International Journal of Engineering Trends and Technology (IJETT) – Volume 20 Number 5 – Feb 2015
Design & Simulation of MEMS Accelerometer Using COMSOL Multiphysics
Software
Divya N#1, Jyothi V*2, Rajesh Kumar B#3
#
M. Tech, M. Tech, M. Tech & Electronic & Instrumentation Department& GITAM University, Gandhi Nagar Campus,
Rushikonda, Visakhapatnam-530045, Andhrapradesh, INDIA
Abstract— MEMS is abbreviated as Micro Electro Mechanical
Systems. It is defined as miniaturized mechanical and electromechanical elements. These are capable of recognizing gestures.
By utilizing the COMSOL software, the accelerometer was
designed and the analytical analysis of the accelerometer was
calculated.
I. INTRODUCTION
Micro Electro Mechanical Systems are small integrated
devices or systems that combine electrical and mechanical
components. They range in size from the sub micrometer
level to the millimetre level and there can be any number,
from a few to millions, in a particular system. MEMS extend
the fabrication techniques developed for the integrated circuit
industry to add mechanical elements such as beams, gears,
diaphragms, and springs to devices. Examples of MEMS
device applications include inkjet-printer cartridges,
accelerometers, miniature robots, micro engines, locks,
inertial sensors, micro transmissions, micro mirrors, micro
actuators, optical scanners, fluid pumps, transducers, and
chemical, pressure and flow sensors. The micro fabrication
technology enables fabrication of large arrays of devices,
which individually perform simple tasks, but in combination
can accomplish complicated functions. MEMS are not about
any one application or device, nor are they defined by a single
fabrication process or limited to a few materials. They are a
fabrication approach that conveys the advantages of
miniaturization, multiple components, and microelectronics to
the design and construction of integrated electromechanical
systems. MEMS are not only about miniaturization of
mechanical systems; they are also a new paradigm for
designing mechanical devices and systems.
II. DESIGNING OF MEMS
The design and modeling of micro electro-mechanical
systems is unique. The design of resonators, gyroscopes,
accelerometers, and actuators consider the effects of several
physical phenomena on their operation. COMSOL
Multiphysics is ideally suited for MEMS applications. The
MEMS Module provides predefined user interfaces, referred
to as physics interfaces, for a variety of coupled physics,
including electromagnetic structure, thermal structure, or fluid
structure interactions. For elastic vibrations and waves,
perfectly matched layers provide state-of-the-art absorption of
outgoing elastic energy.
ISSN: 2231-5381
Best in class piezoelectric and piezoresistive modeling tools
allow for simulations where composite piezo elastic dielectric
materials can be combined in any imaginable configuration.
The MEMS Module includes analyses in the stationary and
transient domains, as well as fully-coupled eigenfrequency,
parametric, quasi-static, and frequency response analyses.
You can easily perform lumped parameter extraction of
capacitance, impedance, and admittance, and connect to
external electrical circuits via SPICE netlists. Built upon the
core capabilities of COMSOL Multiphysics, the MEMS
Module can be used to address virtually any phenomena
related to mechanics at the micro scale.
A. FLUID-STRUCTURE INTERACTION (FSI)
Fluidic MEMS devices, or micro fluidic devices, represent
an increasingly important area of MEMS. COMSOL provides
a separate Micro fluidics Module to specifically address these
applications, but the MEMS Module does include significant
micro fluidic functionality for simulating the interaction of
MEMS structures with fluids.
B. ELECTROSTATIC ACTUATORS AND
ELECTROMECHANICS
Electrostatic forces scale as device dimensions
are reduced, a fact frequently leveraged in MEMS. A
typical application of the MEMS Module within this area
is for electrostatically actuated MEMS resonators, which
operate with an applied DC bias.
C. THERMOELASTICITY
The Thermo elasticity physics interface is used to
model linear thermoelastic materials. It solves for the
displacement of the structure and the temperature
deviations, and resulting heat transfer induced by the
thermoelastic coupling. Thermo elasticity is important in
the modeling of high-quality factor MEMS resonators.
D. THERMAL ACTUATORS AND THERMAL STRESS
Thermal forces scale favourably in comparison to
inertial forces. That makes microscopic thermal actuators
fast enough to be useful on the micro scale, although
thermal actuators are typically slower than capacitive or
piezoelectric actuators. Thermal actuators are also easy to
integrate with semiconductor processes, although they
usually consume large amounts of power compared to
their electrostatic and piezoelectric counterparts.
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International Journal of Engineering Trends and Technology (IJETT) – Volume 20 Number 5 – Feb 2015
Design steps for X-Deformation:
1) Open the COMSOL Multiphysics software.
2) Select 3D and click on forward arrow on top.
3) Select solid mechanics and click on forward arrow.
4) Select stationary and click on flag symbol, then a
new window is created.
5) Select length unit as a µm.
6) Right click on the geometry and then select block.
Likewise different blocks are created according to
required dimensions.
7) To union all the blocks right click on the geometry,
then select Boolean operations in that select Union.
Select all the blocks created.
8) Right click on the solid mechanics and then select
fixed constraints. In that the edges which we have to
fix are to be selected one by one.
9) To add a material to model for this right click on the
materials, then select open material browser, then
select MEMS, then select Semiconductors in that
right click on the Silicon material and then select
Add material to model.
10) Meshing is to be done to the model in order to reduce
the errors. Right click on the mesh 1 and then select
free tetrahedral.
11) Right click on the solid mechanics and then select
boundary load. Select the surface on which we have
to apply force. Note the amount of force that is to be
applied on the surface of the proof mass on the left
side column i.e., Fx=10 N/m2 in X-direction.
12) Right click on Study 1 and then click on compute.
Then the model is subjected to force on X-direction.
13) A graph is plotted so that stress in the beams is
observed. To plot a graph Right click on the 1D plot
group 2, then select line graph. For that select a line
or arc of any one of the beams which the proof mass
is supported.
The amount of displacement occurs in the proof mass is
shown in the form of graph below:
Design steps for Y-Deformation:
Same as X-Deformation from step 1-14 except in the
10th step note the amount of force in the Fy=10N/m2.
.
The amount of displacement occurs in the proof mass is
shown in the form of graph below:
To plot the 3D graph to the model Right click on the 3D
plot group 3 and then click on plot. A 3D model is observed.
Design steps for Z-Deformation:
Same as X and Y-Deformations except in the 10th
step note the amount of force applied in the Z-direction as
Fz=10N/m2.
ISSN: 2231-5381
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International Journal of Engineering Trends and Technology (IJETT) – Volume 20 Number 5 – Feb 2015
The amount of displacement occurs in the proof mass is
shown in the form of graph below:-
The amount of displacement occurs in the proof
mass is shown in the form of graph below:
Analytical Design
The proof-mass length, width, thickness are represented as l1,
b1, h1. The L- Beam dimensions are represented by l2, l3, b2,
and h2 respectively.
The optimized device dimensions are given below. Proofmass size (l1 X b1 X h1): 10 X 10X 2 (μm)3
Length of beam (l2): 4.5 μm
Length of beam (l3): 5 μm
Beam Width (b2): 1 μm
Beam thickness (h2): 1 μm
Air gap: 22 μm
Area of proof-mass (A) = l1 X b1 = 100x10-12 m2
Mass of proof-mass (m) = V. ρ
Perforations:
= (A x h1) x ρ = 23x10-14 Kg
(Density
of
the
silicon
ρ
=
2300kg/m^3, V = Volume of
Same as step 1-14 except in between the step 6 & step 7.
proof-mass)
Perforations (holes) are created one by one of required
Let ‘F’ be the force acting on the proof mass, due to
size. For that right click on the geometry then select block.
1
g
acceleration,
A block is created of required size. Right click on the
geometry, and then select Boolean operations in that F= m x a
select difference. For this select the block (hole) which Where ‘m’ is the mass of the proof-mass and ‘a’ is the
we have to subtract from the proof mass. Difference is acceleration,
F = 23 X 10-14 X 9.81 X 1 = 225.63 X 10-14 N
done and a hole is created on the proof mass. Likewise
Force
acting
on each beam W = F/4 = 0.5640 X 10-12 N
some holes are created on the proof mass. For example a
force is applied to the proof mass in x-direction
b2 h23
I

(
)  0.0833 X 1048 m4
Moment
of
Inertia
of
beams:
i.e.,Fx=10 N/m2.It is shown below:
12
Deflection of the beam:
Where E = Modulus of elasticity for silicon E = 1.69 x 10 11
N/m2.
I = moment of inertia of beam.
For beam having length l2:
For beam having length l3:
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International Journal of Engineering Trends and Technology (IJETT) – Volume 20 Number 5 – Feb 2015
C2  45.16597 109 pF
C  C2  C1
 8.9038 109 pF
Bending stress in beam:
b 
M
y
I
Where,
σb = Bending stress in the beam
M = Bending moment acting on the beam
y = the perpendicular distance to the neutral axis.
At 30 g,
REFERENCES
M  W  l2  30
1. L. Zhao, E. M. Yeatman (Optical and Semiconductor Devices Group,
Department of Electrical & Electronic Engineering, Imperial College London,
SW7 2AZ, UK). Micro Capacitive Tilt Sensor for Human Body Movement
Detection
M  76.14  10 18 Nm h
Zhenchuan Yang*, Guizhen Van, Yilong Hao, Guoying Wu (Institute of
y  2  0.5 106 m2.
For maximum bending stress,
Microelectronics, Peking University, Beijing 100871, China). Design and
2
Fabrication of a Torsional Z-axis Capacitive Accelerometer with Novel Com
b Capacitor
 b  457.022811018 MPa
3. Tolga Kaya, Behrouz Shiari, Kevin Petsch1 and David Yates (Central
Michigan University, University of Michigan). Design of a MEMS Capacitive
Comb drives Accelerometer.
4. Larissa Schudlo (McMaster University)(2010). A System to Quantify
Limb Function . Lab VIEW 2011 Help - National Instruments
Where, Relative permittivity of the dielectric Upper
5. Sam Naghshineh, Golafsoun Ameri, Mazdak Zereshki, Dr. S. Krishnan &
r
medium (for Air)
Dr. M. Abdoli-Eramaki. Human Motion
Capture using Tri-Axial accelerometers.
-2
6.
Martin
Baker.
Maths
Euler
Angle,
from
Permittivity
of
free
space
=
8.85
x
10
F/m.
o
http://www.euclideanspace.com/maths/geometry/rotations/euler/index.html


C0 = 40.227 x 10-9 pF.
C1 
r o a
d 
C1  36.26217 109 pF
 a
C2  r o
d 
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