DSpace at VNU: Analytical modeling of a silicon-polymer electrothermal microactuator

In order to enhance the reliability and safety of the manipulation, the integrated position and force sensors such as piezoelectric sensor, piezoresistive sensor and capacitive sensor we

DOI 10.1007/s00542-015-2700-7

TECHNICAL PAPER

Analytical modeling of a silicon‑polymer electrothermal

microactuator

Huu Phu Phan 1 · Minh Ngoc Nguyen 1 · Ngoc Viet Nguyen 1 · Duc Trinh Chu 1

Received: 13 July 2015 / Accepted: 30 September 2015

© Springer-Verlag Berlin Heidelberg 2015

piezoelectric, pneumatic and electromagnetic approaches have been employed to drive MEMS microgrippers (Jiang

et al 2007; Hsu et al 2002; Chen et al 2009; Beyeler et al

2007; Chu Duc et al 2007) Moreover, the integrated posi-tion and force sensors can deliver real-time feedback sig-nals to protect both the microgripper and grasped object from damaging (Menciassi et al 2003; Chu Duc et al

2006; Chronis and Lee 2005)

Owing to different properties of actuators, the MEMS microgrippers exhibit diverse dedicated performances to various applications For example, electrostatic actuation microgripper can provide a large displacement with no hys-teresis in a low operating temperature along with a simple structure (Chan and Dutton 2000) Specifically, two dif-ferent types of movement configuration in terms of lateral comb drive and transverse comb drive can fulfill the objec-tive of high precision and large movement, respecobjec-tively (Beyeler et al 2007) In addition, electrothermal actuator can generate a large output force and displacements by making use of its thermal expansion with a small-applied voltage (Chu Duc et al 2007) On the other hand, the large force output, precision displacement and rapid response are the attractive points of the piezoelectric actuator Besides, electromagnetic actuator and pneumatic actuator driven microgrippers can provide a relatively large output force and displacement (Butefisch et al 2002; Lee et al 1997)

It is known that force sensing is necessary for a deli-cate micromanipulation task Nonetheless, before the force feedback sensor is applied, the optical method has been widely studied (Miao et al 2004; Rembe et al 2001) Recently, researchers showed a great interest in the sensors with high resolution and sensitivity In order to enhance the reliability and safety of the manipulation, the integrated position and force sensors such as piezoelectric sensor, piezoresistive sensor and capacitive sensor were designed

Abstract This paper illustrates both thermal and

mechan-ical analysis methods for displacement and contact force

calculating of a novel sensing silicon-polymer

microgrip-per when heat sources are applied by an electric current

via its actuators Thermal analysis is used to obtain

tem-perature profile by figuring out a heat conductions and

con-vections model Temperature profile is then applied into

the mechanical structure of the gripper’s actuators to form

the final equation of displacement and contact force of the

jaws Finally, the comparison among the calculation,

simu-lation and actual measurement concludes that

materializa-tion methods are appropriate Achieving the final equamaterializa-tion

of gripper’s jaws displacement and contact force is a major

step to optimize or reform this novel structure for different

sizes to meet specific applications

1 Introduction

In recent years, microelectromechanical systems (MEMS)

have been widely applied in diverse science and

engineer-ing domains (Cheng et al 2008) MEMS-based

microgrip-pers provide advantages in terms of their compact size

and low cost, and hence play an important role in

micro-assembly and micromanipulation fields for manipulating

micromechanical elements, biological cells (Cheng et al

2008; Zhang et al 2013) During the past two decades,

microactuators based on different actuation principles

such as shape-memory alloys, electrostatic, electrothermal,

* Huu Phu Phan

phanhuuphu82@gmail.com

1 University of Engineering and Technology, Vietnam National

University, Hanoi, Vietnam

to provide the real-time position and force information

(Chu Duc et al 2006; Menciassi et al 2003; Chronis and

Lee 2005) Thanks to the advances in the technologies, the

sensitivity and resolution of the sensor have been improved

substantially

A novel design of polymer-silicon electrothermal

inte-grating force sensor microgripper is presented and

charac-terized (Chu Duc et al 2007b, ; 2008) The device consists

of laterally stacked structures based on a three-element

composite: the metal heating layer, heating conducting

sili-con structures and a polymer The heat is highly efficient

transferred from the heater to the polymer by employing

the high heat conduction rate of the deep silicon serpentine

structures that have a large interface with the surrounding

polymer The proposed device is based on the SU8-2002

polymer with a large thermal expansion coefficient This

design overcomes the weakness of the other designs and it

boats a large lateral jaw movement with low coupled

ver-tical motion and fast response time Another advantage is

that the device is made of regular silicon wafers which are

compatible with CMOS technology fabrication process

Thus, control circuits can be integrated into the structure

with the sole manufacturing process

For the characterization of the microgripper, HP4155A

semiconductor parameter analyzer is used The displacement

is monitored by the CCD camera on the top of the probe

station The thermal behavior of the microgripper is

investi-gated by using a built-in external heat source from the

Cas-cade probe station A DSP lock-in amplifier SR850 is used

to characterize the response frequency of this sensing

micro-gripper The sensing microgripper (490 μm long, 350 μm

wide, and 30 μm thick) can be used to grasp an object with

a diameter of 8–40 μm A microgripper jaws displacement

up to 32 μm at applied voltage of 4.5 V is measured with

a maximum average working temperature change of 176 °C

The output voltage of the piezoresistive sensing cantilever

is up to 49 mV when the jaws displacement is 32 μm The

force sensitivity is measured as being up to 1.7 nN/m and

the corresponding displacement sensitivity is 1.5 kV/m The

bandwidth frequency of this sensing microgripper is 29 Hz

The minimum detectable displacement and minimum

detect-able force are estimated to be 1 nm and 770 nN, respectively

(Chu Duc et al 2007b, 2008) These characteristics make the

sensing microgripper entirely suitable for applications where

force feedback is needed, such as microrobotics,

microas-sembly, minimally invasive and living cell surgery

Although measurements were conducted throughout,

initial simulation model for this device was quite simple

COMSOL—a finite element modeling tool is used to

sim-ulate the operation of this sensing micro-gripper

Three-dimensional models are employed to analysis the elasticity,

displacement, temperature distribution of the

microactua-tor The model only comprises one transmission which is

from assumed heat inputs to movements, while the grip-per works base on a voltage source Therefore, completely model (with electrical input parameters) and careful analy-sis are needed to improve the accuracy of the simulated and calculated values and physical properties of the gripper The heat transfer and mechanical calculation of the microgripper basing on thermal, mechanical and thermal– mechanical combination analysis are presented in this paper Firstly, the operation principle of the sensing micro-actuator based on silicon-polymer electrothermal micro-actuator and piezoresistive force sensing cantilever is thoroughly understood using thermal and mechanical analysis Follow-ing these steps, calculation results are compared with 3-D simulation and the fabricated sample characterized param-eters for verification of gripper’s mathematical equations Finally, a method for structure optimization is proposed basing on combination of changing equations’ factors and the simulation

2 Design and operation of silicon‑polymer electrothermal microactuator

The microgripper is designed for the normal opened operat-ing mode with two actuators on opposite sides Each actua-tor has a silicon comb finger structure with the aluminum metal heater on top (Chu Duc et al 2007d) A thin layer

of silicon nitride is employed as the electrical isolation between the aluminum structure and the silicon substrate Each actuator consists of silicon comb fingers with SU8 polymer layers in between When the heater is activated, the generated heat is efficiently transferred to the surround-ing polymer through the deep silicon comb fsurround-inger structure that has a large interface area with the polymer layer The polymer layers expand along lateral direction which leads

to bending displacement of the actuator arms

The design of the actuator is shown on Figs 1 and 2

which is the right arm of the sensing microgripper sys-tem Ideally, both arms of the gripper are similar geometry and characteristic Therefore, calculations and simulations

of the gripper are took place on one arm The structure is based on the combination of a silicon-polymer electro-thermal microactuators and piezoresistive lateral force-sensing cantilever beams When the electrothermal actuator

is warmed up by applying electric current through its alu-minum heater, the microactuator’s arm and also the sensing cantilever are bent This causes a difference in the longitu-dinal stress on the opposite sides of the cantilever, which changes the resistance values of the sensing piezoresistors Due to the correlation of the displacement of the microac-tuator jaws and resistance of piezoresistors, positions of the actuator jaws can be monitored by the output voltage of the Wheatstone bridge of the piezoresistive sensing cantilever

beam Besides that, the contact force between the

microac-tuator jaws and clamped object is then determined, relying

on displacement and stiffness of microactuator arms (Chu

Duc et al 2007b)

Readers are referred to the Ref (Chu Duc et al 2007b,

c, 2008) for further information on this proposed sensing

microactuator

3 Silicon‑polymer electrothermal actuator

The fabricated electrothermal silicon-polymer

microac-tuator and its geometry dimension parameters is shown in

Fig 3 and Table 1 respectively A full sensing

microactua-tor illustrates with 490 µm long, 110 µm wide and 30 µm

thick The design, fabrication and initially characterization

of the proposed sensing microgripper are reported (Chu

Duc et al.)

Figure 3a is SEM picture of the sensing

microgrip-per based on silicon-polymer electrothermal actuator

with a force sensing silicon cantilever Beside the

sens-ing function, the cantilever heat energy in the

electro-thermal actuator is conducted to the anchor through this

cantilever

In this work, the heat transfer is analyzed based on

two configurations without and with the silicon cantilever

(see Fig 3) The configuration without silicon cantilever removes the heat conduction through the sensing cantilever for analyzing the mechanism operation of the electrother-mal actuator (Fig 3b) The actuator displacement is then calculated by using a traditional mechanical method

3.1 Thermal analysis

The whole structure is heated by the aluminum layer on the surface of silicon bone which is considered the main heat source of the microgripper When aluminum filament ter-minals are connected to a power source, that layer is heated

by the Joule-Lenz’s law In that case, the thermal energy is transferred to the silicon-polymer stack The polymer

lay-ers, after heated up, expand in the x-axis, causing bending

displacement of the actuator arms In general, conduction, convection and radiation are three mechanisms of heat flow The electrothermal actuator is operated in the air ambient where two heat transfer mechanisms in analysis: conduc-tion in the actuator and convecconduc-tion to the surrounding air are considered Because the working temperature is lower than 500°K, the radiation transfer can be neglected (Howell and Robert Siegel)

The major thermal dissipation is caused by the conduc-tion to the silicon substrate and the convecconduc-tion to the air Temperature can be assumed to be uniform throughout the thickness because it is very thin; therefore the actuator is regarded as a one-dimensional case Eventually,

calcula-tions and analysis are conducted in x-axis while y-axis is

ignored

In the steady state, the heat is stored in volume unit

between x and x + ∆x given by (Stephen 2001):

(1)

x + ∆x

x

q G.y.dx

Polymer Aluminum heater

GND V+

Silicon Moon direcon Anchor

Fig 1 Schematic drawing of the silicon-polymer electrothermal

microactuator

H SU8 H Si L H Al

Lco

W bone

W gap

W can

L jaw

Silicon SU- 8 polymer Aluminum

Fig 2 Front-side view of the silicon-polymer electrothermal

micro-actuator with geometry symbols and parameters

Fig 3 SEMS pictures of a fully sensing electrothermal silicon-poly-mer microactuator; b removed silicon cantilever configuration

The heat loss from left and right side of polymer-silicon

stack is given by:

The heat loss due to convection is expressed by:

Implying the conservation law:

The equation of temperature by x is then obtained as:

This is the quadratic differential equation which has the

root given by:

Applying boundary conditions: T(0) = T0; dT (x=L)

dx =0

The coefficients C1, C2 and C3 are given by:

For the fabricated microgripper, the resistor of

alu-minum layer is about 149.018 Ω When it is applied a

volt-age of 4 V, the heat power is calculated about 0.107 W

Thus, q G∼= 6.941e6 W/m2 (it is the power dissipation over

the aluminum filament area)

The value of α is in the range from 2 to 25 W/m2K

(Howell and Robert Siegel), thus, the highest value of

2αTair is 15 × 103 W/m2 Comparing to the value of

q G = (6.941) × 106, the convection is neglected, therefore:

Following is the outcome of a similar method, we have

the function describes the temperature distribution in the

actuator:

Figure 5 shows the calculated temperature distribution in

the microgripper It is clear that the steady state temperature

(2)

Q C = .t.y. ∂T (x + ∆x)

∂T (x)

∂

(3)

Q conv = −2α(T (x) − T0).y.∆x

(4)

Q G+Q C+Q conv=0

(5)

T′′(x) −2α

tT (x) = −

q G+2αT air

q G+2αT0

t

(6)

T (x) = C1.e

2α

t x

+C2.e−

2α

t x

+C3

(7)

C1= −

q G

2α.e−

2α

t L

e

2α

t L

+e−

2α

t L

(8)

C2= −

q G

2α.e

2α

t L

e

2α

t L

+e−

2α

t L

(9)

C3=T0+q G

t

(10)

T′′(x) = − q G

t

(11)

T (x) = − q G

2t x

2+q G L

t x + T0

distribution rises dramatically along the actuator in form of half parabola The maximum temperature of actuator peaks nearly 270 °C at the tip when 4 V between two terminals of the aluminum heater is applied

3.2 Mechanical analysis

Considering that the microgripper is a bimorph cantilever that consists of two different materials: the silicon-polymer stack layer and silicon layer It can be supposed as single material bars because these parts are calculated to obtain apparent parameters Therefore, this simplified model is

(a)

(b)

Fig 4 Cross-side and front-side view of the removed silicon

cantile-ver structure for thermal analysis

Table 1 Geometry of the sensing microactuator design

Gap between actuator and silicon cantilever W gap 22 µm

probably appropriate for the structure When the bimorph

cantilever is heated, causing the different expansion of two

materials, the cantilever is bent as shown in Fig 6 (Chu

Duc et al 2007c)

It is assumed that the average temperature increases ∆T,

and the bending displacement of microgripper is d Thus,

the curvature of cantilever can be calculated as follows:

where αSi is the thermal expansion coefficient (CTE) of

silicon; αstack is the apparent CTE of the silicon-polymer

stack; n = E Si

E stack , m = W b

W c ; E Si is the Young’s modulus of

silicon; E stack is the Young’s modulus of silicon-polymer

stack

(12)

k cur= 1

ρ =

6(αstack− αSi )(1 + m)2∆T (W comb + W bone )(3(1 + m)2+ (1 + mn)m2 +mn1)

The displacement d of the bimorph cantilever is:

It is assumed that the zero point of x-axis is the border

between the anchor and the actuator (Fig 4a) Considering

component dx with temperature is T(x), radius of the

acti-vating actuator’s curvature can be calculated by applying

the Timoshenko calculation at x (Stephen 2001), as illus-trates below:

The average temperature:

The average temperature increase ∆T:

The curvature of whole structure based on x coordinate:

(13)

d = k cur L

2

act

2 for L act ≪ ρ

(14)

k cur−x= 6(αstack− αSi)(1 + m)2∆T x

(W c+W b)(3(1 + m)2+ (1 + mn)m2+mn1)

(15)

T x= 1

x

x

0

(−q G 2t x

2

+q G L

t x + T0)dx = −

q G

6t x

2

+ q G L 2t x + T0

(16)

∆T x= −q G

6t x

2+q G L

2t x

(17)

k cur = 1 ρ

= 6(αstack− αSi )(1 + m)

2

(W c+W b )(3(1 + m)2+ (1 + mn)m2+mn1 )

−q G 6t x

2

+q G L 2t x

Fig 5 Calculated temperature distribution on the microgripper

Fig 6 Sketch of the bimorph structure consisting of the silicon bone

and the silicon-polymer lateral stack composite

(a)

(b)

Fig 7 Cross-side and front-side view of the silicon-polymer

electro-thermal microactuator for electro-thermal analysis

Thus, the displacement d of cantilever based on x

coordinate:

4 Microgripper based on silicon polymer

electrothermal actuator with sensing function

4.1 Thermal analysis

Figure 7 shows the cross-side and front-side view of the

proposed silicon-polymer electrothermal microactuator for

thermal analysis Thermal energy in the actuator is diffused

to the anchor as the heat-sink by heat conduction transfer

through the actuator-anchor interface and also silicon

canti-lever, see Fig 7b Beside the conduction, heat energy is lost

by convection to the surrounding air, see Fig 7a

The temperature can be assumed to be uniform

through-out the thickness due to the thickness of the structure is much

smaller than other geometry parameters Thus, the

tempera-ture of y-axis is uniform so that the actuator is regarded a

one-dimensional case Therefore, the electrothermal

micro-actuator can be simplified as a bar shown in Fig 7b

In the steady state, the heat is stored in volume unit between

x and x + ∆x given by (Arfken 1985; Trodden 1999):

The heat loss in the left and right side of silicon-polymer

stack is given by [36]:

The heat loss due to convection is expressed (Arfken

1985; Trodden 1999; Snieder 1994):

Applying the conservation law:

The equation obtains:

This is the quadratic differential equation which has the

root given by:

(18)

d = k cur x

2

2

= 6(αstack− αSi )(1 + m)

2

L act2

(W c+W b )(3(1 + m)2+ (1 + mn)m2+mn1)

q G

4t(−

x4

3 +Lx3)

(19)

x+∆x

x

q G y.dx

(20)

Q C = .t.y. ∂T (x + ∆x)

∂T (x)

∂

(21)

Q conv = −2α(T (x) − T0).y.∆x

(22)

Q G+Q C+Q conv=0

(23)

T′′(x) −2α

tT (x) = −

q G+2αT air

q G+2αT0

t

Inserting the Eq (23) into (24), we obtain:

Applying boundary conditions:

T (0) = T0

Thus,

The sensing actuator has a silicon cantilever beam (Chu Duc et al 2007b, ) where existence of heat transfer between silicon-polymer stack and cantilever beam is:

The equation becomes:

The coefficients C1, C2, C3 are given by

Temperature profile on the silicon cantilever is also cal-culated by:

At x = L, T(L) = T can (L), so that:

The temperature distribution in the actuator is given by inserting the Eq (33) into the Eqs (29), (30), (31)

(24)

T (x) = C1.e

2α

t x

+C2.e−

2α

t x

+C3

(25)

C3=T0+q G

2α

(26)

C1+C2+C3=T0

(27)

Si dT (x = L)

(28)

C1

 2α

t e

2α

t L

−C2

 2α

t e

−

2α

t L

= −q cond

Si

(29)

q cond

Si

2α

t

+q G

2α.e−

2α

t L

e

2α

t L

+e−

2α

t L

(30)

− q cond

Si

2α

t

+q G

2α.e

2α

t L

e

2α

t L

+e−

2α

t L

(31)

C3=T0+q G

2α

(32)

T can (x) = q cond

Si x + T0

(33)

q cond = Si

q G

2α( 2

e

 2α

t L+e−

 2α

t L

−1)

1

2α

t

e−

 2α

t L−e

 2α

t L

e

 2α

t L+e−

 2α

t L

−L

Let τ = L2α

t

Thus,

C1, C2 are given in Eqs (34) and (35)

Basing on the function of temperature with real

param-eters coming from fabricated version of the gripper, Fig 8

plots profile of temperature versus the length (the resistor of

aluminum layer is about 149.018 Ω, heat power is 0.136 W

when applied voltage of 4.5 V, and q G∼= 8.784e6W/m2)

As shown in the results of temperature distributions

chart, temperature is varied from the base to tip with a

par-abolic form appropriate to earlier calculation The

arrange-ment on the cantilever is linear and peaks at nearly 200 °C

at the tip

Due to the existence of cantilever, the former analytical

manner to attain tip’s displacement is ineffective The

dis-placement and gripping force at the tip is calculated by the

direct displacement method

4.2 Thermal–mechanical analysis

A simplified structure which is used to analyze the sensing

microactuator under the change of temperature is shown in

Fig 9 It can be seen from the figure that lines AB, CD and

EF denote beam elements representative of silicon-polymer

stack, silicon bone, and silicon sensing layers, respectively

Those beam elements are fixed on one end, and connected

together by a rigid beam BDF on the other end Denote E ij,

A ij and I ij to be Young’s modulus of material, cross-section

area and moment of inertia of cross-section for the beam ij,

respectively

The silicon-polymer stack beam AB length increases

when power is applied The performance of the

silicon-polymer stack is analyzed based on the hydrostatic

pres-sure according to the constraint effect (Chu Duc et al

2007d) Note that for the beam AB, equivalent values of

the above parameters are adopted on (Chu Duc et al

2007d)

In this calculation, it is assumed that the change of

aver-age temperature on elements AB and CD is ΔT.

(34)

C1= −q G

2α

( 2

eτ +e−τ−1)

e−τ −eτ

eτ +e−τ

−τ +e−τ

eτ +e−τ

(35)

C2= −q G

2α

−(

2

eτ +e−τ−1)

e−τ −eτ

eτ +e−τ

−τ +eτ

eτ+e−τ

(36)

T (x) = C1.eτL x+C2.e−τL x+T0+q G

2α

4.3 Sensing microactuator displacement analysis

Figure 10 shows the deformation of the structure under the

change of temperature in beams AB and CD As shown in the graph, Z 1 and Z 2 denote the unknown rotation and

verti-cal deflection of the rigid beam BDF Here, it is assumed that the axial expansion of elements EF is neglected.

In order to calculate the displacement and the output force at the jaw tip of the sensing micro gripper, the direct

Fig 8 The calculated temperature profile on sensing microactuator

G

E AB , A AB , I AB

E EF , I EF

h 1

h 2 h

E CD , A CD , I CD

Fig 9 Frame structure to analyse the sensing microactuator

Z 1

Z 2

F’

D’

B’

y(T)

∆Τ

∆Τ

Fig 10 Deformation of the structure

displacement method is used Under the change of

temper-ature ΔT, the governing equation for the system is given

by:

where

Equations (38) denote stiffness matrix of the structure,

displacement vector and output force vector, respectively

To determine stiffness coefficients, unit displacements are

applied Diagrams of bending moments in structural

ele-ments are performed in Figs 11 and 12 in the cases of

Z1 = 1 and Z2 = 1

Axial forces in elements AB and CD under the applied

unit displacement Z1 = 1 are given by:

(37)

KZ(T ) = R(T )

(38)

K =

r11 r12

r21 r22

Z1(T )

Z2(T )

; andR(T ) =

R1(T )

R2(T )

(39)

N AB1 =∆L AB E AB A AB

L = hE AB A AB

L ,

N CD1 = ∆L CD E CD A CD

L = h2E CD A CD

L

Note that axial forces in elements AB and CD due to

Z2 = 1 are zero Based on conditions for static balance of the structure, stiffness coefficients are given by:

Components R1(T) and R2(T) of the force vector are cal-culated basing on axial forces on elements AB and CD due

to the change of temperature ∆T We have

Solving the Eq (1), we yield

where det K = r11r22 − (r12)2

Vertical displacement y(T) of the microactuator jaw tip

under the change of temperature is therefore given by

Sensing microactuator output force analysis Figure 13 illustrates the structure which estimates the contact force between the microactuator jaw and the manipulating object

The unknown force F is calculated from the following

condition:

where y(F) denotes the vertical displacement due to the reaction force F.

Like the above procedure, the governing equation for

solving the displacement y(F) is given by:

(40)

r11 =4E AB I AB

L +4E CD I CD

L +4E EF I EF

L +h2E AB A AB

2E CD A CD

r22 =12E AB I AB

L3 +12E CD I CD

L3 +12E EF I EF

L3 ,

r12 = r21 = −6E AB I AB

L2 +6E CD I CD

L2 +6E EF I EF

L2

(41)

R1(T ) = α1∆TE AB A AB h + α2∆TE CD A CD h2,

R2(T ) = 0

(42)

Z1(T ) = r22R1(T )

det K ; Z2(T ) = −

r12R1(T )

det K

(43)

y(T ) = Z1(T )L Jaw+Z2(T ) = R1(T )

det K r22L jaw−r12

(44)

y(T ) + y(F) = h3

(45)

KZ(F) = R(F)

Z 1 = 1

2E I AB AB

L

2E I CD CD

L

4E I CD CD L

EF

2E I EF

Fig 11 Diagram of the bending moment due to Z1 = 1

2

6E I AB AB L

Z 2 = 1

2

6E I CD CD L

2

6E I EF EF

L

Fig 12 Diagram of the bending moment due to Z2 = 1

F’

D’

B’

∆Τ

∆Τ

F

F G

h 1

h 2 h

h 3

Manipulating object

Fig 13 Structure for solving the output force

Solving the Eq (45), we yield

The vertical displacement of the jaw tip due to the

reac-tion F is given by:

Taking the above result into Eq (44), we obtain the

value of gripping force:

5 Measurement, calculation, simulation results

and discussions

The design, fabrication and initially characterization of

the proposed sensing microgripper is reported in the ref

(Chu Duc et al 2007b; Chu Duc et al.) and calculation

results were mention in this paper In addition, a

3-Dimen-tion computer model of this device which comprises two

conversions (electricity to heat and heat to movement) for

simulating in virtual medium Elasticity, movement,

tem-perature profile, power consumption of the actuator are

generated by COMSOL (Comsol Inc.)—a finite element

modeling tool - based on conversion of electricity to heat

R1(F) = −FL jaw; R2(F) = −F

(46)

Z1(F) = det K1 {r22R1(F) − r12R2(F)},

Z2(F) = − det K1 {r12R1(F) − r11R2(F)}

(47)

y(F) = Z1(F)L Jaw + Z2(F)

= det K1 r22R1(F) − r12R2(F)L jaw + R2(F)r11− R1(F)r12

(48)

F = R1(T ) r22L jaw−r12 − h3det K

r11−2r12L jaw+r22(L jaw)2

and then heat to movement It is necessary to make com-parisons with relevant results to conclude the consistency

of each deductive method Therefore, those methods are tethered for an effective reconfirmation of the new size sensing microgripper system such as optimization param-eters for a specific application before fabrication steps are carried out

Figure 14 shows calculation, simulation and measure-ment results over the average working temperature of the sensing microgripper As can be seen from the chart, there are similar patterns of calculation and simulation which have approximately 30 % of deviation To clarify, errors of each method can contribute to this nonconformity Firstly,

in calculation, there was not mention resistance changes

of aluminum layer when temperature varies, and some variables such as convection and radiation were neglected Besides, there could be unknown structural ties that skipped

in simplifying gripper’s structure for the calculation Sec-ondly, some parameters of the model are fixed in ideal con-ditions and simulation results are gathered from perfectly surrounded environment Regarding measured results, most

of discrete points are in the range of the two lines of simu-lation and calcusimu-lation In addition, these plots can be linear fitted into a single line that in the same channel with previ-ous lines In short, results of displacement versus average working temperature of three methods are uniform

As regard to distribution of heat at steady state when voltage source (4.5 V) is applied to activate the gripper, Fig 15 illustrates temperature profiles on both actuator and cantilever which are obtained by calculation and simulation Due to the limitation of the measurement method (Chu Duc et al.), temperature on each position

of actuator and cantilever could not be gathered pre-cisely Thus, the results measured in comparison with

Fig 14 Displacement of the microgripper jaw tips at steady state vs

average working temperature

Fig 15 The temperature profile on sensing microactuator

these of other methods are ignored Obviously, there are

striking similarities in the results of calculation and

sim-ulation, and therefore, not only the mathematics

method-ology but also simulation model of the microgripper are

confirmed

As is shown in the results comparison among methods,

one methodology has confirmed the accuracy of others and

vice versa Although there are some errors and tolerances

of each method itself, the model for simulations and

calcu-lation scheme is appropriate Consequently, it is an

impor-tant factor to improve or adapt the gripper’s structure to

specific application Moreover, it can be used to optimize

the structure in a particular aspect For example, a new

microgripper which performs the same range of

displace-ment with the original one, but the operating temperature

below 100 °C can be designed Firstly, determine size of

the gripper (the number of polymer stacks or the length of

actuator) by using the final equation After that,

conduct-ing the simulation with model which has obtained

param-eters from the first steps, and therefore, the design via those

results is affirmed

6 Conclusions

The design of sensing polymer-silicon electrothermal

microgripper was proposed, characterized and simulated

This device has many advantages in comparison with other

actuators, such as large movement, fast response time,

low driving voltage and CMOS compatible However, it

is required analytical modeling to fully comprehend each

parameter of the design Therefore, optimization and

adap-tation for the new dimensional microgripper are based on

mathematical functions that have obtained

Analysis methods for this proposed sensing

silicon-polymer microgripper are introduced in this paper Firstly,

gripper’s temperature profile is calculated by using the

heat conductions and convections model Secondly, final

displacement and contact force equations are formed by

inserting temperature profile into the mechanical model

Finally, the direct displacement method is used for this

device’s displacement and output force analysis Besides,

functional parts of the gripper is considered and analyzed

separately

Microgripper operation is based on two main

trans-formations: electricity to heat and then heat to mechanic

The computation following these two models in turn to

form displacement and clamp force of the actuator is

applied Deviations between simulation, measurement

and calculation results are not significant There are great

steps to understand the devices better, and more scientific

approaches to determine the new size of actuator to suit

each specific requirement or optimize the design This pro-posed microgripper could be potentially used for micro-particle manipulation, minimally invasive surgery, and microrobotics

References

Arfken G (1985) Mathematical methods for physics, 3rd edn Aca-demic Press, Waltham

Beyeler F, Neild A, Oberti S, Bell DJ, Sun Y, Dual J et al (2007a) Monolithically fabricated microgripper with integrated force sensor for manipulating microobjects and biological cells aligned

in an ultrasonic field J Microelectromech Syst 16(1):7–15 Beyeler F, Neild A, Oberti S, Bell DJ, Sun Y, Dual J et al (2007b) Mono-lithically fabricated microgripper with integrated force sensor for manipulating microobjects and biological cells aligned

in an ultra-sonic field J Microelectromech Syst 16(1):7–15 Butefisch S, Seidemann V, Buttgenbach S (2002) Novel micro-pneu-matic actuator for MEMS Sens Actuator A-Phys 97(8):638–645 Carrozza MC, Dario P, Jay LPS (2003) Micromechanics in surgery Trans Inst Meas Control 25(4):309–327

Chan EK, Dutton RW (2000) Electrostatic micromechanical actua-tor with extended range of travel J Microelectromech Syst 9(3):321–328

Chen L, Liu B, Chen T, Shao B (2009) Design of hybrid-type MEMS microgripper In: Proceedings of the International Conference on Manufacturing Automation HongKong

Cheng CH, Chan CK, Cheng TC, Hsu CW, Lai GJ (2008) Modeling, fabrication and performance test of an electro-thermal microac-tuator Sens Actuator A-Phys 143:360–369

Chronis N, Lee LP (2005) Electrothermally activated SU-8 micro-actuator for single cell manipulation in solution J MEMS 14(4):857–863

Chu Duc T, Creemer JF, Sarro PM (2006) Piezoresistive cantile-ver beam for force sensing in two dimensions IEEE J Sens 7(1):96–104

Chu Duc T, Lau GK, Sarro PM (2007a) Polymeric thermal micro-actuator with embedded silicon skeleton: part II—fabrication, characterization and application for 2D Microactuator, JMEMS Chu Duc T, Lau GK, Creemer JF, Sarro PM (2007b) Electrothermal microactuator with large jaw dispalcement and intergrated force sensors In: Proceeding 21th IEEE Conference on MEMS, Tuc-son, USA, 13–17 January 2008, pp 519–522

Chu Duc T, Lau GK, Wei J, Sarro PM (2007c) 2D electro-thermal microactuators with large clamping and rotation motion at low driving voltage In:Proceeding 20th IEEE Conference on MEMS, Kobe, Japan, 21–25 January 2007, pp 687–690

Chu Duc T, Lau GK, Sarro PM (2007d) Polymer constraint effect for electro-thermal bimorph microactuators Appl Phys Lett 91:101902–101903

Chu Duc T, Lau G-K, Creemer JF, Sarro PM (2008) Electrothermal microactuator with large jaw displacement and integrated force sensors J Microelectromechanical Syst 17: 1546–1555

Howell JR, Siegel R, Menguc MP (2011) Thermal radiation heat transfer, 5th edn CRC Press, Boca Raton, London, NY, p 38 Hsu C, Tai WC, Hsu W (2002) Design and analysis of an electrother-mally driven long-stretch micro drive with cascaded structure In: Proceedings of ASME International Mechanical Engineering Congress New Orleans, Louisiana

Jiang J, Hilleringmann U, Shui X (2007) Electro-thermo-mechanical analytical modeling of multilayer cantilever microactuator Sens Actuator A-Phys 137:302–307