Lecture #6

Mechanical Properties of Micro-machined Structures

Dr. Shady Abdelnasser, Ph.D.

Department of Energy and Renewable Energy Engineering

Egyptian Chinese University
Outline

Sources of Stresses
Failure Modes
Material Properties
❖ Stress
❖ Strain
❖ Elastic Modulus
❖ Poisson ratio
Contact Mechanics
❖ Hertzian Spherical Contact
❖ Hertzian Cylindrical Contact
Mechanics of Solids in MEMS cantilever
Stress Relief
MEMS are used in diverse applications such as pressure sensors, accelerometers, mass flow
sensors, Radio-frequency (RF) switches…. etc.

MEMS devices showed many advantages over the large-scale counterparts.

• One of the great promises of MEMS and surface micromachining is the small size
of the devices that can be fabricated.

• Smaller means more components to fit into integrated circuits, allowing for more powerful
and energy-efficient electronic devices with reduced power consumption.

• The mechanical properties like stress, strain, elastic modulus, poisson’s ratio of materials
are of critical importance in design, fabrication and its applications in MEMS devices.

• They affect the productivity, reliability, quality and performance of MEMS devices
 Sources of Stresses

• In MEMS devices, a thin film deposited on a substrate can form some stresses.

• These stress typically arises from the mismatches in thermal expansion between the film
and the substrate.

• Thermal expansion describes the state of matter to increase in length, dimension, in response
to an increase in temperature
• Coefficient of thermal expansion is the ratio of fractional change in size of a material to its
change in temperature (K-1 or C-1)
 Sources of Stress
Stresses is strongly affected by the deposition conditions and the flow of the techniques
utilized to deposit these materials have a great impact on their final properties
Substrate undergoes a heating during
deposition, This causes the substrate to
expand as shown by the dotted lines outside of
the unheated boundaries of the substrate in
figure b.

In figure c, a thin-film is deposited on the top

of the substrate. Noting, the deposition occurs
when the substrate and the deposited film are
both at an elevated temperature.

Compatibility requires that the substrate and

thin-film have the same length. After
deposition, the substrate and thin-film are
cooled to room temperature.
 Sources of Stress
Once the substrate and thin-film reach an
equilibrium state at room temperature, if
the thin-film has higher CTE than the
substrate it will contract more than the
substrate hence result in the situation
shown in Figure d, where the curvature of
the substrate and thin-film on the top is
concave-shaped. In such case, the thin-film
will be in a state of tensile stress

If the thin-film layer had less CTE than the

substrate, it would contract less upon
cooling and result in the substrate with the
thin-film having the opposite curvature,
that is, a convex shape. In this case, the
stress would be compressive.
Failure Modes due to Stresses

• High stress concentration at the

attachment point of the film leads
to extra forces called peel forces
that tend to detach the film from
the substrate

• Debonding of the films tends to

occur at the edges of patterned
features
 Failure Modes due to Stresses
• Excessive stress can result in buckling or cracking that can influence the performance of the
below structures.
• In addition, Excessive stress (compressive or tensile) in a film may cause crack for the film
and substrate and therefore it should be minimized

Buckled MEMS bridge structure

Cantilever beam may curl easily, and such non-symmetric orientation of the beam can affect its performance
 Failure Modes due to Stresses
Microsystems are comprised of many different types of structural elements.

Tethers for parallel plate

Tethers for accelerometers
capacitors
Actuation voltage refers to the minimum voltage required to activate a micro or nano
electromechanical (MEMS/NEMS) system, causing it to perform its intended function.
Variation in actuation voltage for RF MEMS switches (for example) is observed as a
result of stress-generated in MEMS structures.
Stress and Strain

• When any body supports a load, the material is said to be under stress. It is the measure
of the intensity of the the load occurred on the subjected area.
• Expressed as the force per unit cross-sectional area. In SI units, stress is measured in
Pascals (Newtons per square meter) or (Joule per meter cube).
• The average stress, 𝜎 , is equal to the load divided by the cross-sectional area:

𝜎=F/A
Stress and Strain
• Tension is stress tends to lengthen the body, and compression is stress tends to
shorten the body.
• The deformation, 𝛿 , of a body under load is dependent on the size and shape of the
body.
• The amount of deformation, 𝛿, normalized by the dimensions of the body, 𝐿 , is called
strain, 𝜀.
• Strain is represented mathematically as:

𝜀=𝛿L/L
Modulus of Elasticity
• In a body undergoing an elastic deformation in the normal direction, the ratio of stress to
strain is known as the Young’s modulus, 𝐸, which is also called the modulus of elasticity:
𝐸 = 𝜎/𝜀

If the body is undergoing shear (when deforming forces act parallel to the object’s surface,
it is called ‘shear’ forces), the corresponding proportionality constant is called the modulus
of rigidity; G

These material properties describe the stiffness of the material.

A material, such as rubber, has a small Young’s modulus (0.5𝐺𝑃𝑎); more hard material, such
as stainless steel has larger Young’s modulus (190𝐺𝑃𝑎); and a single-crystal diamond has a
Young’s modulus of (1035𝐺𝑃𝑎).
 Poisson’s ratio
• Poisson’s ratio, υ, describes the ratio of the transverse strain to the axial (longitudinal) strain
when a body is subjected to an axial load.

• This can be visualized by thinking about a component being stretched (a positive axial
strain), while the transverse strain becomes narrower, that is negative.

• The strain that occurs parallel to the longitudinal axis is called longitudinal strain.

• The strain that takes place perpendicular to the longitudinal axis is known as lateral strain.

• Defines the ratio between lateral strain “εL” to the axial strain “εa” υ=-(εtran/ εaxial)

• Since the axial and lateral strains will always have different signs, The negative sign in the
equation makes the ratio positive

• In most cases, υ has a value between 0.2 and 0.5.

• The following relationship relates the shear modulus with 𝐸 and υ

𝐸 = 2𝐺 1 + υ
 Mechanics of Solids in MEMS cantilever

The uniform stress is 𝛔 = F/A, If the

beam is comprised of a linearly
elastic material, then the strain is
ε = 𝛔/E= F/EA (Hooke's Law).

The corresponding change in the

length of the beam is 𝛿L= εL= FL/EA

You can get the spring constant for

the loaded beam as Force = Spring
Constant x Deflection; F=k 𝛿L

Hence, Spring Constant k= EA/L

 Contact Mechanics
Contact stress is a description of the stress within mating parts that is the stress arising from the
contact between two bodies. It is called Hertz contact stresses

This kind of stress may cause serious problems most of the time as mentioned above.

Hertzian spherical contact (contact between two spheres) and Hertzian cylindrical contact (contact
between two cylinders)

Micro Gear transmission system based

on MEMS electrostatic actuator
Flexible MEMS Flow Sensor
 Contact Mechanics

The theory of contact between two

spheres of radii R1 and R2, the area of
contact is a circle of radius a, as showed
in the figure.
The radius of the contact area is given
by:

Where E1 and E2 are the moduli of

elasticity for spheres 1 and 2 and ν1 and
ν2 are the Poisson’s ratios, respectively.
 Contact Mechanics

Hertzian Cylindrical Contact

Contact between two cylinders
with parallel axes
The figure shows the contact
between two cylinders with the
radii of R1 and R2 with parallel
axes.
The half-width b of the
rectangular contact area of two
parallel cylinders is found as:
 Stress Relief
❖ One of the traditional methods to eliminate or control the residual stress in the thin film is to
change the deposition parameters. Though this method can effectively reduce the stress in the
aspect of the thin film, it is very limited in eliminating the deterioration of stresses
❖ Another method of relieving stresses is to change the structure design to be
corrugated that is producing folded structures containing grooves.
❖ This eliminates most of the stress caused by the fabrication process and by thermal expansion
mismatches between the film and the substrate
❖ It is found that the addition of folded structures will significantly reduce the stress, which can
be reduced to a five times the stress of the flat structure.
❖ Introducing a folded structure with groove into the design of MEMS device is an effective way to
suppress the generation of stress, thus enhancing the reliability of MEMS devices.
 Stress Relief
• The process for fabricating the
folded structure.
• The first step, silicon oxide
deposition.
• The second step, silicon oxide
pattern was done.
• The third step, etching using
KOH solution was done for the
formation of V-shaped Groove to
produce a corrugated structure.
• The fourth step, silicon nitride
deposition was performed using
CVD. Top view of folded structure
• The fifth step, wet etching was
performed by using KOH
solution to release the structure.
Design & Finite Element Simulation Results

(a) Residual stress profiles of flat structure. (b) profiles of folded

structure

Stresses of flat structure and folded structure for different samples

The stresses of all folded structures

with V-shaped grooves are lower than
that of flat structures.

SEM image of fabricated folded structure device