Forces, Orientation, Scaling

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Forces, Orientation, Scaling
Diamond lattice (Si)
Picture from U of UTAH
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Directions and Planes in Crystals
Directions (vector components a single direction
is expressed as a set of 3 integers,
equivalent directions (family) are expressed as lt
a set of 3 integers gt Planes a single plane is
expressed as (a set of 3 integers h k l Miler
indices) and equivalent planes are expressed as
a set of 3 integers
Miler indices take a,b,c (multiple of basic
vectors ex. x4a, y3a, z2a) reciprocals (1/4,
1/3, 1/2)-gt common denominator (3/12, 4/12, 6/12)
-gt the smallest numerators (3 4 6)
lattice constant
Plummer
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Properties of crystals are determined by their
orientation
Diamond lattice of Si
viewed in lt100gt lt110gt
lt111gt
(111)
(100)
(100)
(110)
(111)
go to http//stokes.byu.edu/diamond.htm to rate
the crystal and see lattice symmetry. You can
also calculate angles between various
crytallographic planes and access many
clickable material/device/process parameters
calculated here http//www.ee.byu.edu/cleanroom/EW
_orientation.phtml?flagtopic_index
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Crystallographic orientation of Si
Charges in MOS systems (measured in C-V) and many
other properties depend on crystal orientation.
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CRYSTAL
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Orientation of Silicon Wafers is Important for
MEMS
Primary and Secondary Flats
After Shimura
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Stress and Strain

• Static and dynamic behaviors of MEMS under
  loading determined by Newton Laws

Orientation effects are coming soon Basic
mechanical engineering info can be found here on
http//en.wikipedia.org/wiki/Main_Page using
Force, Stress, Strain, Hooks Law, Newton's laws
of motion as key words, etc. as well as
http//www.ami.ac.uk/courses/topics/0123_mpm/index
.html
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Examples of Mechanical Structures

• Force balance analysis

• (Traverse direction) Force and moment balance
  analysis

remove the wall
The wall reacts on the bar with an axial forceF
(see - sign)
A pair of forces create a torque (couple or
moment)
Newton 3rd Law
?F0 Newton 1-st Law total force0
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Shear Stress and Strain
Pa

• Definition of normal Stress and
  Strain
• Shear stress ??does not cause elongation or
  shortening of the element but deformation.
• Shear strain ? represents
• angular displacement

Poissons ratio
imaginary cut
Normal Stress can be tensile or
compressive Strain refers to elongation (normal
strain if it is ? to area A)
E is modulus of elasticity or Youngs modulus
(intrinsic material property)
GShear modulus of elasticity
(later)
G is material not dimension property
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Poissons Ratio
Deformations along the load (force F) and
perpendicular to the load lead to an axial strain
and a transverse strain sl is tensile and
st is compressive so they have opposite signs
?
v (Poissons ratio) typically is 0.3-0.5. for
metals 0.3, for rubber 0.5, for cork 0 (does
not expand at all), polysilicon 0.22.
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Mechanical Stress and Strain

• Stress causes elongation and reduction of the
  cross-sectional area. Poissons ratio v describes
  this effect
• Stress and strain, for small deformations, are
  described by Hookes law E is modulus of
  elasticity or Youngs modulus

Shear modulus of elasticity G
For isotropic materials
K is bulk modulus representing volume change
under pressure (water K1E9 N/m2, Al K7E10,
steel K14E10 N/m2
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Scalar Relation Between Stress and Strain

• ? Generic stress-strain curve ? Non-generic
  Stress-strain relations
• Important properties of materials used in MEMS
  ductility, toughness, hardness, brittleness. Sign
  of applied load is important - some materials
  will fail at lower stresses in shear, others in
  tension.
• Fatique failure is also important in MEMS -
  materials can develop cracks or weak points
  specially if operating under stress and/or harsh
  conditions. Thin films (lt100 nm) can even work
  trillions of cycles w/o failure.

Hooke's lawmaterial deforms linearly with load
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Silicon and Related Thin Films

• Dimensions, crystal orientation affect mechanical
  properties of silicon
• Youngs modulus in c-Si
• In 100 planes in direction of 110
  168GPagt100 130GPa
• In 110 planes 111 187 GPa
• Youngs modulus in poly-Si (120-160 GPa) depends
  on structure and grains therefore depends on
  processing
• deposition conditions and subsequent annealing
  are important
• Shear modulus depends on crystal orientation
• Poissons ratio for c-Si varies from 0.055 to
  0.36 and for poly-Si it is 0.15-0.36.
• See Appendix A for specific data.

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General Stress-Strain Relations

• Stress and strain are tensors. Use matrix to
  express normal stress components ?xx ?yy ?zz
  (noted as T1-T3) and shear stress ?yz, ?xz, ?xy
  (noted as T4-T6) as vectors.
• s1-s2 are three independent strains,
• s4-s6 are three shear strains.

C is the Stiffness matrix
s- Strain matrix
S is the compliance matrix
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Example for Silicon Orientation Effects
C matrix is very much simplified for Si along
lt100gt direction
It can be used to calculate normal stress
components T1, T2, T3 and find Youngs modulus
(see Example 3.5 for E100T1/s1130GPa)
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Flexural Beam Bending Analysis Under Simple
Loading Conditions
Beams are described by how they are supported and
how load is applied.
degree of freedom
cantilevers are basic MEMS structures
no movement at the support
rotation is restricted
linear movement and rotation allowed
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Load and Boundary Conditions
There is always a direct relation between the
deflection and the load (for any boundary
conditions)
Kovacs
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Bending of Cantilevers Under Various Boundary
Conditions
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Longitudinal Strain Under Pure Bending and
Deflection of the Beams
h
Imoments of inertia, which for a beam with
rectangular cross section is Strain depends on
total torque M smaxMt/2EI
Mbending moment or total torque
A more complex case since the Moment along the
beam is not constant. It is important to find the
maximum displacement of a cantilever.
under compression
tu neutral axis
under tension
equal max values of tensile and compressive
stress ?max! Maximum stress is constant through
the length of the beam
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Finding Spring Constants k
Stiffness is characterize by the spring constant
k (or force constant).
To see how changes in the weight of an object and
spring properties (length, stiffness, stretch)
affect mechanical response of the system - watch
these video. They show how scaling is used in
MEMSs http//streamer.cen.uiuc.edu/me_mems/Video2
.wmv http//streamer.cen.uiuc.edu/me_mems/Video3.w
mv More can be found in http//www.engr.uiuc.edu/
OCEE/outreach.htm.
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Cantilevers
Bending of a cantilever (by the angle ? and
deflecting by x) depends on force, geometry and
Youngs modulus.
so the spring constant is
The stiffness depends on the force direction and
on the direction of bending. The beam is said
that provide compliance in one direction and
resistance to movement in another.
Spring constant decreases with length. Soft
material (small E) would deform more so spring
constant is small.
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Force Constants of Beams Various Applications of
Mechanical Structures
Force can be of various origin
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Applications of Mechanical Structures
Selected from many

• Accelerometer is shown in this http//streamer.cen
  .uiuc.edu/me_mems/Video6.wmv
• in http//www.engr.uiuc.edu/OCEE/outreach.htm

2. Digital Mirrors made by Texas Instruments
(will come soon in Chapter 4)
http//www.dlp.com/Default.asp?bhcp1
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Plates (thick) and Membranes (thin)
The spring constant k associated with each
fixed-guided beam
Each spring shares the load so for plates
supported by two fixed-guided beams it is and
by four fixed-guided beams it is
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Torsional Deflection
Maximum shear stress in the bar is ?max and it is
distributed along the bar. Maximum shear strain
is
Maximum shear stress is related to the torque
Torsional moment of inertiaJ for a circular
bar and square-cross section
For the circular beams the magnitude of the
maximum shear stress is
and the angular displacement of the torsional
bar is
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Intrinsic Stress
Internal stress can be present if layered
structures are made. It is due to fabrication
processes that use materials/processes that have
different thermo-mechanical properties.
Intrinsic stress can be uniform within a layer
or have gradients in its distribution across the
film thickness. Removal of the substrate layer
releases the stress but causes deformation.
Warped film
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Intrinsic Stress Introduced by Fabrication and
Process History
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Stress Compensation
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Measuring of Intrinsic Stress
Testing of planar (large) areas.
Testing local deformation/stress
Horizontal beams under intrinsic stress
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Measuring of Intrinsic Stress
Uniform compressive stress causes elongation or
buckling of a double supported beam. Both tension
and compression stress can be measured by such
structures.
Ring and beam structure For tensile stress in
the ring when relaxed (underlying film released
by etching) the ring expands and makes the beam
compressed - up to the point of buckling (optical
microscopy)
Kovacs
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Measuring of Intrinsic Stress if There is a
Stress Gradient
Nonuniform stress in the film causes the film to
curl. If stress gradient is positive (larger
away from the substrate) the spiral will open as
a bowl. If stress gradient is negative (smaller
away from the substrate) the spiral will buckle
down. Each type requires anchoring either in the
center or at the perimeter.
Kovacs
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Measuring of Intrinsic Stress
Piezoelectric or piezoresitive sensor respond to
curling of the film.
Kovacs
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Dynamics of the Beam
Lumped mechanical structure is described as
follows
Any force can act as an external force gravity,
electrostatics etc. If the force has frequency
dependence it will cause mechanical oscillations
where the amplitude will be affected by
damping.
Damping is due to drag forces and/or to
deformation in the sprig or other parts.
Kovacs
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Analogy to Electrical Filters
At resonance, the deflection is Q times larger
than in steady state. Damping is represented by
resistance, which reduces the quality factor Q
Working as in DC
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Multifunctional Sensors

Integration of various functions possible in
array sensors
Control of arrays parameters (material
dimensions spring constant
oscillation frequency deflection) is ensured by
IC technology
Characterization techniques known in various
science disciplines will have significantly
improved sensitivity if used on the diving
boards.
Bending and oscillation depend on stress and mass
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Smart Force Sensors Cantilevers Physical and
Chemical Functions of Cantilevers

• Transduce signals from almost every domain to
  nanomechanical motion (bend/oscillate)
• thermal
• chemical
• biochemical (no labeling
• for biding recognitions)
• biological
• magnetic
• electrical
• optical
• mechanical (stress)
• Have high sensitivity (force
• 1.4x10-18N/Hz1/2, pH 1nm/5x10-5,
• mass 1fg/Hz) and high speed
• Use minute quantities of analytes
• Fabricated by IC processing
• Si, Si3N4 with sensitizing films
• for tailored applications
• Dimensions µm range

Bimetal
AFM Origin
10-5 K
Bending 0.05 Å)
phase transformation
H2 O2 on Pt
SAM
pW fJ
active layer (Au)
photo induced stress
absorption swelling
1.1 Hz/fg
pJ
viscosity temperature
mH2Ong in zeolite
m(T)
or magnetic alloys
magnetic moment 10-12 Am2
interface charges voltamograms
pN (5.6x10-18N)
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Cantilever Arrays for Multifunction Sensors
Operation of cantilever arrays with various
coatings

• Signal Detection
• Electrical (Piezoresistors)
• Optical (laser detection systems)
• static mode (bending)
• dynamic mode (tracking of resonance frequency)
• Future Wireless (magnetic)

Position-Sensitive-Detector
signal pre-processing
Integration with optoelectronics for
miniaturization and functionality
IBM Zurich/Concentris/Basel University
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Identification and Elimination of Artifacts
Versatility of cantilevers allows to diminish
main artifact effects flow and temperature
nonuniformity Differential measurements with a
reference cantilever
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Fabrication of Cantilevers Using Si Technology
ITE, Poland
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ITE, Poland
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Fabrication of Piezoresistors Cantilevers
ITE, Poland
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Measurements of Differencial Deflection
Two cantilevers covered by single stranded DNA.
baseline
Bending of the first cantilever by hybridization.
Bending of the second cantilever by hybridization.
Differential Bending also increases with
concentrations
The cantilevers bend by docking of molecules
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Single Cell Detection
Anti-E. coli antibodies
Si3N4 L15-400 µm W5-50 µm
Attachment of heat killed E. coli in various
colonies
Cell dimentions 1.46 µmx730 nmx350nm
15x5 µm
5µm
JVST B, J. Illic et al. 2001.
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Force Amplified Biological Sensors
0.5 pN force removes nonspecifically bound
particles sensitivity pg/l
NRL, Baselt et al.
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(Galis and Khatri, 2002)
Outward arterial remodeling
Normal artery
Foam cell/macrophage-driven
Unstable plaque
Constrictive arterial remodeling
Stable plaque
Smooth muscle cell-driven
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Examples of Cantilever Operation (Vulnerable
Plaque Applications)
pH Sensor - Plaque has increased acidicity
Interfacial stress depends on pH and sensitizing
(thiol/acid) layers on Au due to electrostatic
force (Q-) in MHA
Protein Recognition
use lipid layer
Immunocytochemistry for plaque
monolayers
Thermal Effects - Inflammation
Biochemical combined with magnetic sensor - SPIO
in the macrophage rich regions
7.8 ng
Phase transition at T32.5øC
NRL
IBM Zurich
(40 pN antigen-antibody)
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Application to Vulnerable Plaque

• Array of multifunctional cantilevers to monitor
  
• Temperature (inflammation)
• pH
• Flow (affects endothelium)
• Selected biochemical reactions (C-RP, MMP,
  bacteria-Chlamydia, etc.)
• SPIO (agglomeration within VP)
• Realization
• Integration of Si based cantilevers with
• Magnetic layers (regions)
• wireless transmitter (if magnetostrictive layer
  is below the active sensing layer)
• sensor (hard or soft magnetic tips)
• Piezo-resistive, - electric or dielectric layers
  for sensing or detection
• Passivation layers for biocompatibility

here
IBM Zurich/Basel Univ.
NRL
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Summary
See a video on applications of various
phenomena, known from the macro world, in MEMS.