7th WSEAS International Conference on Electric Power Systems, High Voltages, Electric Machines, Venice, Italy, November 21-23,

2007 115

Finite Element Analysis of Micro – Electro – Mechanical Systems by

using the ANSYS software
JOHN K. SAKELLARIS
Faculty of Applied Mathematics and Physics
National Technical University of Athens
9, Heroon Poytechniou, 15780 Zografou
GREECE
ioannissakellaris@yahoo.com

Abstract: - Microelectromechanical Systems (MEMS) is the technology of the very small, and merges at the
nano-scale into "Nanoelectromechanical" Systems (NEMS) and Nanotechnology. MEMS are also referred to
as micro machines, or Micro Systems Technology (MST). MEMS are separate and distinct from the
hypothetical vision of Molecular nanotechnology or Molecular Electronics. MEMS generally range in size
from a micrometer (a millionth of a meter) to a millimeter (thousandth of a meter). At these size scales, the
standard constructs of classical physics do not always hold true. Due to MEMS' large surface area to volume
ratio, surface effects such as electrostatics and wetting dominate volume effects such as inertia or thermal
mass. Finite element analysis is an important part of MEMS design.

Key-Words: - Finite Element Analysis, Micro – Electro – Mechanical Systems, ANSYS software, Coupled
problems, Microactuator; Bistable electromagnetic actuation; UV-LIGA technology; Simulation

1. Introduction The electromagnetic actuators have received much

Micro-electro-mechanical systems (i.e., MEMS) are attention for their capabilities of realizing both large
integrated systems of microelectronics (IC), force and displacement and suitability in harsh
microactuator and, in most cases, microsensors [1]. environment [13] and [14], thus electromagnetic
MEMS technology offers unique advantages actuators with various structures have been fabricated
including miniaturization, mass fabrication and [7], [15] and [16]. Compared with electrostatic
monolithic integration with microelectronics, and microactuators, the electromagnetic ones increase the
makes it possible to fabricated small devices and displacement with low actuation voltage that can
systems with high functionality, precision and effectively enhance the stability of the devices. The
performance. More important, MEMS technology can disadvantage of such devices is that they have higher
enable new circuit components and new functions [2] power consumption, which is obviously an
and [3]. Therefore, MEMS have attracted considerable unfavorable factor for the heat dissipation of the
attention since 1987 [1]. Microactuators are the key microactuators with a compact structure. The high
part of MEMS. For many MEMS devices such as power consumption mainly comes from holding the
switches, optical attenuators, pumps, valves, etc., state of the devices. To overcome the disadvantage
microactuators are required to realize their physical above, electromagnetic actuation with bistable
functions. The controlled actuation or motion of mechanisms was suggested. A type of latching
microactuators can be achieved by several kinds of electromagnetic microactuator with two stable states
actuation mechanisms. Electrostatic, piezoelectric, for reducing power consumption has been
magnetostrictive, magnetic, thermomechanical demonstrated by Ruan et al. [17]. The device was
actuators have been reported [4], [5], [6], [7] and [8]. based on preferential magnetization of a permalloy
Among the different actuation principles, the cantilever in a permanent external magnetic field. But
electrostatic actuation is predominantly employed for the force for the stable states came from the
the electrostatic microactuators’ characteristics of magnetizing cantilever in a magnetic field, which led
simple structures, small energy loss and being to a low efficiency of electromagnetic effect. Ren and
compatible with integrated circuit processes [9] and Gerhard [18] reported a bistable magnetic
[10]. However, electrostatic actuation mechanism has microactuator, where the device employed lateral
the disadvantages of high driving voltage and small movement and the motion was based on the bending
displacement [11]; the high driving voltage has an of the cantilever. In this paper, an electrical - thermal
adverse effect on the lifetime of devices [12]. MEMS microactuator will be presented.
7th WSEAS International Conference on Electric Power Systems, High Voltages, Electric Machines, Venice, Italy, November 21-23, 2007 116

2. Microsystem Analysis Features 11 High Frequency Electromagnetics.

ANSYS Multiphysics has an extremely broad physics (Full wave, frequency domain).
capability directly applicable to many areas of 12 Circuit coupling - voltage & current
microsystem design. Coupling between these physics driven.
enables accurate, real world simulation of devices 13 Acoustic - Structural coupling.
such as electrostatic driven comb drives. 14 Electrostatic-structural coupling.
The ability to compute fluid structural damping 15 Capacitance and electrostatic force
effects is critical in determining the switching extraction.
response time of devices such as micromirrors. 16 Fluid-Structural capability to evaluate
Electro-thermal-structural effects are employed in damping effects on device response
thermal actuators. time.
Fluid (CFD) capabilities are used to compute flow and 17 Microfluidics: Newtonian & non
free surface droplet formation useful in the design of Newtonian continuum flow
ink-jet printer nozzles, and lab-on-chip applications. 18 Free Surface VOF with temperature
The following figure (Fig. 1) explains how ANSYS dependent surface tension.
Multiphysics capabilities fits into the 19 Charged particle tracing in
Microsystem/MEMS design process: electrostatic and magnetostatic fields.
20 Electro-thermal-structural coupling.
21 Piezoelectric & Piezoresistive
transducers: Direct coupled structural-
electric physics. Full isotropic,
orthotropic parameters.
22 Advanced themrolelectirc effect such
as Seebeck, Peltier & thermocouple.

3. ANSYS MEMS Applications

Overview
ANSYS Multiphysics can be applied to a broad range
of Microsystem/MEMS analysis. The following table
(Tab. 1) shows the analysis capability relevant for a
range of applications.
Fig. 1: ANSYS Multiphysics integration into the
Microsystem/MEMS design process.

A sample of the features included in ANSYS

Multiphysics are listed below:
1 Structural static, modal, harmonic,
transient mechanical deformation.
2 Large deformation structural
nonlinearities.
3 Full contact with friction and thermal
contact.
4 Linear & non linear materials.
5 Buckling, creep.
6 Material properties: Temperature
dependent, isotropic, orthotropic,
anisotropic.
7 Loads/Boundary conditions: Tabular,
polynomial and function of a function
loads.
8 Plasticity, viscoplasticity, phase
change.
9 Electrostatics & Magnetostatics.
10 Low Frequency Electromagnetics.
7th WSEAS International Conference on Electric Power Systems, High Voltages, Electric Machines, Venice, Italy, November 21-23, 2007 117

Microsystem Application ANSYS Multiphysics 4. Problem Definition

Capability
This paper demonstrates how to analyze an
Inertial Devices: Structural modal, Static,
electrical-thermal actuator used in a micro-
Accelerometers & Transient, Electrostatic-
Gyroscopes Structural, Reduced order electromechanical system (MEMS). The thermal
macro modeling for actuator is fabricated from polysilicon and is shown
system level. below.
Surface Acoustic Wave Acoustic - Structural The thermal actuator works on the basis of a
Devices coupling differential thermal expansion between the thin arm
MicroStripline High Frequency and blade.
Components electromagnetics. The required analysis is a coupled-field multiphysics
Micro-patch and Fractal High Frequency analysis that accounts for the interaction (coupling)
Antennas electromagnetics. between thermal, electric, and structural fields.
Thermal actuation: A potential difference applied across the electrical
Electro-thermal - connection pads induces a current to flow through
Piezo Inkjet Printheads structural coupled
physics. Thermal-
the arm and blade.
structural coupled physics The current flow and the resistivity of the
Piezoelectric actuation: polysilicon produce Joule heating (I2R) in the arm
Direct coupled structural- blade.
Thermal Inkjet Printheads electric physics. VOF The Joule heating causes the arm and the blade to
Free surfaces & capillary heat up.
action. Temperatures in the range of 700 - 1300oK are
Electromagnetics & generated.
Micro mass spectrometers
charged particle tracing These temperatures produce thermal strain and
Electrostatic - structural thermally induced deflections.
Electrostatic comb drives coupling. Capacitance The resistance in the thin arm is greater than the
extraction.
resistance in the blade.
Newtonian/non-
Microfluidic Channels Newtonian continuum
Therefore, the thin arm heats up more than the blade,
flow which causes the actuator to bend towards the blade.
Full isotropic & The maximum deformation occurs at the actuator
Piezoelectric actuators tip. The amount of tip deflection (or force applied if
orthotropic parameters
Capacitance based: the tip is restrained) is a direct function of the
Electrostatic structural applied potential difference.
Pressure transducers:
coupling. Therefore, the amount of tip deflection (or applied
Piezo-resistive based: force) can be accurately calibrated as a function of
Electro-Structural indirect applied voltage.
coupling These thermal actuators are used to move micro
Electrostatic - structural devices, such as ratchets and gear trains.
Electromechanical RF
coupling.
filters
Capacitance extraction.
Arrays of thermal actuators can be connected
Electrostatic - structural together at their blade tips to multiply the effective
coupling. Fluidic force.
Micromirror technology The main objective of the analysis is to compute the
structural capability to
evaluate damping effects blade tip deflection for an applied potential
Electro-Thermal- difference across the electrical connection pads.
Micro-grippers
structural Additional objectives are to: Obtain temperature,
Electrostatics & charged voltage, and displacement plots, Determine total
Micro TIP field emitters
particle tracing current and heat flow.
Mechanical with complex
Micro-Gear assemblies
contact, friction.
Electro-thermal -
Thermoelectric actuators
structural coupled physics
5.1 Given
Dimensions are in micrometers. The thermal
Magnetostrictive Low Frequency
actuators electromagnetics
actuator has an overall length of approximately 250
micrometers, and a thickness of 2 micrometers.
Tab. 1: The analysis capability o ANSYS relevant The given potential difference across the electrical
for a range of applications connection pads is 5 volts. In Tab.2 are given the
7th WSEAS International Conference on Electric Power Systems, High Voltages, Electric Machines, Venice, Italy, November 21-23, 2007 118

characteristic magnitudes of the actuator Material

Properties for
Material Polysilicon
Properties for (µMKSV units)
Polysilicon Young's modulus 169e3 MPa
Young's modulus 169e3 GPa Poisson's ratio 0.22
Poisson's ratio 0.22 Resistivity 2.3e-11 ohm-µm
Resistivity 2.3e-5 ohm-µm Coefficient of 2.9e-6/oK
Coefficient of 2.9e-6/oK thermal expansion
thermal expansion Thermal 150e6 pW/µmoK
o
Thermal 150e6 W/m K conductivity
conductivity
Tab. 3: Units’ conversion
Tab. 2: Characteristic magnitudes of the actuator
Next, the model is meshed with the coupled field
elements. Then, voltages are applied to the electrical
5.2 Approach and Assumptions connection pads and set their temperature to an
Coupled-field problems can be solved using the assumed 30oC. Next, the electrical connection pads
direct method or the sequential method. The direct are mechanically fixed in the X, Y, and Z directions.
method performs the coupled-field analysis in one Finally, the solution is obtained and post processing
step using coupled-field elements. The sequential of the results to achieve the analysis objectives, as
method performs the coupled-field analysis in stated above.
multiple steps, where the results from one step are
used as input to the next step. Coupled field
elements are not required for the sequential method. 6. Results
This paper uses the direct method to evaluate the The geometry to be modelled appears in the next
actuator. The direct approach is the most efficient figure (Fig. 2):
method for this problem. However, if it were
necessary to include the effects of temperature-
dependent material properties and/or thermal
radiation, it would probably be more efficient to use
the sequential method. The nonlinear thermal-
electric problem could be solved using SOLID98
elements with only the TEMP and VOLT degrees of
freedom active, and the mechanical problem could
be solved using SOLID92 elements. The
temperatures calculated in the thermal analysis could
be applied as loading to the mechanical model using
the LDREAD command.
It must defined the element type as SOLID98 using
the default degrees of freedom [KEYOPT(1)]: UX,
UY, UZ, TEMP, VOLT, MAG. The element
simulates the coupled thermal-electric-structural
response. The MAG degree of freedom is not
required for this analysis so it will not be assigned a Fig. 2: Geometry to be modelled
magnetic material property.
To define material properties for this analysis, it The next figure presents a zoom of meshing (Fig. 3):
must be converted the given units for Young's
modulus, resistivity, and thermal conductivity to
µMKSV units. The units have been converted to
µMKSV, and are shown in the following table (Tab.
3).
7th WSEAS International Conference on Electric Power Systems, High Voltages, Electric Machines, Venice, Italy, November 21-23, 2007 119

Fig. 5: Voltage results

Fig. 3: Zoom of meshing

It may be noted, that the electrical connection pads

First, the temperature results will be plotted. This is
are distinctly two different colors, reflecting the
one of the objectives of this analysis (Fig. 4):
voltage difference across the pads. It may be noted,
also, that there is a change in color in the blade, as
viewed from the pads end to the blade tip end,
indicating that the voltage drop from pad 1 to pad 2
is distributed along the electrical conduction path of
the actuator.
Finally, the displacement results will be plotted and
more precisely those according to the Y – direction
(Fig. 6):

Fig. 4: Temperature results

It may be noted, that the electrical connection pads

are the same color, reflecting the constant
temperature boundary condition. It may be noted,
also, that there is a change in color in the blade, as
viewed from the pads end to the blade tip end,
indicating that the voltage difference across the pads
causes a temperature difference across the blade.
Finally, it may be noted, that the thin arm is at Fig. 6: Displacement results will be plotted and more
higher temperatures than the blade. precisely those according to the Y – direction.
Next, the voltage results will be plotted (Fig. 5):
It may be noted, that the electrical connection pads
are the same color, reflecting that the pads are
constrained in all directions. It may be noted,
especially, the gradual change in color in the blade
and thin arm, as viewed from the pads end to the
blade tip end.
It may be noted, also, from the legend that the color
7th WSEAS International Conference on Electric Power Systems, High Voltages, Electric Machines, Venice, Italy, November 21-23, 2007 120

of the tip of the blade indicates a deflection of USA, 1989. p. 1559–64.

approximately 3.07 micrometers. This deflection [10] E. Thielicke and E. Obermeier, Microactuators
results from the 5 volts applied across the pads. and their technologies, Mechatronics 10 (2000), pp.
The total heat flow is approximately 8.07e9 pW and 431–455.
the total current is approximately 3.23e9 pA. [11] Poddar AK, Pandey KN. Microwave switch
using MEMS-technology. In: Proceedings of the
IEEE eighth international symposium on high
7. Conclusion performance electron devices for microwave and
In this paper, an electrical - thermal MEMS optoelectronic application, 2000. p. 134–9.
microactuator modelling was presented. The ambition [12] Goldsmith C, Ehmke J, Pillans B, et al.,
of the author was to explain, how ANSYS Lifetime characterization of capacitive RF MEMS
Multiphysics capabilities fits into the switch. In: IEEE MTT-S international microwave
Microsystem/MEMS design process. Basic symposium digest, Phoenix, AZ, 2001, p. 227–30.
characteristics of the behaviour of such a [13] C. Liu, Development of surface micromachined
microactuator were identified. A further step of study magnetic actuators using electroplated permalloy,
will be to take into account the dependence of the Mechatronics 8 (1998), pp. 613–633.
electric conductivity on temperature. [14] T.S. Chin, Permanent magnet films for
applications in microelectromechanical systems, J
Magn Magn Mater 209 (2000), pp. 75–79.
[15] W.P. Taylor, O. Brand and M.G. Allen, Fully
integrated magnetically actuated micromachined
References: relays, IEEE J Microelectromech Syst 7 (1998) (2),
[1] M.-H. Bao and W. Wang, Future of pp. 181–191.
microelectromechanical systems (MEMS), Sens [16] Williams J, Wang W. UV-LIGA fabrication of
Actuators, A 56 (1996), pp. 135–141. electromagnetic power micro-relays. In: Proceedings
[2] Liu C. Micro electromechanical systems of the international symposium on test and
(MEMS): technology and future applications in measurement, 2001. p. 1–9.
circuits. In: Proceedings of the IEEE fifth [17] M. Ruan, J. Shen and C.B. Wheeler, Latching
international conference on solid-state and microelectromagnetic relays, Sens Actuators, A 91
integrated circuit technology, 1998. p. 928–31. (2001), pp. 346–350.
[3] Sugiyama S. Synchrotron radiation micro [18] H. Ren and E. Gerhard, Design and fabrication
lithography and etching (SMILE) for MEMS of a current-pulse-excited bistable magnetic
fabrication. In: Proceedings of the IEEE microactuator, Sens Actuators, A 58 (1997), pp.
international conference on microprocesses and 259–264.
nanotechnology, 2001. p. 264–5.
[4] Arjun Selvakumar, Khalil Najafi and Vertical
comb array microactuators, J Micro-electromech
Syst 12 (2003) (4), pp. 440–449.
[5] H. Debeda, T.V. Freyhold, J. Mohr, U. Wallrabe
and J. Wengelink, Development of miniaturized
piezoelectric actuators for optical applications
realized using LIGA technology, IEEE J
Microelectromech Syst 8 (1999) (3), pp. 258–263.
[6] E. Quandt and K. Seemann, Fabrication and
simulation of magnetostrictive thin-film actuators,
Sens Actuators, A 50 (1995), pp. 105–109.
[7] J.W. Judy and R.S. Muller, Magnetic
microactuation of torsional polysilicon structures,
Sen Actuators, A 53 (1996), pp. 392–397.
[8] W. Riethmüller and W. Benecke, Thermally
excited silicon microactuators, IEEE Trans Electron
Dev 35 (1988) (6), pp. 758–763.
[9] Fujita Hiroyuki. Studies of micro actuators in
Japan. In: Proceedings of the IEEE international
conference robotics and automation, Scottsdale, AZ