Displacement Amplification of Electrostatically-Driven Microgripper in A Hybrid Design With Electrothermal Actuation

Mohsen Hamedi1,a, Parisa Salimi2,b and Milad Vismeh3,c 1,2,3 Department of Mechanical Engineering, University of Tehran, Tehran, Iran

amhamedi@ut.ac.ir, bparisasalimi@ut.ac.ir, cmiladvisme@ut.ac.ir

Keywords: MEMS, Electrostatic Microgripper, Comb-drive, Electrothermal Actuator

Abstract. By the growing development of micro electromechanical systems, the application of

microgrippers for handling and assembling of microparts attracts more attention. In this paper, an

electrostatic microgripper using comb drive mechanism is designed and a formulation is presented

to predict the critical voltage for pull-in instability threshold. Then the advantages of a modified

model of electrothermal U-shape actuator with large forces and bilateral displacement are utilized to

amplify the output displacement range of microgripper prongs. To show this amplification, finite

element simulations are performed on the primary and modified microgripper proposed models.

Introduction

Picking, handling and releasing of micron objects in diverse areas especially in micro

electromechanical systems (MEMS) is a challenging concept which merits accurate design and

performance analysis of the related devices. Since microgrippers are the preferred tools for

microassebly applications, wide researches have been performed on their mechanism and actuation

principles. The most popular actuation techniques include electrostatic [1], electrothermal [2],

magnetic [3] and shape memory alloys (SMA) [4]. Among these actuation methods,

electrostatically-driven microgrippers are better choices for biological and medical applications.

A significant strategy to run electrostatic microgrippers is to use comb-drive actuators.

Typically, two interdigitated finger structures form the basis of a comb drive actuator. One of the

combs is fixed and the other which is connected to a compliant suspension, will produce deflection

upon applying voltage to the device anchors due to electrostatic force. Though electrostatic

microgrippers exploit small displacements that are limited to few microns, little efforts have been

made on increasing deflection ranges. The mechanical changes in the design of comb-drive

mechanisms are discussed in [5] in which spring designs such as clamped-clamped beams, crab-leg

flexure and folded-beam flexure are investigated for the improvement of comb-drive performance

and the microgripper deflection.

In this paper, electrothermal actuators (heatuators) are added to the basic design of an

electrostatic microgripper which operates with comb-drive mechanism. Doing this, not only will

enhance the range of arms’ motion, but also is appropriate for introducing further forces when

handling objects with micron dimensions.

Microgripper Design

General Design. The schematic drawing of the microgripper is illustrated in Fig. 1. As mentioned

above, comb-drive is utilized for actuating the designed tool. By applying potential difference to the

anchors of the microgripper, comb fingers act as parallel capacitors and the resulting electrostatic

force between the fixed and movable fingers drives the movable fingers towards the fixed ones.

This produces small displacement in the movable fingers’ direction of movement. Since rotational

deflection of arms is desired to open and close the prongs of microgripper, S-type flexible beam

system is applied to convert the small horizontal motion to big rotational motion of the arms.

Advanced Materials Research Vol. 159 (2011) pp 313-320Online available since 2010/Dec/06 at www.scientific.net© (2011) Trans Tech Publications, Switzerlanddoi:10.4028/www.scientific.net/AMR.159.313

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Plunger. Because of the fact that surface tension forces dominate the gravitational forces in

micro/nano scales, there will be problems in releasing microparts from the prongs [6]. One of the

techniques to reduce the effects of this phenomenon is structural changes in the design of tools. In

this paper, a plunger is used between the two arms of the microgripper in order to help the

micropart release conveniently from the prongs when it is absolutely positioned. This is done by

applying voltage to the anchors of plunger; it becomes heated and expands linearly and causes

parts’ separation by exerting forces to them.

Fig. 1. The schematic drawing of microgripper.

Material and Dimensions. Polysilicon, monocrystaline silicon and nickel are known materials

in microfabrication processes and are suitable for wide range of applications in MEMS components.

In our case study, Polysilicon is considered to be the microgripper material for simulations. The

overall dimension of microgripper is 8020×4800 micrometers.

Description of Two Models for Output Deflection

In this work, we have investigated two approaches for evaluating the output displacement of the

microgripper arms as shown in Fig. 2. The first one (model A) uses the power of electrostatic force

through the comb-drive mechanism to open and close the prongs of microgripper. The second

model (model B) with hybrid electrostatic-electrothermal actuation is featured with modified U-

shape electrothermal actuators. These actuators are connected to the end of microgripper arms and

the bilateral in-plane motion that they produce will amplify the range of opening and closing

deflection of the prongs.

Fig. 2. Electrostatic and hybrid electrostatic-electrothermal models of microgripper.

The standard U-shape heatuators (Fig. 3) work under the principles of joule heating. In the

standard form, the anchor which is connected to thin arm will accept voltage and the other anchor is

electrically grounded. In this case, the thin arm heats up more than the wide arm due to higher

electrical resistivity and joule heating is produced in polysilicon as structural and active material.

314 Micro Nano Devices, Structure and Computing Systems

Then because of further linear thermal expansion of the thin arm, in-plane rotation of actuator will

occur which can affect the displacement range of microgripper prongs. The keypoint to use another

actuation method for electrothermal actuators is the favourable output displacement through

applying lower voltage with lower input power. Therefore, the modified configuration for U-shape

actuators as depicted in Fig. 3 is developed here in which polysilicon acts as structural material and

Cr/Au thin layers are considered to be heating electrodes. The size of arms in the modified design

are equal and this is the linear thermal expansion of each arm that produces motion in the desired

direction. When potential difference is applied to anchors of electrode a, the actuator bends towards

direction 1, and similarly the actuator rotates towards direction 2 when voltage is introduced to

electrode b. Thus, the modified design is able to increase and decrease the prongs’ distance through

its bilateral motion. Since the electrical resistivity of Cr/Au is significantly lower than polysilicon,

all the current related to input voltage passes through Cr/Au layer in real situation and so it is

responsible for heating up the polysilicon structure.

Fig. 3. Standard and modified designs of U-shape electrothermal actuators.

Pull-in Instability Phenomenon

Electrostatic comb-drives are widely used in MEMS applications. These fingers are usually

designed with rectangular shapes to produce constant output force [7]. A typical configuration of

comb finger electrodes and its design parameters is shown in Fig. 4, where h and b stands for

thickness and the width of each finger, respectively. d is the distance between the plates and a is the

distance between movable finger top and fixed finger root. Also y shows the comb fingers overlap

length which is increased to y+∆y upon applying voltage. The dimensions of comb-drive in our

designed structure are listed in Table 1.

Fig. 4. A typical configuration of comb finger electrodes and its design parameters.

Advanced Materials Research Vol. 159 315

Table 1. Typical dimensions of microgripper.

Design Parameter h b d a y

Dimension (µm) 25 5 5 20 10

The most important issue in utilizing comb-drive mechanisms is the pull-in instability which

usually occurs because of the misalignment in fabrication process such as lithography or other

environmental disturbances. In other words, when a voltage is applied to the device anchors, a

longitudinal electrostatic force is generated to drive the movable comb fingers. This force should be

kept equal at both sides of the movable finger so as to maintain it at the center line between two

fingers of the fixed electrode. Meanwhile, lateral forces are also generated between adjacent comb

fingers and so the lateral forces balance out. In cases with high input voltage, however, the lateral

forces increase, and with small disturbance, the moving part could become unstable and the

movable fingers move laterally and collapse to fixed ones [8]. Then short circuit happens and it

prevents microgripper performance. Therefore, finding a critical voltage of pull-in threshold, is a

big challenge in designing comb-drive structures. Doing this, the below formulation is proposed

according to depicted simplified model in Fig. 5.

Fig. 5. Simplified model for instability investigation of a comb finger.

The capacity of capacitors are explained with Eq. 1 and Eq. 2:

xyd

hdydc

−−=

θε

sin.

..1 (1)

xyd

hdydc

++=

θε

sin.

..2 (2)

The equivalent capacity of these parallel capacitors is calculated as follows:

xyd

hdy

xyd

hdydcdcdcT ++

+−−

=+=θ

εθ

εsin.

..

sin.

..21 (3)

( )xydh

xyd

hdcc TT +++

−−== ∫ θ

θε

θθε

sin.lnsin

.

sin.

1ln

sin

. (4)

316 Micro Nano Devices, Structure and Computing Systems

( ) ( )[ ]xydxydh

xydxyd

hcT

++−++

+

−−−

−−=

θθθ

ε

θθθε

sin.lnsin.lnsin

.

sin.

1ln

sin.

1ln

sin

.

12

12 (5)

2

2

1cvw = (6)

++−

+++

−−−

−−=⇒=

xydxydxydxydv

hF

dx

dwF

θθθθθε

sin.

1

sin.

1

sin.

1

sin.

1

sin.2

.

1212

2 (7)

+−−

+−=

2

1

22

2

2

2

)sin.()sin.(sin

.

xyd

d

xyd

dv

hF

θθθε (8)

( )( )( )xyyxyydh

xkxydxydv x

.2sin..2sin....

..)sin.(.)sin.(.

2

2

21

2

1

2

1

22

2

2

2

++−−

+−+−=

θθε

θθ (9)

( )( )( )xyyxyydh

xkxydxydv x

.2sin.).2sin....

..)sin.(.)sin.(.

2

2

21

2

1

2

1

22

2

2

++−−

+−+−=

θθεθθ

(10)

Now if we assume Kθ is large enough, θ could be considered as zero and so the Eq. 10 could be

simplified to Eq. 11.

( )( )22

12 .....2xd

yydh

kv x −

−=

ε (11)

In Eq. 11 x must be zero so as to prevent pull-in phenomenon. Therefore, if we put zero instead

of x in this equation, the critical voltage for pull-in threshold will be obtained.

( )

−= 2

3

12

max....2d

yyh

kv x

ε (12)

( ) overlaplyy =− .. 12

(13)

= 2

3

max..2

dlh

kv

overlap

x

ε (14)

As we can see the maximum possible input voltage in which the fingers remain stable, with

constant thickness, changes in terms of the overlap length of fingers (loverlap) and the distance

between plates (d). It is possible to increase the magnitude of this critical voltage by increasing d

and reducing loverlap.

According to the suspension system, crab-leg flexure type suspension system is utilized in our

tool; thus, Eq. 15 will be used to obtain the stiffness (Kx) of springs [5]:

Advanced Materials Research Vol. 159 317

+

+=

1221

1221

3

1

1

4

24

ILIL

ILIL

L

EIkx (15)

( )

+

+= 2

3

3

11221

12211max

...).4.(2

24d

lhLILIL

ILILEIv

overlapε (16)

By the proposed formulation here, the stiffness of the beams according to the dimensions of our

model is calculated and consequently the critical voltage obtained and showed to be 33 volts. It

means that if we apply voltages more than 33 volts, our structure will become unstable and does not

work properly.

Finite Element Simulation

To evaluate the output displacements of the microgripper prongs, finite element simulation using

commercial FEM software [9] is performed. As mentioned above, two models are proposed to

investigate the increase in deflection of the prongs. Half of the 2D model of microgripper is

modeled in software due to the symmetric geometry of the tool and since plunger has no effect on

prongs’ deflection, it is eliminated in simulations. The input voltage to actuate the microgripper is

33 volts according to results of maximum possible input voltage in the previous section. The

considerations for analysis of each model are as follows:

Model A. In model A, structural-electrical coupled field analysis is performed. The input voltage

will produce electrostatic force in comb-drive mechanism and its longitudinal motion will be

converted to rotational movement of the prongs.

The only material which exists in this analysis is polysilicon and its structural and electrical

properties should be considered as outlined in Table 2. The permittivity constant which is attributed

to the air between electrodes is 8.85e-12 F/m.

Model B. In the second model, the analysis is more complicated. In addition to structural-

electrical coupled field for the base structure of microgripper, another structural-thermal-electrical

coupled field should be analyzed for the modified U-shape electrothermal actuators which are

added to the arms. By applying the same voltage as model A (20 volts in parallel) to the anchors of

microgripper and electrodes a and b of heatuators (refer to Fig. 3), open and closed states of prongs

are simulated respectively and the results are measured.

Because of the thermal field which is added model B, thermophysical properties for polysilicon

should be considered in the simulation too. Moreover, the Cr/Au thin layers are the current

conducting elements and their structural-thermoelectric properties according to Table 2 are essential

for analysis.

Table 2. Thermophysical Properties for Poly-Si [10], Cr [11] and Au [12].

Property Poly-Si Cr Au

Young’s modulus [GPa] 169 279 79

Poisson Ratio 0.3 0.21 0.44

Electrical Resistivity [Ω.m] 4.2 e-4 125e-9 22.4e-9

Thermal Expansion Coefficient [µm/mK] 2.568 4.9 14.2

Emissivity 0.7 0.26 0.07

Thermal Conductivity [W/mK] 146.4 93.7 318

Results and Discussion

As described in the previous section, a potential difference (20 volts) lower than the pull-in

threshold voltage (33 volts) is applied to the anchors of microgripper and heatuators in analysis.

Fig. 6 shows the displacement contour of the primary model (model A) of microgripper. The right

figure is a focused view of the arm, prong and s-type flexible beam to clarify the motion. Maximum

displacement of 19.215 micrometers is achieved upon applied voltage in model A.

318 Micro Nano Devices, Structure and Computing Systems

Fig. 6. Displacement contour of model A. (V=20 volts).

In the second model (model B) again 20 volts is applied to microgripper arms and also

heatuators in parallel. The observed deflection increased to 39.603 micrometers in closing state and

31.427 micrometers in opening state. In Fig. 7, the left and right contours show closing and opening

motions of the microgripper prong, respectively. In closing operation, there is an overlap between

the displacements of electrostatically-driven arm and heatuators, while the only actuating element to

open arms is the electrothermal actuator. This is the reason why forward displacement in closing

operation is greater than backward displacement in opening state. In other words, our designed tool

is normally open and there exists no electrostatic element to open arms; adding electrothermal

actuators not only will enhance the range of displacements, but also serves to be the opener of

microgripper prongs.

Fig. 7. Displacement contour of model B. Closing state (left), Opening state (right) (V=20 volts).

It is inferred from the results that the modified actuator in this paper which is facilitated with

heatuators produced maximum deflection of 39.603 micrometers with input potential difference of

20 volts which is far from the likelihood of pull-in threshold with a safe margin. While the reported

magnitudes of maximum output displacement from the identical micrigrippers with s-type spring

beams [13] only reaches to 25 micrometers under 80 volts potential difference which obviously

involves much more electrical power consumption.

Summary

We have designed a hybrid type electrostatic-electrothermal microgripper to hold and manipulate

objecs with micron dimensions. Electrostatic part is driven using comb-drive mechanism. The

electrothermal part consists of two modified U-shape electrothermal actuators (heatuators) in which

Cr/Au heating electrodes drive the actuator rather than joule heating. The efficiency of modified

Advanced Materials Research Vol. 159 319

heatuator is enhanced by eliminating parasitic joule heating which drives the common types of U-

shape actuators. S-type spring beams are used to convert the longitudinal displacement to arms’

rotational movement. Moreover, to prevent parts’ sticking to the prongs of actuator,

electrothermally-actuated plunger is settled between comb-drive mechanisms.

Coupled field finite element analysis performed on the basic and hybrid model of microgripper.

Though being actuated by the same voltage, results of simulation showed that hybrid microgripper

produces 20.388 and 12.212 micrometers greater in forward and backward displacements,

respectively in comparison with the basic model. The input voltage has been considered to be 20

volts and maximum output deflection reached to 39.603 micrometers. While reported values of

maximum deflection in microgrippers which resemble our basic design, is 25 micrometers with 80

volts actuating potential difference and so the efficiency is not comparable to our proposed model.

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Micro Nano Devices, Structure and Computing Systems 10.4028/www.scientific.net/AMR.159 Displacement Amplification of Electrostatically-Driven Microgripper in a Hybrid Design with

Electrothermal Actuation 10.4028/www.scientific.net/AMR.159.313

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