MEMS force microactuator with displacement

sensing for mechanobiology experiments

F. Cerini, M. Ferrari, V. Ferrari

Department of Information Engineering

University of Brescia

Brescia, Italy

fabrizio.cerini@ing.unibs.it

A. Russo, M. Azpeitia Urquia

STMicroelectronics

Italy

R. Ardito, B. De Masi

Department of Civil and Environmental Engineering

Politecnico di Milano

Milano, Italy

M. Serzanti, P. Dell’Era

Department of Molecular and Translational Medicine

University of Brescia

Brescia, Italy

Abstract—This paper presents a Micro Electro-Mechanical

System (MEMS) that performs electrostatic force actuation and

capacitive microdisplacement sensing in the same chip. By

driving the actuator with a given voltage, a known force can be

applied to a microsample under test by using a silicon probe tip,

while the obtained displacement is measured. This allows to

extract the mechanical properties of the microsample entirely on

chip, and to derive its force-displacement curve without external

equipment. The proposed device is intended for mechanobiology

experiments, where the microsample is made of biological tissues

or cells. The device generates a force in the order of few

micronewtons and a maximum displacement of 1.8 µm can be

measured.

Keywords—MEMS, electrostatic force actuator, capacitive

displacement sensing, mechanobiology.

I. INTRODUCTION

The use of micro electro-mechanical systems (MEMS) to

test mechanical properties of materials at the microscale is

especially promising for probing microbiological samples in

in-vitro mechanobiology experiments [1]. Mechanical

properties of cells are important factors to define their

functionality, to differentiate them, and play a role in tissue

formation. Moreover, changes in elasticity of the cells can be used as a marker to identify cell abnormalities that can be possibly correlated with various human diseases [2].

In order to measure the mechanical properties of microbiological samples, MEMS force actuators and sensors

have been proposed in the last years, employing different

actuation methods such as the electrothermal [3, 4] and

electrostatic [5] principles. Flexible-beam optical [6-8] and

capacitive [9, 10] force sensors have been also reported for

cellular force measurement and for mechanical

characterization of biomembranes [11]. Typically, the reported

configurations require external equipment to apply either the

force or displacement, while the complementary quantity is

measured by the microsystem.

In this context, the approach of this work is to integrate

both force actuation and displacement sensing on the same

chip that only has a pair of electrical input and output ports,

therefore enabling the measurement of the microsample

mechanical properties entirely on chip. Quantitative

biomechanics studies on single molecules or cells are expected

to be possible. The paper presents early results that validate

the principle.

The device description, operating principle and proposed

electro-mechanical model are illustrated in Section II,

experimental results are presented in Section III, and

conclusions are given in Section IV.

II. DEVICE DESCRIPTION, OPERATING PRINCIPLE AND

MODELLING

Fig. 1 shows the layout, relevant measured dimensions and

SEM images of the MEMS device.

The device has been designed and fabricated by using the

ThELMA process (Thick Epipoly Layer for Microactuators

and Accelerometers), developed by STMicroelectronics for

inertial sensors and actuators based on heavily doped

poly-silicon [12].

The mechanical microstructure consists of a central rigid

movable shuttle (denoted as R), which is supported and

anchored to the substrate by four folded-beam springs, as

shown in Fig. 1. Interleaved comb structures extending

laterally from the shuttle form variable-gap parallel-plate

comb-finger capacitors with similar structures on the stator

(denoted as S) solidly linked to the fixed frame.The resulting

configuration denoted as transverse combs has a capacitance

. The device also contains four variable-area comb-finger

capacitors between driver armatures (denoted as D) on the

frame and corresponding armatures on the shuttle R. The

resulting configuration denoted as lateral combs has a

capacitance .

Figure 2: Monodimensional equivalent mechanical model of the device with the electrical setup (a) and equivalent electro-mechanical lumped-element circuit (b).

Figure 1: Layout, measured geometrical dimensions and SEM images of the investigated MEMS device with enlarged views of drivers and spring (a), a set of

parallel-plate combs of the displacement sensor (b) and the probe tip (c).

The presence of both lateral combs (D-R) and transverse

combs (S-R) configurations offers a double possibility of

actuation of the movable shuttle together with the flexibility to

set different values of electrostatic force between fixed and

movable parts, independently of the parallel-plate distance.

In displacement sensing, transverse combs offer higher

sensitivity compared to the lateral combs configuration,

though the response is nonlinear [5]. For these reasons, in this

work, we use the D-R part for electrostatic force actuation and

the S-R part for capacitive displacement sensing, respectively.

Due to the device geometry, the movement direction of the

shuttle is along the longitudinal axis .

Fig. 2 illustrates the device operating principle by the use

of equivalent models based on the direct electromechanical

analogy (Voltage-Force; Current-Velocity).

The probe tip, visible in the inset of Fig. 1c connected to

the shuttle R, is used to press the microsample under test,

represented by its mechanical impedance , by applying a

known force , which can be set by imposing a proper

driving voltage to the driver capacitor . The sensing

capacitor is used to measure the probe tip displacement .

In the simplified monodimensional lumped-element model

of Fig. 2a, the shuttle is represented by a mass supported

by a spring with mechanical stiffness , accounting for the

a) b)

km d

MEMS

driver, CDR sensor, CSR

D

S

VDR

VSR(t)

LCR meterHP 4274A

H

L

substrate

R

PCGPIB

Data acquisitionand control

s

shuttlex

ZL

FDR m

m

dD

lS

+

-

probetipe

microsample

x'

x0

wkm d

MEMS

driver, CDR sensor, CSR

D

S

VDR

VSR(t)

LCR meterHP 4274A

H

L

substrate

R

PCGPIB

Data acquisitionand control

s

shuttlex

ZL

FDR m

m

dD

lS

+

-

+-

1/km

ẋprobe

tipeVDR FDR

CSR

x∫

microsample

FL ZL

x'

x0

w

a) b)

Drivers D[comb fingers]

shuttle R

Drivers D[comb fingers]

springs

# D1b

# D2b

# D3b

# D4b

# D1a

# D2a

# D3a

# D4a

probe tip

Sensor S[parallel plates]

driver # 1

driver # 2

# 1

# 2

driver # 3

driver # 4

# 3

# 41

.3 m

m

springs

springs

sen

so

r co

mb

s C

SR

sen

so

r co

mb

s C

SR

sh

utt

le R

370 µm

R

9.3

µm

4.2

µm

S

R

spring 300 µm

# 2

# 1drivers

ThELMA process

highly doped poly-silicon

sensor combs CSR

probe

tip

a)

b)

c)

y

x

z

mo

vem

en

t

Device part Length

(µm)

Width

(µm)

Gap

(µm) Number/note

Comb-fingers 13.5a 2.5 1.6 98

Parallel-plates 379 4.2 2.5 202

Flexural springsb 306 3.0 7.5 3-Folded

Central shuttle 1300 34.3 - Holes 6.3x6.3 µm2

Probe tip 169 5.3 - -

Out-of-plane

thickness 23.6 - - -

a. Initial overlapping length

b. Measures for each beam

Figure 5: Theoretical and measured electro-mechanical transduction factor

DR as a function of the applied voltage VDR.

Figure 3: Measured capacitance as a function of the tilt angle for a

driven voltage kept constant to 25 V. In the insets, pictures of device

tilted to -90°, 0° and +120° respect to the y axis.

Figure 4: Experimental values of measured at different levels of .

For each level, tilting angles of , and were applied,

while was kept constant to its no-tilting value ( ° case) by adjusting

. The blue line is the experimental behavior of as a function of

when no-tilting occurs.

14 16 18 20 22 24 26

22

24

26

28

30

32

34

36

VDR

[V]

CS

R [

pF

]

24.5 25 25.5

29

29.2

29.4

29.6

29.8

0° -90°

+90°

0°- behavior

+90° 0° -90°

total elasticity of the four folder beams. The parameters and

represent the spacing between two S-lamellae and the width

of an R-lamella, respectively. The position represents the

initial mechanical equilibrium point of the shuttle without

external electrical sources applied to the electrodes. The

equilibrium point can be influenced by an initial asymmetry due, for example, to a pre-stress of the folded beams, or the

initial offset due to contact of the microsample with the probe

tip before measurement. Consequently, can be expressed

as:

(1)

The quantity , representing the shorter distance between any

R-lamella and the neighboring lamella, and can be defined as:

(2)

The voltage applied between the terminals D and R as

shown in Fig. 2, results in the electrostatic force acting on

the shuttle given by:

(3)

The coefficient , representing the electro-mechanical

transduction factor between the force and the squared

voltage , can be expressed as:

[

(

)] (4)

where and are the dielectric permittivity of vacuum

and the relative dielectric constant of the gaseous medium,

respectively, the total number of R-lamellae faced to

D-lamellae, the gap between D- and R-lamellae, the

out-of-plane thickness lamella, and a parameter

which properly tunes the Palmer’s fringing field effect, as

reported in [13].

15 16 17 18 19 20 21 22 23 24 25 26 278.5

8.6

8.7

8.8

8.9

9

9.1

9.2

9.3

9.4

9.5

9.6

9.7

VDR

[V]

D

R [

nN

/V2]

15 16 17 18 19 20 21 22 23 24 25 268.5

8.6

8.7

8.8

8.9

9

9.1

9.2

9.3

9.4

9.5

VDR

[V]

D

R [

nN

/V2]

Experimental

Theoretical

15 16 17 18 19 20 21 22 23 24 25 268.5

8.6

8.7

8.8

8.9

9

9.1

9.2

9.3

9.4

9.5

VDR

[V]

D

R [

nN

/V2]

Experimental

Theoretical

-120 -90 -60 -30 0 30 60 90 12027.5

28

28.5

29

29.5

30

30.5

31

CS

R [

pF

]

Angle [°]

-90°

0°

+120°

y

x z

x y

z

y

x

z

Angle

Ø = 1 µm

MEMS

probe tip

glass

microtip

MEMS

probe tip

fixed cell

10 µm

3-axis micro-manipulator

with micropipet

TEST A TEST B

system

for cell

suction

MEMS chip

Figure 6: Experimental setup for positioning of the microsample with enlarged views of mechanical characterization of a glass bending microtip (Test A) and a

fixed fibroblast cell (Test B).

The total capacitance between the S and the R terminals,

can be expressed as:

(

) (5)

where is the sum of the parasitic capacitances, the

total number of R-lamellae faced to S-lamellae, and the

overlapping length.

From the expression of in Eq. (5), the following

close-form expression of the distance can be derived:

{ √ |

| } (6)

By inserting Eq. (6) into Eq. (2), the value of the displacement

, for a given force caused by an applied voltage , is

obtained.

Assuming that the chip plane is held horizontally and no

microsample is initially present (free conditions), than the

mechanical stiffness , can be derived by:

without microsample

(free conditions) (7)

If a microsample as the load is present, under the

simplifying assumption that it behaves as a spring with

mechanical stiffness , Eq. (7) becomes:

with microsample

as the load (8)

and the total stiffness, which increases up to , can be

determined. By subtracting the known value of , the

estimation of can be obtained.

III. EXPERIMENTAL RESULTS

The characterization tests described in this section were

performed using the experimental setup shown in Fig. 2a. In

order to measure , the LCR meter was set to provide a

sinusoidal signal with amplitude of and

frequency of , i.e. far from the resonant frequency of

the movable part that is around . The results presented in

this work were obtained by using the driver D2 only. The

terminals R, substrate SUB, and the unused driver terminals

D1, D3 and D4 are connected to the low terminal of the

LCR meter in order to avoid parasitic electrostatic phenomena

[14].

Given the geometrical layout, by tilting the device around

the axis, it becomes sensitive to the in-plane component of

Figure 7: Force-displacement characteristics measured in free conditions

(zero load) and with the glass bending microtip as the load. The mechanical

stiffness km of the spring and of the load kL results 3.62 N/m and 1.39 N/m,

respectively. The inset shows the measured capacitance CSR versus VDR .

Figure 8: Measured capacitance CSR as a function of the voltage VDR in free

conditions and with a fixed fibroblast cell on a micropipette as the load.

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 3420

22

24

26

28

30

32

34

36

38

VDR

[V]

CS

R [

pF

] with fixed cell

in free conditions

(zero load)

contact loss

between the

fixed cell and

the probe tip

residual position and

orientation changes of

the fixed cell with respect

to the probe tip

TEST A TEST B

the weight force acting onto the shuttle. Under tilting

around the axis of an angle between the axis and the

vertical direction, Eq. (7) can rewritten as:

(9)

where with is the gravitational

acceleration.

Fig. 3 shows the measured capacitance (in free

conditions) as a function of the tilt angle for an applied

kept constant to . As expected, the behaviour is

sinusoidal. In accordance with Eq. (9), the minimum and

maximum values of are reached for and

, respectively. In particular, when the

sign of is the same of the spring force and it is

opposite to , and vice-versa when . To calibrate the applied force as a function of the

voltage , an experimental calibration procedure by using

as reference has been adopted. During the tilting of the

device to and - , the displacement has been kept

unaltered by adjusting the voltage to the required level in

order to maintain constant. In this way, the mechanical

stiffness of the spring has no effect on the calibration.

Fig. 4 shows as the experimental values of measured at

different levels of . For each level, tilting angles of

, and were applied, while was kept constant

to its no-tilting value ( case) by adjusting . Each

value represented by a circle is the average of 30 consecutive

acquisitions with the error bars representing the interval

where is the standard deviation. The blue line shows the

experimental behavior of (in free conditions) versus

for . Under the condition of unaltered displacement , Eq. (9) can

be evaluated for and , and combined

with Eq. (3) to obtain the close-form expression of given

by:

(10)

where and are the values for

and , respectively.

Fig. 5 shows the experimental values of derived by

using Eq. (10) for different applied voltages VDR. The mass

, estimated from a SEM geometry analysis with a

poly-silicon density of , results to be of 24 µg. The

value of constant with

is in agreement with the theoretical value of Eq. (4)

within few percents.

When reaches the minimum value of for

, the shuttle is at the distance (i.e. in

condition of geometrical symmetry), and the total parasitic

capacitances estimated from Eq. (5) results to be

.

Fig. 6 shows the experimental setup adopted for testing the

microsystem and for the positioning of the microsample into

the device. The enlarged views show the glass bending

microtip and a fixed fibroblast cell used during the experiment

as two types of load under test.

-0.5 -0.2 0.1 0.4 0.7 1 1.3 1.6 1.9

0

2

4

6

8

10

x [m]

F [N

]

glass microtip

free conditions

(zero load)

0 5 10 15 20 25 3020

25

30

35

VDR

[V]

CS

R [pF

]

eq. FDR = 3.62 x + 0.16

eq. FDR = 5.01 x + 0.67

km + kL

km x' = 134 nm

x' = 45 nm

FL

FD

R

0 0.1

Fig. 7 shows the results of test A in which the

force-displacement characteristics of the device have been

measured in free conditions (zero load) and with a glass

bending microtip as the load . In free conditions, the

stiffness of results, constant throughout the

displacement range since no electrostatic effect on stiffness is

produced due to the variable-area configuration of the comb

actuator. With the bending microtip as the load, the stiffness

increases to and a change in the slope of the

force-displacement characteristic occurs. From the intercept at

, it is possible to extract the estimation of the initial

asymmetry of and in free conditions and

with the glass bending microtip as the load, respectively.

Fig. 8 shows the results of test B in which a single cell

(fibroblast) fixed for min in PFA (paraformaldehyde)

on a rigid micropipette has been used as the load . It can be

observed that the plot of versus clearly evidences a

specific behaviour when the cell is present. During the

measurement, some residual position and orientation changes

of the fixed cell with respect to the probe tip are visible, and

for higher than the contact between the cell and the

probe tip it is lost.

IV. CONCLUSIONS

A MEMS that performs electrostatic force actuation and

capacitive microdisplacement sensing on the same chip is

presented.

A monodimensional equivalent mechanical model of the

device and an equivalent electro-mechanical lumped-element

circuit based on the direct electromechanical analogy have

been proposed and validated in order to illustrate the device

operating principle.

An experimental calibration procedure by using the weight

force as reference has been adopted to estimate the value of

the electro-mechanical transduction factor . In this way, a

known force can be applied to a microsample under test by

using a silicon probe tip, while the obtained displacement is

measured from the measured capacitance .

The device has been used to measure the force-displacement

characteristics in free conditions (zero load) and with a glass

bending microtip as the load, resulting in mechanical stiffness

of and , respectively.

Measurements of the capacitance CSR as a function of the

voltage have been performed with a single fibroblast fixed

for min in PFA (paraformaldehyde), evidencing a

specific behaviour when the cell is present. This allows to

extract the mechanical properties of the microsample entirely

on chip, and to derive its force-displacement curve without

external equipment.

The proposed device allows to measure in both static and

dynamic regimes, therefore it can derive the complete

viscoelastic behavior of the microsample in mechanobiology

experiments.

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