A STUDY ON BIMETALLIC EFFECTS IN MICROCANTILEVER

BIOSENSORS

Mohd. Zahid Ansari and Chongdu Cho

Department of Mechanical Engineering, Inha University, Incheon, Republic of Korea

Keywords: Coefficient of thermal expansion (CTE), Thermal strain, Bimetallic effects, Microcantilever biosensor.

Abstract: This study investigates the bimetallic effects in a microcantilever biosensor induced due to change in

ambient temperature. The cantilever is subject to both thermal and surface stresses. The biosensor exploits

the surface-stress induced deflection to analyse the unknown molecules. However, due to bilayer structure

of the cantilever thermal deflections are produced, which are a common source of noise in the deflection

measurement. Thus, distinguishing surface-stress induced deflections from the thermal deflections is critical

in accurate measurement by the biosensor. In this theoretical work, we show that both thermal stress and

surface stress have linear effect on the cantilever deflections, and hence can be added algebraically to

determine the absolute deflection produced entirely due to the surface stress variation.

1 INTRODUCTION

Microcantilever based sensors are getting

increasingly popular in a variety of physical,

chemical, and biological studies. They can be

operated in both liquid and gaseous environments.

They have been successfully used in many cases

including calorimetric (Barness, 1994), rheometric

(Hennemeyer, 2008), gas sensor (Qazi, 2008), DNA

assaying (McKendry, 2002) and DNA hybridization

(Mertens, 2008). Due to label-free, rapid and real-

time detection abilities, microcantilever based

biosensors are very attractive. The sensors normally

use optical deflection readout techniques to measure

the deflections generated due to the change in

surface stress on the functionalized surface of the

biosensor. By measuring the deflection, the target

analytes are determined.

The overall accuracy of a microcantilever sensor

depends on the design sensitivity of the cantilever

and the measurement sensitivity of the deflection

measurement system. An efficient cantilever design

should convert the surface-stress induced stimulus

into large deflection of the cantilever, whereas, an

efficient measurement technique should ensure that

the deflections measured are induced entirely

because of the change in surface stress. Most of the

noise in deflection signal is due to thermal drifting

(Fritz, 2000). Thermal effects arise due to the bilayer

structure of the cantilever and change in the ambient

temperature. Microcantilever biosensor comprises

gold-coated thin silicon or polymer substrate

cantilever and laser-based optical deflection readout

scheme. The gold film helps formation of monolayer

of receptor molecules on the cantilever surface

during functionalization. The presence of gold film

coating on the cantilever, however, causes bimetallic

effects in the biosensor. The temperature change can

occur due to extrinsic or intrinsic sources. The

extrinsic sources can be the bulk fluid temperature

change in the fluidic cell during solution loading,

whereas, the intrinsic reasons can be the exothermic

or endothermic molecular reactions at the cantilever

surface. Depending on the thermoelastic properties

of film and substrate and the temperature change,

thermal deflection can easily exceed the surface

stress induced deflections, thus producing large

noise in the deflection signal.

In this work, we show that by knowing the

thermoelastic properties of the film and cantilever

material, analytical and numerical approaches can be

used to accurately predict the thermal-induced

deflections in microcantilever biosensors. Thermal

deflections induced due to variation in the ambient

temperature are calculated using analytical and

simulation results; and are then compared against

available experimental result. Finally, the combined

effect of thermal and adsorbate-induced surface

stress changes on the cantilever deflection is

Ansari M. and Cho C. (2010).

A STUDY ON BIMETALLIC EFFECTS IN MICROCANTILEVER BIOSENSORS.

In Proceedings of the Third International Conference on Biomedical Electronics and Devices, pages 28-31

DOI: 10.5220/0002725600280031

 SciTePress

investigated. A finite element analysis (FEA) code

ANSYS Multiphysics is used in simulations.

2 THEORY AND SIMULATION

Bimetallic effects are common phenomena that arise

in multilayered structures when subjected to

temperature change. The mismatch in their

coefficients of thermal expansion (CTEs) results in

thermal strain, causing deflections in the structure.

The amount and direction of motion depends on the

CTEs of the layers. If the CTE of substrate is higher

than that of film and the change in temperature is

positive, the deflection will be upwards. Surface or

film stresses are generated either due to the

adsorbtion of foreign atoms onto a surface to

saturate the dangling bonds or due to residual

thermal stresses induced during fabrication and/or

operation of the element.

Assuming the film thickness (t

) is infinitesimal

compared to the substrate thickness (t

), Stoney

expression (Stoney, 1909) relating the transverse

deflection (Δz

) in a microcantilever to adsorbtion-

induced surface stress change (Δσ

) can be given as

4(1 )

sss

νσ

⎛⎞

−Δ

Δ=

⎜⎟

⎝⎠

(1)

where E

and ν

are elastic modulus and Poisson’s

ratio of the cantilever material, and L is cantilever

length. Similarly, the Stoney relation between

thermal deflection (Δz

) and thermal-induced

surface stress (Δσ

) can be given as

4(1 )

sth

νσ

⎛⎞

−Δ

Δ=

⎜⎟

⎝⎠

(2)

where

()

th f f s f

tE T

αα

Δ= − Δ(Hsueh, 2002) is the

film stress induced due to temperature change ΔT;

and α

are the CTEs of the substrate and film.

Equation (1) is used commonly in microcantilever

biosensor applications to determine the analyte

biomolecules and to measure their concentrations.

Equation (2) is generally used in micro-electro-

mechanical systems (MEMS) applications to

determine the residual thermal stresses in thin film

structures.

Figure 1: Schematic showing functionalized cantilever

(top) and total deflection due to thermal and adsorbtion-

induced surface stress (below).

A commonly used expression for predicting the

transverse deflection in a layered beam due to

bimetallic effect is (Finot, 2008)

3( )( )

sfsf

αα

−+

⎛⎞

=Δ

⎜⎟

⎝⎠

(3)

where,

46 4

ff ff

ss ss ff

ttEt

t t Et Et

⎛⎞⎛⎞

⎛⎞ ⎛⎞ ⎛ ⎞⎛⎞

=+ + + +

⎜⎟⎜⎟

⎜⎟ ⎜⎟ ⎜ ⎟⎜⎟

⎜⎟⎜⎟

⎝⎠ ⎝⎠ ⎝ ⎠⎝⎠

⎝⎠⎝⎠

This study used all the above models to

investigate the thermal and adsorbtion-induced

deflections in a microcantilever biosensor. By taking

advantage of the cantilever geometry, 2-D FE model

was used. The model was meshed by 8-node

coupled-field PLANE223 elements. Solution

convergence and mesh-size effects were analysed

before the final simulations. First we performed

thermal analysis and then a coupled thermal-

structural analysis involving both thermal- and

adsorbtion-induced stresses. In the first case, the

microcantilever was subjected to temperature change

alone, whereas, in the other, it was subjected to a

constant surface stress as well as increased

temperature. The cantilever was coated with a 20-

nm-thick film of gold. The cantilever size was

500×100×1 µm; and an adsorbtion-induced surface

stress of 0.05 N/m was applied on its top surface.

The surface stress was modelled as a tensile force

applied to the top, free edge of the cantilever

(Ansari, 2009). The applied tensile force was F =

Δσ

× b = 0.05 × 100×10

-6

= 5×10

-6

N, where b is the

cantilever width. The geometric and thermoelastic

properties of film and substrate are L = 500 µm, t

1 µm, t

= 0.02 µm, E

= 130 GPa, E

= 78 GPa, α

2.6×10

−6

/°C, α

= 14.2×10

−6

/°C, ν

= 0.28, ν

= 0.44,

= 149 W/m°C and k

f =

315 W/m°C.

A STUDY ON BIMETALLIC EFFECTS IN MICROCANTILEVER BIOSENSORS

3 RESULTS AND DISCUSSION

Table 1 compares the analytical and simulation

results against the experimental result in (Ramos,

2007). The thermoelastic material and geometric

properties were adopted from it. In the experiment, a

20-nm gold coated silicon microcantilever of size

400×100×1 µm was subjected to a temperature

change of −12 °C. The analytical study used (2) and

(3), and FEA result is from ANSYS. It is obvious in

the table that the experimental and the analytical and

simulation results have good accord in predicting the

thermal deflection, indicating the conformity of

analytical and simulation analysis.

Table 1: Comparison between experimental, analytical,

and FEA results.

ΔT (°C)

Thermal deflection, Δz

(µm)

Exp. Stoney (2) Beam (3) FEA

-12 0.56 0.60 0.61

0.62

Figure 2 shows a comparison between Stoney

model (2), beam model (3) and simulation results for

the deflections in the cantilever biosensor with and

without adsorbtion surface stress. Figure 2 (a) shows

the effect of temperature variation on the cantilever

deflection. All the three curves show good accord in

predicting the thermal deflections. Furthermore, the

simulations results corroborate the linear relation

between deflection and temperature, which is

suggested in the analytical models (2) and (3).

Figure 2 (b) shows the combined effect of

temperature variation and adsorbate-induced surface

stress on the cantilever deflection. The total

deflection (Δz

total

) is sum of thermal and adsorbate-

induced deflections. Equation (1) was used in

calculating the adsorbate-induced deflection. The

Stoney models used (1) and (2), whereas, the Stoney

+ beam models used (1) and (3). As can be seen in

the figure, at ΔT = 0 the cantilever shows a

deflection of about 0.28 µm, which is induced

entirely due to the surface stress of 0.05 N/m. In the

figure, for ΔT > 3°C, thermal deflections exceed the

surface-stress induced deflections. In Figure 2, we

also observe that as the temperature increases, the

deflection curves show deviation, which suggests the

analytical and simulation results are accurate for ΔT

< 10°C. The higher the temperature change, the

higher the thermal noise will be. However, by

knowing the thermoelastic and geometric properties

of the cantilever, thermal deflection can be readily

calculated from analytical relations (2) or (3). Since

both the thermal and surface-stress deflections show

linear and additive characteristics, thermal noise can

be isolated easily by deducting the thermal

deflection from the total deflection.

Figure 2: Cantilever deflection due to (a) thermal and (b)

thermal and adsorbtion-induced deflections.

Thermal noise problem is more pronounced in

liquid medium than in gaseous. In microcantilever

biosensor system, the cantilevers array is immersed

in a fluidic cell chamber and solution stream

containing the analyte molecules is flowed across it.

During purging the chamber and/or changing

solution samples, the fluid filling the chamber alters

the ambient temperature around the cantilever array.

It induces thermal strain in the cantilever, which

eventually produces thermal deflections. Bimetallic

effects present more serious problems in SU8

polymer microcantilever biosensors, mainly due to

the large mismatch between the thermoelastic

properties of SU8 substrate and gold film. The CTE

and elastic modulus of SU8 and gold are about

52×10

−6

/°C and 2 GPa, and 14.2×10

−6

/°C and 78

GPa, respectively. Since the CTE of SU8 is

considerably higher than that of gold, the cantilever

will bend upwards when the temperature is

increased. In addition, the large difference between

(a)

(b)

BIODEVICES 2010 - International Conference on Biomedical Electronics and Devices

the elastic moduli will generate substantial shear

strain at the gold-SU8 interface, which may lead to

de-lamination of the film from the substrate.

If the film thickness is significant, (2) and (3)

can still be used for predicting deflections by

replacing the substrate modulus (E

) with the

effective substrate modulus (E

eff

) given as (Yi, 2002)

24 24 2 2

2(223)

fs fs

eff

E a E b E E ab a b ab

Ea Eb

++ ++

(4)

where a = t

/t and b = t

/t, and t is total thickness of

the cantilever. To elucidate (4), consider the

geometric and material properties of the gold coated

cantilever analysed in this study. Though E

is 130

GPa, the E

eff

is about 127 GPa.

4 CONCLUSIONS

Microcantilever biosensors provide a universal,

rapid, and highly sensitive mean to many

applications. The measurement accuracy of the

sensor depends on its ability to isolate and eliminate

the noise from the signal. Since bimetallic effects are

a major source of noise in the signal, we investigated

the effect of temperature on the deflection

characteristics of the cantilever. The results

indicated that thermal deflections can be determined

accurately using analytical and simulation models.

By studying the combined effect of thermal- and

adsorbate-induced surface stresses on the cantilever

deflection, we found that the two stresses act linearly

and additively. We found that even for small

temperature variation, the thermal deflections can

easily exceed the adsorbate-induced deflections, and

hence produce noise in the deflection signal.

However, by deducting the thermal deflection from

the total deflection amount, the exact adsorbate-

induced deflection or stress can be determined.

Further, the large mismatch in the thermoelastic

properties makes SU8 microcantilever biosensors

more susceptible to bimetallic effects.

ACKNOWLEDGEMENTS

This study was supported by Inha University.

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A STUDY ON BIMETALLIC EFFECTS IN MICROCANTILEVER BIOSENSORS