mechanical and electrical loadings for varying boundary conditions. Different types of porosity distributions are introduced by dispersing perforations (holes) over the plate. The center displacement was observed to increase when the porosity of an evenly distributed porous plate was increased. On the other hand, a decreasing trend in the center displacement was obtained when the porosity for an unevenly distributed porous plate was increased. As such, one can tune the porosity of the functionally graded as per the application of interest.

As demonstrated, the distinctive merits of the inclusion of perforations in macro/microstructures have been demonstrated over several research studies [36,39,40,41]. However, there is still room for further exploitation of this kind of structural feature, especially when properly tuning its geometry and distribution to improve the operation of microgrippers comprising electrothermal actuators. Therefore, we propose, in this work, a novel design for microgrippers that benefits from the presence of perforations in order to achieve superior performance in comparison to their conventional counterparts. Previous research works have only studied other geometrical and material aspects to enhance the design of microgrippers [16,17,18,19,20,21,24,25,26,28,31,32,42,43].

In this work, we develop a computational model of a microgripper actuated via U-shaped electrothermal actuators using the finite element software tool COMSOL Multiphysics, Version 5.6. We validate the model using previously published experimental studies. We show the potential enhancement in the design of microgrippers by adding perforations of different shapes and distributions, proposed for the first time. The simulation results show an improvement in the performance of the microgripper by achieving larger deformation while operating at lower temperatures. Furthermore, lower von-Mises stresses and faster responses are achieved when adding perforations. The present study provides a baseline and guidance for the design enhancement of microgrippers using available microfabrication techniques.

2. Materials and Methods

2.1. Electrothermal Actuation: Theoretical Background

The working principle of electrothermal actuation is based on the heating of a microstructure by passing a current I through the microstructure or resistors placed on it. Due to the resistance of resistors or the structure itself, Joule heating is generated according to [10]:

$$P=I^{2}R$$

(1)

where P is the generated power and R represents either the resistance of deposited resistors or is the resistance of the structure itself which can be calculated as follows [10]:

$$R=\frac{{\rho }^{E}L}{A}$$

(2)

here, L denotes the total length of the structure, A is the cross-sectional area, and ${\rho }^E$ represents the resistivity of the structure. In the U-shaped actuator, due to geometry differences between the two arms, one arm is more resistive than the other, inducing different Joule heating generation in each arm. This results in a temperature difference between arms and hence leads to having one arm with more thermal expansion than the other one has. This thermal expansion is the main driving force of the tip deflection of the electrothermal actuator [13].

We display, in Figure 1, the main modeling steps used to simulate the mechanical and thermal response of the U-shaped actuator.

After introducing the geometry and material properties of the U-shaped actuator, the structure mesh is generated. Next, The Joule heating and thermal expansion interface is used. It constitutes a Multiphysics module which accounts for thermal expansion, the fundamental mechanism by which motion is generated in thermal actuators, and electromagnetic heating physics. Thermal expansion is treated as a continuum behavior. The thermal strain is computed as follows:

$${\epsilon }_{th}=\alpha \left(T\right)(T-T_{ref})$$

(3)

where ε_th is the thermal strain, α(T) is the thermal expansion coefficient, and T_ref is the reference temperature. COMSOL uses a secant coefficient of thermal expansion by default. Hence, the thermal expansion coefficient can be treated as a temperature independent constant value which is obtained from the defined material properties [44].

Electromagnetic heating uses electric currents and heat transfer in solids interfaces to solve the Joule heating problems. The electric current interface includes the implementation of the following equations to perform time-invariant (stationary) analysis [44]:

$$\nabla ·J=0$$

(4)

$$J=\sigma E$$

(5)

$$E=-\nabla V$$

(6)

where σ is the electrical conductivity, J is the current density, E is the electric field intensity, and V is the electric potential. The temperature variation in the thermal actuator is dictated by the heat generation and heat transfer throughout its structure. The thermal behavior is governed by the following equations which couple the electric currents and heat transfer in solids interfaces:

$$\rho c_{p}u · \nabla T=\nabla · \left(k\nabla T\right)+Q_e$$

(7)

$$Q_e=J ·E$$

(8)

where ρ is the density, c_p is the specific heat capacity at constant stress, u is the velocity vector, T is the absolute temperature, k is the thermal conductivity, and Q_e is the Joule heating-introduced heat load [44].

Different boundary conditions have been imposed on the model in order to closely replicate the real model. In the solid mechanics interface, a fixed constraint boundary condition is imposed on the appropriate edges which sets the displacement to zero in all the three (x, y, z) directions. The two main important boundary conditions used in the electric currents interface are the terminal and ground boundary conditions. For the terminal boundary condition, the electric potential is set to be equal to the input voltage at the given boundary, whereas for the ground condition, the potential is set to zero. The main boundary condition imposed in the heat transfer in solids interface is the convective heat flux boundary condition which uses the following equations:

$$-n · q=q_0$$

(9)

$$q_0=h · \left(T_{ext}-T\right)$$

(10)

here n is the normal vector on the boundary, q is the conductive heat flux vector, q₀ is the inward heat flux, h is the convection heat transfer coefficient, and T_ext is the temperature far from the domain under study. The thermal insulation boundary condition is another condition imposed on the model where q₀ is set to zero in this case.

We also follow an analytical approach based on beam theory to estimate the static response of the electrothermal actuator when subjected to an input voltage, as per the model reported in [45]. The tip displacement is expressed as:

$$w_t=\frac{\alpha \rho L_t^2{I}^2}{K_{xx}{W}_t{t}_{a}d}$$

(11)

where α is the linear thermal expansion coefficient, ρ is the specific electrical resistance, L_t is the thin arm effective length, I is the input current obtained from the applied voltage, K_xx is the conductivity coefficient, W_t is the thin arm width, t_a is the arm thickness, and d is the distance between the thin arm and wide arm’s centerlines. The thermal conductivity used in this analytical model for polysilicon micro-actuators is 30 W/m·°C, and electrical resistivity is 1.1 × 10⁻⁵ Ω·m [46]. The analytical solutions will be computed for different electrothermal actuators and compared to their numerical counterparts.

Figure 2 illustrates the electrothermal actuator design process. Given the selected geometry and material, an FEM model is implemented. A mesh analysis is conducted to ensure the appropriate discretization scheme of the microsystem. Next, an experimental verification is carried out by comparing the numerical results to their experimental counterparts reported in the literature. Next, the design is modified by incorporating perforations while varying their shape, size, number, and distribution. Finally, a performance analysis is conducted to demonstrate the design enhancement.

2.2. Electrothermal Actuation: Model Implementation

The design parameters of the present thermal actuator are similar to those reported in Kumar and Sharma’s work [12] for the sake of validation. In [12], two actuator designs have been proposed and experimentally tested. The difference between these two actuators is the width of the cold arm in which actuator 1 has a cold arm width of 10 μm and actuator 2 has a cold arm width of 30 μm. The thickness of both actuators is set equally to 25 μm. The dimensions and material properties of the thermal actuators under investigation are presented in

Table 1. Material properties and geometric dimensions for the micro-actuators [12].

Properties	Numerical Value
Young’s modulus (Pa)	170 × 109
Density (kg/m3)	2320
Poisson’s ratio	0.28
Thermal conductivity (W/m·K)	146
Electrical conductivity (s/m)	0.25 × 104
Thermal expansion coefficient	2.6 × 10−6
Dimensions (μm)	Actuator 1	Actuator 2
Lc	200	200
Wc	10	30
Lh	250	250
Wh	3	3
Lf	50	50
Wf	3	3
Lch	5	5
Ga	5	5

.

COMSOL Multiphysics is used to simulate the response of the electrothermal actuator in this study. To do so, the Joule Heating and Thermal Expansion Multiphysics module available in COMSOL is deployed in the subsequent simulations. There are three main interferences embedded in the computational model, which are solid mechanics, heat transfer in solids, and electric currents. Static and dynamic analyses are carried out to assess the performance of the thermal actuators. For each interference used in the simulations, certain boundary conditions are imposed on the model, which are discussed next in detail.

For solid mechanics interference, fixed constraints boundary conditions are placed on the left side of the actuator in which it is assumed to be connected to the anchors. For heat transfer in solids interference, heat convection boundary conditions are imposed on the surface of the actuator which is in contact with air. The reference and ambient temperature for this module is set at 295.15 K. The selection of the heat convection coefficient for the heat flux boundary condition will be later discussed in this section. Lastly, for electric currents interference, a terminal voltage is applied to the left edge of the hot arm. Ground boundary conditions are applied to the left edge of the cold arm. The reference impedance for both actuators is set equally to 50 Ohms. For the effect of perforation analysis on the electrothermal micro-actuator, square holes with a width and length of 5 μm are placed on the top of the hot arm of the actuator. The number of holes for actuator 1 is equal to actuator 2. In later sections, the number and geometry of perforations will be varied to examine the impact of the shape and locations of perforation on the response of the microgripper. Figure 3a shows the schematic of the thermal actuator along with its corresponding dimensions, and Figure 3b represents the boundary conditions imposed on the actuator.

Mesh independence analysis is performed for both types of actuators to determine the optimal number of elements which provide accurate results with reasonable computation time. For all the simulated cases, all systems’ parameters are held constant. For actuator 1’s design, a “Fine” mesh grid has been chosen, whereas for actuator 2, a “Finer” mesh grid is chosen. The change in tip displacement and temperature while increasing the number of elements for the two actuators under inspection is shown in Figure 4. The simulation time using the meshes shown in Figure 4 varied between 25 to 45 s. The selected mesh configurations for both actuators 1 and 2 are also indicated in Figure 3.

For all the simulations performed in this investigation, the ambient temperature is considered to be equal to 295.15 K. For the convection coefficient h, the value of 11,500 (W/m²·K) and 5000 (W/m²·K) are used for actuator 1 and actuator 2, respectively. Usually, the convection coefficient of air is within the range of 5–25 (W/m²·K) when operating at the macro scale. In a MEMS-related application, its value is increased by an approximate factor of 103 given the high operating temperatures and the small-scale geometry as reported in [47].

2.3. Electrothermal Actuator Model Validation

To validate the computational model implemented using the COMSOL Multiphysics FEA tool, the results obtained are compared against the previously published numerical and experimental results reported in [12]. Figure 5 shows the variations of the tip displacement and temperature with the applied DC voltage obtained for actuators 1 and 2, respectively. The simulation results for actuator 1 agree with the simulation results shown in the literature [12]. Figure 5a reveals the relationship between the voltage, tip displacement, and temperature of the actuator 1. In Figure 5a, the tip displacement is approximately zero at 1 V. On the other hand, the tip displacement and temperature increase with the applied voltage following a nonlinear trend. At 9 V, the tip temperature observed was 1255.65 °C, which is close to the approximate value of 1256.73 °C reported in the literature for actuator 1 subjected to the same voltage. The tip displacement obtained when setting the voltage at 9 V was 2.269 μm, whereas the work in the literature reported an approximate value of 2.443 μm. This slight deviation in results is mostly associated with the difference in the boundary conditions. Regardless, the present model demonstrates a great capability to predict the thermal and mechanical responses of the actuator. In Figure 5b, the variations of the temperature and the tip displacement of actuator 2 are plotted with the applied voltage and compared to their numerical counterparts reported in the literature [12]. Similar to the previous case, the two sets of data show good agreement. At 9 V, the temperature and tip displacement values obtained from the present simulations were 1353.77 °C and 3.911 μm, respectively, which slightly differ from the values of 1249.66 °C and 3.62 μm, obtained in [12]. The slight discrepancy observed in the tip displacement can be associated with the boundary conditions imposed in the simulations. Fixed constraints are considered. However, the actual actuator may have imperfect clamping.

To further verify the present computational model, the simulation results are compared against their experimental counterparts obtained by Kumar and Sharma [12]. The actuator is fabricated using three-level Silicon-on-Insulator (SOI) mask patterning. The top surface of the silicon layer is annealed with Phosphosilicate Glass (PSG) material for 1 h in Argon. Next, a stack of 25 nm chrome and 500 nm Gold are patterned on the structure. Finally, Deep Reactive Ion Etching (DRIE) is used to etch the front surface of the actuator [12]. The material selected for the microgripper is polysilicon due to its physical and chemical properties, which make it a versatile material in accomplishing structural, mechanical, and electrical tasks in the fabrication of a microgripper [12]. It also gives a similar performance as the material used in the previous experimental work [12].

Figure 6a,b shows a comparison between the numerical (FEM model), analytical (as given by Equation (11)), and experimental results for actuator 1 and actuator 2, respectively. A good agreement is obtained when comparing the analytical solution to the experimental and simulation results for actuator 1. However, the analytical solution for actuator 2 largely deviates from the experimental and simulation results. This discrepancy is mostly due to the change in the mechanical and electrical properties of the polysilicon at the micro scale which is caused by the dimensional change of the cold arm of the electrothermal actuator. We recall that actuator 2 has a thicker arm (larger $W_c$) in comparison to actuator 1. Any impurity in the constituent material (assumed perfectly homogeneous) will be magnified when enlarging the system. This can be the reason for the discrepancy observed in the comparative study performed for actuator 2. For both actuators, experimental and simulation data for the tip displacement value at different voltages are in close agreement. For the present simulations, a single material is selected with the effective properties shown in Table 1, whereas the actual microstructure consists of layers of different materials as mentioned above. This presents the main limitation of the current computational model. There are other sources of errors that may lead to such deviations observed between the experimental and simulation results. The difference in the ambient temperature, variations in the convective heat transfer coefficient, and faults in the measuring devices are some of the possible sources of errors.

2.4. Electrothermal Actuator Design Enhancement

In order to improve the performance of micro-electrothermal actuators, a single row of square-shaped perforations with a width of 5μm are added on the top surface of the hot arm of both actuator 1 and actuator 2. The position of these perforations on the surface of the hot arm are depicted in Figure 7a. Additionally, Figure 7 shows the considered configurations for the placement of the perforations considered in this study. Indeed, Figure 7b–d shows the geometry and position of perforations for different scenarios on the surface of the non-extended hot arm. The radius of circular perforations is selected to be 2.82 μm so that the volume reductions caused by square and circular perforation are the same.

We plot, in Figure 8, the variations of the tip displacement and temperature with the applied voltage for perforated and non-perforated actuators 1 and 2 when considering a single/double row of square/circular-shaped perforations on the top surface of the hot arm for both actuators, as illustrated in Figure 7a. The presence of perforations on the hot arm of the actuator enhances the response of the thermal actuator, as manifested by the increase in the displacement and the decrease in the operating temperature. Indeed, the displacement magnitude for actuator 1 without perforations at 8 V is found to be equal to 1.793 μm, whereas for the single-row square-perforated actuator 1, the displacement at the same voltage reaches 1.921 μm. The tip displacement is further increased to 2.061 μm when switching to a double-row square perforation. The same observations are made for actuator 2 in which the tip displacement magnitude at 8 V increases from 3.090 μm to 3.7286 μm when adding a double row of square perforations. This behavior may be attributed to the decrease in the overall stiffness of the system and hence an increase in their displacements. As per Equation (2), the perforated arms have higher electrical resistance given the associated reduction in the surface area, and this leads to higher power generation induced by Joule heating, as shown in Equation (1). This would explain the capability to achieve larger deformation at the same electric actuation level. Furthermore, using the analytical approach based on beam theory, Equation (11), we notice that the incorporation of perforation reduces the effective width and thickness of the arm, and this results in a larger tip displacement for the same electric actuation. The temperatures at the tip are reduced when perforations are added on the top of the hot arm and there is larger tip displacement as the temperatures are reduced; these are two of the most important effects of perforations on the U-shaped electrothermal micro-actuators. We report, in

Table 2. Relative changes in tip displacement and temperature of actuator 1 and 2 after adding different cases of perforations when operating at 8 V.

	Actuator 1	Actuator 2
Single-row square tip displacement	7.1388%	4.5819%
Single-row circular tip displacement	7.0831%	4.53%
Double-row square tip displacement	14.9470%	9.1521%
Double-row circular tip displacement	14.6848%	8.809%
Single-row square tip temperature	−11.6684%	−12.6766%
Single-row circular tip temperature	−4.73%	−5.36%
Double-row square tip temperature	−10.4046%	−5.5351%
Double-row circular tip temperature	−10.0923%	−11.255%

, the relative changes in tip displacement and temperature for both actuators 1 and 2 after adding perforations when operating at 8 V.

Contour plots displaying the temperature and displacement for both single-row square-perforated and non-perforated actuators when applying 5 V are shown in Figure 9. Clearly, the incorporation of perforations results in lower temperatures and higher displacement for both actuators. Displacement contour plots show maximum displacements occurring at the tip, since the other side of actuator is connected to the anchor and the boundary has a fixed constraint condition. The temperature contour plots show that the hot arm (thinner arm) of the U-shaped actuator undergoes higher temperatures than that of the cold arm (thicker arm) at any applied voltage.

To verify the operational reliability and the structural resistance to the electrothermal, we analyze the von-Mises stress generation and present the corresponding results when applying 5 V, as shown in Figure 10. The maximum von-Mises stress occurs at the connection between the arms and the anchor. Of interest, the inclusion of perforations results in lower von-Mises stresses at the hinge where the micro-actuator is connected to the supporting anchors. The maximum von-Mises stress when applying 8 V for the non-perforated actuator 1 is 1.36 GPa, whereas, for the perforated actuator 1, it is found to be equal to 0.89 GPa, that is, 34.5% lower in magnitude. For actuator 2, the maximum von-Mises stress is found to be equal to 1.35 GPa for the microstructure without perforations. On the other hand, when adding the perforations, the maximum von-Mises stress decreases to 1.21 GPa. For both actuators 1 and 2, the maximum von-Mises stresses do not exceed 4 GPa, which is the approximate ultimate tensile strength of polysilicon [48]. The results indicate the safe operation of actuators 1 and 2 without potential mechanical failures.

The response time is an essential design consideration, especially for an application requiring an immediate response. To investigate this aspect, we examine the time response characteristics of the electrothermal actuator when subjected to an applied DC voltage. We plot in Figure 11a,b the time responses of actuators 1 and 2, respectively. We present in

Table 3. Time response characteristics of single-row square-perforated and non-perforated actuators 1 and 2.

	Rise Time (ms)	Settling Time (ms)	Overshoot	Peak	Peak Time (ms)
Non-Perforated actuator 1	0.6929	5.8266	0	1.7913	15
Single-row perforated actuator 1	0.5107	0.8769	0.0366	1.9217	1.6
Non-Perforated actuator 2	0.6277	3.6230	0.0018	3.0901	45
Single-row perforated actuator 2	0.5530	0.9925	0.4759	3.2464	1.8

the characteristics of the time response of both actuators at 8 V. Of interest, the introduction of the single-row square perforations on the surface of the hot arm is observed to speed up the mechanical response. Indeed, the displacement-perforated actuator takes less time to reach the steady-state response.

2.5. Microgripper Design and Modeling

In this section, we show how the design enhancement of the thermal actuators based on the added perforations can improve the operation of the microgrippers. The microgripper designed in this study consists of two hot/cold arm actuators where the hot arms are expected to extend and act as grippers. By applying a voltage, the Joule heating induces the thermal expansion of the arm with more generated heat compared to the other arm, causing the deflection and resulting in the opening of the microgripper. Disconnecting the voltage will lead the gripping arms to return to their original position.

We consider a microgripper made of two thermal actuators with similar properties to those of actuator 2 reported in Table 1. We apply the same boundary conditions as those defined in earlier sections. Three anchors are added: the bottom and top anchors are supplied with the terminal voltage, and the middle anchor is connected to the ground. The layout of the proposed microgripper along with the imposed boundary conditions are presented in Figure 12. We note that the length of the hot arm of the microstructure is increased to 400 μm to facilitate the operation of the microgripper, as will be discussed next. We show in Figure 13 the detailed geometry of the microgripper, including its main elements. It consists of three main parts: three anchors, two gripping arms, and two electrothermal actuators. The two symmetrical gripping arms have a length of 150 μm, width of 3 μm, thickness of 25 μm, and their initial opening distance is 10 μm (before applying any voltage). The microgripper is designed to function via an integrated thermal element (hot/cold arm) which is controlled by applying a voltage. The application of a voltage to the thermal layers will produce the further opening of the microgripper to enable the gripping of micro objects with diameters larger than 10 μm. Releasing the micro objects after manipulation requires the application of higher voltages. When the voltage is switched off, the gripping arms of the structure will return to their original position with a gap distance of 10 μm.

Mesh independence analysis is also carried out for the proposed microgripper design in order to obtain accurate results at reasonable simulation times. The results show that the same mesh settings applied to actuator 2 are also suitable for the microgripper analysis. We show, in Figure 14, the variations of the gripping arm tip displacement, temperature (with respect to the initial opening) and the corresponding simulation time with the number of mesh elements. The mesh setting is selected based on the convergence behavior of the microsystem while the simulation time is minimized in order to speed up the numerical study.

3. Results

We examine the effect of the number, shape, and distribution of the perforations on the response of the microgripper. Four different settings are considered, as shown in Figure 7. These include single-row square, single-row circular, double-row square, and double-row circular perforations. In all of these four scenarios, the imposed boundary conditions are held constant and only the number or geometry of perforation is altered. Moreover, similar to the perforations added to micro-actuators analyzed in the previous section, the perforations on the microgripper are only added on the top surface of non-extended hot arms. In all cases, the added perforations go through the entire depth of the hot arm surface. When a voltage is applied on the microgripper, due to geometry differences in the hot and cold arms, one side will expand more than the other, causing the microgripper to open. When the voltage is disconnected, the microgripper returns to its initial state.

Figure 15 shows the upper and lower tip displacements of the microgrippers. In the same figure, displacement contours for the non-perforated microgripper and double-row square-perforated microgripper are also presented. The simulation results indicate that the microgripper without perforations has the lowest tip displacement compared to perforated microgrippers in this study. Moreover, the presence of more holes on the surface of the hot arm leads to a slight increase in the tip displacement. For instance, when applying a voltage of 8 V, the microgripper with a single row of square perforations undergoes a 10.707 μm tip displacement whereas the microgripper with a double row of square perforations reaches a tip displacement of 11.240 μm. Similar trend is observed for the cases of single- and double-row circular perforations. Another important observation that can be made from Figure 15 is the similarity in the results obtained for the scenarios where the number of holes held constant and only the geometry of the holes has changed. Such results are expected since the radius of circular holes is intentionally selected in a way that the volume reductions caused by the added perforations in both scenarios remain unchanged. At an excitation voltage of 8 V, the single-row circular-perforated microgripper achieves a tip displacement of 10.685 μm, which is 0.022 μm lower than that of the single-row square-perforated microgripper at the same voltage. Similarly, the double-row circular-perforated microgripper reaches a 11.176 μm tip displacement, which is 0.064 μm lower than that of the double-row square-perforated microgripper. The overall trend observed in Figure 15 for the upper and lower tip displacements of microgrippers is also consistent with the results reported in the literature [16,17,18,25,26,32]. In [18], the designed polysilicon microgripper achieved tip displacements of approximately 3.0 μm when applying a voltage of 3 V, whereas, in the same study, the single crystal silicone microgripper achieved displacement of approximately 1.5 μm at 14 volts. Cauchi et al. [25] presented an electrothermally-actuated microgripper for biomedical applications and reported a tip displacement of about 2.5 μm at 12 V. As shown in Figure 15, the simulation results show evidence of superior performance in the current microgripper, especially when incorporating perforations. Indeed, the application of a lower voltage of 8 V results in a tip displacement of 11.240 μm for the microgripper with a double row of square perforations.

Figure 16 shows the total gap opening obtained from each microgripper under study. The initial gap for the microgripper is set at 10 μm (the voltage actuation is switched off). A nonlinear increasing trend in the gap opening is obtained when increasing the applied voltage. The case of the double row of square perforations shows a superior performance. The highest gap opening of 21.240 μm is obtained for the case of the double-row square-perforated microgripper when applying a voltage of 8 V. The simulation results reveal the importance of the shape and distribution of the perforations as design aspects for the performance and operational reliability of microgrippers.

For the tip temperature analysis, only the upper tip of the gripping arm is reported since the values for upper and lower tip temperatures are found close to each other. Figure 17 shows the variations in the tip temperatures with the applied voltage obtained for the different microgrippers under study. The incorporation of perforations on the surface of the hot arm results in lower tip temperatures, which constitutes an important aspect for microgripping applications in which operating at high temperatures may cause complications to the surrounding electronics and to the gripped object. Moreover, the simulation results reveal that more perforations result in more reduction in the tip temperature. Low voltage actuation leads to relatively low tip displacement and temperature which makes the effect of the perforation minimal. On the other hand, this effect is more pronounced at higher voltages given the significant increase in the tip temperature and displacement that can be achieved thanks to the Joule effect. For example, when applying a voltage of 2 V, switching from no perforations to a double row of square perforations results in an 8.51% decrease in the tip temperature, whereas the temperature decrease reaches 25.24% when adding perforations and operating at a voltage of 8 V.

To gain more insight into the temperature distribution over the entire group of microgrippers during operation, the temperature contour plots for different microgrippers are displayed in Figure 18. The simulation results are shown for different applied voltages, ranging from 2 V to 8 V. As expected, in all cases, the hot arm of the microgripper is subjected to higher temperatures than the other parts of the microgripper. Moreover, the overall structure of the microgrippers with double rows of square and circular perforations reach lower temperatures than the other cases as indicated by the brighter colors in Figure 18.

One essential design consideration is to inspect any potential mechanical failures that may result from the electrothermal actuation. As such, a stress analysis is performed, and the obtained results are presented as contour plots of von-Mises stresses for the different microgrippers under investigation (see Figure 19). The highest von-Mises stresses in all cases take place at the hinges connecting the hot/cold arm to the anchors. This observation is consistent with the results reported in the literature which revealed the same location of the stress concentration [17,18]. The simulation results obtained for all microgrippers at 8 V are summarized in

Table 4. Performance characteristics of the different microgrippers when operating at 8 V.

	Total Tip Displacement (μm)	Upper Tip Temperature (°C)	Lower Tip Temperature (°C)	Von-Mises Stresses (GPa)
No perforation	9.885	978.29	978.29	2.25
Single row square	10.707	867.01	867.02	2.23
Single row circular	10.685	871.22	871.25	2.26
Double row square	11.240	731.30	731.30	2.01
Double row circular	11.176	739.71	739.72	1.89

. The maximum von-Mises stress of the microgrippers under investigation is found between 1.89 GPa and 2.26 GPa, all below the yield strength of polysilicon [48]. These results demonstrate the safe and proper operation of the microgrippers.

4. Discussion

In this work, we investigated the impact of perforations on the operation and performance of electrothermally actuated microgrippers. To do so, we first conducted finite element simulations in order to generate the temperature distribution and displacement of electrothermal actuators when subjected to different voltages and verify them against previously published experimental results. The present simulation results showed good agreement with their experimental counterparts. Then, we introduced and analyzed a novel design of microgrippers, including perforated electrothermal actuators. Different perforation configurations were tested. The simulation results revealed that adding perforations to the hot arm of the electrothermal actuators resulted in a larger displacement and lower temperature of the gripping arm without affecting the mechanical strength of the microgripper. The maximum operating voltage of the microgripper was set equal to 8 V. At this voltage, the gap opening was observed to reach an increase of 13% when adding perforations. Moreover, the tip temperature of the perforated microgripper was reduced to 731.30 °C in comparison to the 978.29 °C obtained in absence of perforations. A stress analysis of the perforated microgripper showed that the highest von-Mises stresses are achieved at the hinges connecting the hot/cold arm to the anchors. The values of these stresses were found in the range of 1.89 GPa to 2.26 GPa, which is smaller than the yield strength of the core material of the microgripper (polysilicon). This indicates the safe operation of the perforated microgripper while simultaneously gaining a larger gap opening and lower operating temperature when compared to its non-perforated counterpart actuated with the same voltage. The present study provides a baseline for the implementation of an unconventional design of microgrippers which exploits the impact of perforations on their operation with lower power requirements and temperatures.

A potential extension of the present work is to implement and experimentally test the performance of perforated microgrippers, proposed for the first time in this study. Their capability to achieve sufficient movement of the arms in order to handle small objects, while operating at lower temperatures and consuming less power, will be assessed. Different perforation configurations in terms of shape, number, and distribution can be considered. The experimental results can also be used to further validate the present FEM-based computational model to simulate the response of electrothermally-actuated microgrippers. Fatigue is also an important aspect to consider in order to ensure the appropriate operation of the microgripper over many cycles, which involve the heating/cooling process along with recurring deformation of the arms. A fatigue analysis can be considered as a future direction of the present study.