17-05-2012, 11:44 AM
Design and Simulation of MEMS Devices using Interval Analysis
[attachment=22221]
Introduction
Micro-electromechanical systems (MEMS) is a process technology used to create tiny integrated
devices or systems that combine mechanical and electrical components. They are fabricated using
integrated circuit (IC) batch processing techniques and can range in size from a few micrometers to
millimeters these devices (or systems) have the ability to sense, control and actuate on the micro scale,
and generate effects on the macro scale[6]. Electrostatic MEMS is a special branch under
micromechanics with a wide range of application specific devices such as switches, micro-mirrors,
micro-resonators etc. Modelling and simulation of electrostatic MEMS devices play an important role
in the design phase in predicting device characteristics. Electrostatic pull-in is a well-known sharp
instability in the behavior of an elastically supported structure subjected to parallel plate electrostatic
actuation [1].
Uncertainty analysis is a technique by which one can determine, with good approximation, whether
a system will work within raw specification limits when the parameters vary between their limits
[2].The manufacturing of structural components is generally associated with manufacturing
imperfections. In general, geometry of a component cannot be reproduced only within certain finite
tolerances. If the influencing variables are uncertain, a direct consequence is that the response
parameters are uncertain as well [3].In the present work, interval analysis is implemented for pull-in
voltage analysis of a micro fixed-fixed beam by using IntLab for analytical simulation and using
Coventorware for numerical simulation, by considering uncertainty in geometric and material property
simultaneously, and individually.
Pullin analysis of fixed-fixed beam
A simple representation of an electrostatic pull-in device is shown in figure (1). It consists of two
parallel conductive plates forming a capacitor with an effective overlap area Aeff and separated by a
gap spacing d. The bottom plate is fixed and the top plate is suspended by a spring with stiffness Keff.
By applying a dc voltage VDC across the plates, an electrostatic attractive force Fel is induced which
leads to a decrease of the gap spacing, thereby stretching the spring. This results in an increase of the
spring force Fs which counteracts the electrostatic force. Pull-in instability occurs as a result of the fact
that the electrostatic force increases non-linearly with decreasing gap spacing, whereas the spring
force is a linear function of the change in the gap spacing. In simple terms, the pull-in voltage VPI can
be defined as the voltage at which the restoring spring force can no longer balance the attractive
electrostatic force. In effect, the gap spacing is closed to zero at the onset of pull-in. In real MEMS
pull-in structures, however, the situation is more complicated as the elastic member is not a simple
lumped spring, but typically a continuous member.
Design of fixed-fixed beam
A micro fixed-fixed beam of the dimensions given in the table 1 is designed in Coventorware. Pullin
voltage is analyzed using Cosolve solver for the actual dimension of the beam and the analysis gives
the pull in voltage to be 38.4188V.
Table 1. Dimensions of the fixed-fixed beam
Parameters Nominal Value
Length of the beam (l), μm 300
Width of the beam (b), μm 50
Thickness of the beam (h), μm 3
Zero voltage gap spacing (d0), μm 1
Young’s modulus (E), GPa 77
Built-in stress (
[attachment=22221]
Introduction
Micro-electromechanical systems (MEMS) is a process technology used to create tiny integrated
devices or systems that combine mechanical and electrical components. They are fabricated using
integrated circuit (IC) batch processing techniques and can range in size from a few micrometers to
millimeters these devices (or systems) have the ability to sense, control and actuate on the micro scale,
and generate effects on the macro scale[6]. Electrostatic MEMS is a special branch under
micromechanics with a wide range of application specific devices such as switches, micro-mirrors,
micro-resonators etc. Modelling and simulation of electrostatic MEMS devices play an important role
in the design phase in predicting device characteristics. Electrostatic pull-in is a well-known sharp
instability in the behavior of an elastically supported structure subjected to parallel plate electrostatic
actuation [1].
Uncertainty analysis is a technique by which one can determine, with good approximation, whether
a system will work within raw specification limits when the parameters vary between their limits
[2].The manufacturing of structural components is generally associated with manufacturing
imperfections. In general, geometry of a component cannot be reproduced only within certain finite
tolerances. If the influencing variables are uncertain, a direct consequence is that the response
parameters are uncertain as well [3].In the present work, interval analysis is implemented for pull-in
voltage analysis of a micro fixed-fixed beam by using IntLab for analytical simulation and using
Coventorware for numerical simulation, by considering uncertainty in geometric and material property
simultaneously, and individually.
Pullin analysis of fixed-fixed beam
A simple representation of an electrostatic pull-in device is shown in figure (1). It consists of two
parallel conductive plates forming a capacitor with an effective overlap area Aeff and separated by a
gap spacing d. The bottom plate is fixed and the top plate is suspended by a spring with stiffness Keff.
By applying a dc voltage VDC across the plates, an electrostatic attractive force Fel is induced which
leads to a decrease of the gap spacing, thereby stretching the spring. This results in an increase of the
spring force Fs which counteracts the electrostatic force. Pull-in instability occurs as a result of the fact
that the electrostatic force increases non-linearly with decreasing gap spacing, whereas the spring
force is a linear function of the change in the gap spacing. In simple terms, the pull-in voltage VPI can
be defined as the voltage at which the restoring spring force can no longer balance the attractive
electrostatic force. In effect, the gap spacing is closed to zero at the onset of pull-in. In real MEMS
pull-in structures, however, the situation is more complicated as the elastic member is not a simple
lumped spring, but typically a continuous member.
Design of fixed-fixed beam
A micro fixed-fixed beam of the dimensions given in the table 1 is designed in Coventorware. Pullin
voltage is analyzed using Cosolve solver for the actual dimension of the beam and the analysis gives
the pull in voltage to be 38.4188V.
Table 1. Dimensions of the fixed-fixed beam
Parameters Nominal Value
Length of the beam (l), μm 300
Width of the beam (b), μm 50
Thickness of the beam (h), μm 3
Zero voltage gap spacing (d0), μm 1
Young’s modulus (E), GPa 77
Built-in stress (