Homework:

Resemble the case of trapezoid cross section in Page 47-48, try to calculate the moment of inertia of a “T”-shaped cross-sectional beam

a1

a2

b1

b2

Review of important formulas for bending stress and strain of a beam

Uniform acceleration

How about a double-clamped beam with self-weight loading?

Analysis and design rule of the beam bending problem

Cantilever can be used not only for mechanical sensors and probes, but also for bio/chemical sensors

1.1. How Cantilever as a Sensing Platform?

Cantilever-mass micromachining structures have been long-period used in MEMS inertial sensors: Accelerometers and Gyroscopes, etc.

Piezoresistor embedded axial beams

Reference resistors

Bending cantilever beam

Mass legs

Seismic mass

a

Comb damper

S. Huang, Xinxin Li, Transducers’03

Xinxin Li, M. Bao, Transducers’99

• In an inertial sensor, the spring deformation is forced by a seismic mass, i.e. a bulk effect

• In a bio/chemical sensing cantilever, the seismic mass is no use but surface effect becomes to work

Antibodies with bacteria

What causes this change?

Different sensing mechanism for bio/chemicals

Bio/Chemical Physical Informatics

Analyte Circuit Recognizing

materials Transducers Signal

Electrochemical: Amperometer, Potentiometer, I SFET, …

Thermal: Calorimeters, DSC…

Mass or Mechanical: SAW, QCM, Cantilever, …

Optical: I nterferometer, Spectrometer, SPR, …

…

Signal

Processing

Circuit

Enzymatic

Microbial / Cell

Immunological

DNA

Organic

…

Two sensing interfaces: both contribute to sensitivity/selectivity in different ways

Science, 1997 by IBM Zurich reported that self-assembly of SAM on Au surface generates nano-mechanical surface-stress that was measured by a micro-cantilever and signal read out by an AFM photonic detector.

Although studies have tried to find the origin of surface-stress generation, the molecule-level mechanism on the self-assembly induced surface-stress is still ambiguous.

During the chemical sensing experiment in last section, using ammonia to replace the tri-methylamine vapor in the experiment results in no significant frequency-shift measured. Though their chemical principles are similar, apparently the size of the ammonia molecule is much smaller than that of the tri-methylamine.

Thus, the mechanism of surface-stress generation during specific molecules binding on a solid surface is strongly dependent of the molecule size or other principles.

1.2. Why Cantilever Promising for Bio/Chemical Detection?

(1) Static cantilever for specific-reaction-induced surface-stress sensing

“Translating Bio-molecular Recognition into Nano-mechanics”

Science 288 (2000) by IBMP. Li, Xinxin Li, APL 2000

Single DNA hybridization recognizedSub-nanometer bending is self-sensed

Proxi-Lever with thiol-SAM of 6MNA on Au surface for 20ppt-resoluble trace TNT detection

S S S S S

Cu2+

CF2F2C

CF2F2C

CF2F2C

CF2F2C

CF3

CF2F2C

CF2F2C

CF2F2C

CF2F2C

CF3

CF2F2C

CF2F2C

CF2F2C

CF2F2C

CF3

Si

O

OSi

O

OSi

O

O

CF2F2C

CF2F2C

CF2F2C

CF2F2C

CF3

Si

O

O

SS

Cu2+Cu2+Cu2+Cu2+Cu2+

Sens. cant.

CF2F2C

CF2F2C

CF2F2C

CF2F2C

CF3

CF2F2C

CF2F2C

CF2F2C

CF2F2C

CF3

CF2F2C

CF2F2C

CF2F2C

CF2F2C

CF3

Si

O

OSi

O

OSi

O

O

CF2F2C

CF2F2C

CF2F2C

CF2F2C

CF3

Si

O

O

CF2

F2CCF2

F2CCF2

F2CCF2

F2CCF3

CF2

F2CCF2

F2CCF2

F2CCF2

F2CCF3

CF2

F2CCF2

F2CCF2

F2CCF2

F2CCF3

Si

O

O Si

O

O Si

O

O

CF2

F2CCF2

F2CCF2

F2CCF2

F2CCF3

Si

O

O

Ref. Cant.

SiO2 surface

SiO2 surface

Au surface

P. Li, Xinxin Li, et al, APL 2006 and JMM 2007

0 5 10 15 20 25

0

20

40

60

80

100

95%

74%

51%

33%Res

pons

e vo

ltage

(V

)

Time (min)

SiO2 surface w/o FAS-17 modification

SiO2 surface modifed with FAS-17

11%

Sensing Canti.

Sensing Canti.

0 5 10 15 20 25 30

-12

-10

-8

-6

-4

-2

0

2

Resp

on

e V

olt

ag

e(V

)

Time(min)

quad-cantilever sensor

Siloxane-head bi-layer modified on SiO2 surface for long life-time TNT detection

How to design the static cantilever for specific-reaction induced surface-stress

Stoney’s equation:

sEt

Lz

2

2 )1(3

When the cantilever is bent by uniformly distributed loading surface stressσs, the free-end bending moment is M=Δσst/2, where w is the cantilever width.

eff

ns

eff EI

wh

EI

M

R )(

1

)))(12/(1

()( 23niii

i

i

ieff hhttE

wEI

i i iiiiin tEthEh )/()(

the radius of the deflective cantilever, R, can be expressed as

and

.

The bending stress at the piezoresistive layer can be expressed is

RhhE tnsi

1)(

where Esi is Young’s module of silicon, ht is the distance between the upper s

urface of the cantilever and the piezoresistor layer.

represents the mechanical sensitivity of the piezoresistive cantilever

( )

( )si n n t

s eff

E h h h

EI

How to know the surface-stress value induced by a certain specific molecule binding? Only be experimental results? Is there and design model?

By now no people in the world knows it in details? You can try and publish the results in Science or Nature

Top down

Bottom upCombination

Atomic behavior Continuum mechanismSeamless coupling

Bio-molecule

Nano

Informatics BNIFusion

Key points for micro-nano compatible cantilevers:

Bio-Nano Binding Nano-Micro CouplingBio-Nano-Informatics (BNI) Fusion

Road map for recent work

In farther future … …

“There's plenty of room at the bottom” (R. P. Feynman)