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 massComb 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 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 IBM P. Li, Xinxin Li, APL 2000 Single DNA hybridization recognized Sub-nanometer bending is self-sensed

Proxi-Lever with thiol-SAM of 6MNA on Au surface for 20ppt-resoluble trace TNT detection P. Li, Xinxin Li, et al, APL 2006 and JMM 2007

Sensing Canti. Siloxane-head bi-layer modified on SiO 2 surface for long life-time TNT detection

How to design the static cantilever for specific-reaction induced surface-stress Stoney ’ s equation:

When the cantilever is bent by uniformly distributed loading surface stressσs, the free-end bending moment is M=Δσ s t/2, where w is the cantilever width. the radius of the deflective cantilever, R, can be expressed as and.

The bending stress at the piezoresistive layer can be expressed is where E si is Young ’ s module of silicon, h t is the distance between the upper surface of the cantilever and the piezoresistor layer. represents the mechanical sensitivity of the piezoresistive cantilever

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 up Combination Atomic behavior Continuum mechanism Seamless coupling Bio-molecule Nano Informatics BNI Fusion Key points for micro-nano compatible cantilevers:

Bio-Nano Binding Nano-Micro Coupling Bio-Nano-Informatics (BNI) Fusion Road map for recent work

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