ansys
DESCRIPTION
MEMSTRANSCRIPT
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ANSYS MEMS Features
MEMSCAP®
Yiching LiangMarch 6, 2002
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Finite Element Analysis¨ 3D models built and exported from MEMS Pro
– .ANF format: ANSYS neutral format– .SAT format: ACIS text format (compatible with most FEA, RF &
solvers)
¨ Preprocessing in ANSYS– Boundary conditions/loads– Meshing– Material/element properties
¨ ANSYS solver¨MEMS Pro add-ons in ANSYS
– 3D to layout– Reduced order modeler
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ANSYS MEMS Initiative¨ ANSYS/Multiphysics¨MEMS analysis requirements
– Devices are inherently multiphysics– System of units applicable to small scale– Meshing of high aspect ratio devices & features– Unique material properties– Lumped parameter extraction (into SPICE, VHDL-A/MS)– Capability to model large field domains associated with
electromagnetics & CFD
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ANSYS MEMS Related Features¨ Electrostatics¨ Electrostatic-Structural Coupling¨ Trefftz Electrostatics¨ Capacitance Matrix Extraction¨ Reduced Order Macro Modeling¨ Piezoelectric ¨ Pre-stressed modal¨ Fluid-Structural Coupling¨ Free Surface Fluids¨ High Frequency Electromagnetics¨ Composite Beams¨ Initial/Residual Stress¨ System of Units
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Electrostatics¨ Important in MEMS
– To determine both capacitance and electrostatic forces – Typically used to actuate devices such as comb drives and
switches
¨ Open domain modeled either using infinite boundary elements (INFIN110, and INFIN111) or Trefftz domain technology
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Adaptive P-Elements¨ 3D P-elements for electrostatics
– SOLID128 Brick/Wedge elements– SOLID127 Tetrahedral elements
¨ Polynomial order of element increased automatically to satisfy convergence to a prescribed degree of accuracy– P-order may extend from 2 - 8
¨ Supports – All electrostatics boundary conditions
and loads– node coupling and constraint equations– Trefftz Domain & CMATRIX.
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Electrostatic Analysis with P-Elements¨ Adaptive P-element study on comb drive structure
– Color code on elements: polynomial orders– Electrostatic field contour plot
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Electrostatic-Structural Coupling¨ Allows the actual electrostatic actuation of a MEMS
device to be simulated ¨ Three methods for electrostatic -structural simulation
– ESSOLV macro tool: a sequential coupled field macro– TRANS126: Reduced order macro model element– Manual sequential coupled: using the ANSYS APDL macro
language
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ESSOLV Macro¨ Solves coupled electrostatic-structural static analysis¨Macro automates a sequential solution process:
– Electrostatic solution– Structural solution (LDREAD of forces from electrostatics)– Automatic mesh morphing of electrostatic mesh – Convergence monitoring
¨ Electrostatic field mesh morphs to accommodate the deformed structure
¨ Useful for obtaining “pull-in” voltages, deflections, fields, forces, etc.
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Trans126 Element¨ Electromechanical transducer (EMT) macro element
for electrostatic-structural simulation¨ Characterized by capacitance vs. displacement curve¨ Couples directly to:
– FEA Solid models (solid elements, shell elements, beams)– Other macro models– FEA substructure models
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Resonator Example¨ Electrostatic analysis with EMT elements
– Perform electrostatic analysis and capacitance extraction on onecomb drive
– Table or curve fit results to define displacement vs. capacitance function, apply to TRANS126
– Replace full model with TRANS126 elements
– Comb drive: 250k DOF’s -> 2 DOF’s
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Electrostatics: 3D Trefftz Domain¨ For handling open boundary domains in electrostatics ¨ Hybrid FEA - BEA technology
– The open domain is not meshed– Substantial reduction in the size of model -> solution time
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Trefftz Method¨May be used to connect multiple finite element
electrostatic field domains– Eliminating the need to mesh the field regions between
component regions
¨ Electrostatic field around two charged spheres:
Spheres with individual finite element meshes “connected” by a Trefftz domain.
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Trefftz Example¨ Example: charged, isolated sphere in free space
– 200 DOF’s– Within 3% of closed form solution
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Trefftz Convergence Characteristics ¨ Infinite elements vs. Trefftz domain
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Mesh Refinement Parameter
% E
rro
r (C
apac
itan
ce)
Infinte Elements
Trefftz Domain
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CMATRIX Macro¨ Automates computation of systems capacitance matrix
– Extracts capacitance change as a function of device displacement
¨ Applicable to any number of conductors/dielectric materials
¨ Derives ground and lumped matrices– Lump matrix provides the self and mutual capacitance between
conductors.
¨ Useful for extracting lumped capacitance for use in system level circuit-simulations
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Comb Drive Example¨ Cross-section electric field contour plots for an
analysis on a small section (2 teeth) of a comb drive¨ Contour plots shows electric fields used to compute
the self and mutual capacitance
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P12
P11
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CMATRIX Example Output
¨ The results can be listed on screen, output to a file, or accessed by the ANSYS APDL macro language
¨ Lumped capacitance can be used in – System level simulation– Input to ANSYS Trans126 EMT element
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Macro Model Elements¨ Simplified representations
– Enable rapid simulation of complex MEMS structures
¨Mechanical elements:– Springs, lumped mass, dampers
¨ Circuit elements: – Resistors, capacitors, inductors, transformers, diodes, V/I
sources
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Resonator Example¨ Comb drive resonator
– Comb drives: 2 Trans126 elements (EMT1 & EMT2) – Folded springs: 1 spring element (K1)– Proof mass: 1 mass element (M1)– Squeeze film damping: 1 damper element (D1)
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Piezoelectric Analysis¨MEMS piezoelectric transducers
– Large deformations – Typically more efficient actuator performance than both
electrostatic and thermal actuators
¨ Piezoelectric capabilities:– Geometric nonlinearities: large deflections/rotations – Stress stiffening– Pre-stressed modal and harmonic analyses– Accurately accounts for changes in the electromechanical field in
bending motion– Direct input of the piezoelectric strain matrix [d] – Calculation of the correction to the permittivity matrix [epsT]-
[epsS]
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Beam Steerer Example¨ The two support arms have a layer of piezoelectric
material that move the square-shaped reflecting surface
Courtesy Waveprecision, a division of GSI Lumonics
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Pre-Stressed Modal Analysis¨ In MEMS, pre-stress is sometimes used to adjust or
fine tune the response of the structure– Can compensate for variations in device geometry and material
properties (primarily due to fabrication process variations)
¨ ANSYS/Multiphysics supports the following types of pre-stressed modal analysis:– Mechanical pre-stress directly applied as a mechanical load– Electrostatic pre-stress applied via Trans126 EMT element– Piezoelectric pre-stress applied as a voltage to the piezoelectric
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Pre-Stressed Examples¨ Piezoelectric pre-
stressed modal analysis– First four modes
¨ Electrostatic pre-stressed modal analysis– First mode
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Coupled Fluid – Structural Analysis¨ Fluidic-structural damping
– At higher velocity the fluid does not have enough time to move and is simply compressed
– Fluid damping changes drastically when the transition from compressible to incompressible flow occurs
– Can change the structural response of MEMS devices
¨ FSSOLV macro automates the simulation– Mesh morphing– Convergence monitoring
¨ Capabilities– Allows for large deformations – Time transient problems: user-specified displacement & velocity
time history for moving body– Computes both lift and drag forces– Incompressible and compressible flow– Equivalent resistance and damping terms can be extracted as
macro models2626
Mirror Example¨ End view of a parallel plate capacitor/mirror assembly
– Upper plate rotates – Blue areas is the meshed fluidic domain
Pressure contour
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Free Surface Fluidics¨ Simulates capillary forces & surface tension¨ Volume of Fluids (VOF) technology
– Models time transient problems involving moving liquids with a free surface
– Fluid moves through the mesh– No mesh morphing is required
¨ Gas and liquid interface: continuum surface force (CSF) method to model the surface tension
¨ Surface tension material properties can be temperature dependent
¨ Available results– Contour plots of the fluid boundaries– Pressure distributions within the fluid
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Inkjet Nozzle Example¨ 3-D visualization of an inkjet printer nozzle droplet
formation
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High Frequency Electromagnetics¨ Full wave, frequency domain solvers allow RF MEMS
devices to be easily analyzed ¨ Solves Maxwell's equations in the frequency domain
– Interior class problems such as wave guides and cavities– Exterior problems such as antenna radiation patterns
¨ Includes dielectric and eddy current losses – Can compute heat generation rates that can be sequentially
coupled into thermal and thermal-structural physics
¨ Perfectly Matched Layer/absorber (PML) for open boundaries
¨ Near and far field post-processing tools
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Bandpass Filter Example¨ S11 scattering parameter vs. frequency for a
bandpass filter– Good correlation with alternative analysis methods such as finite
difference time domain (FDTD)
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Composite Beams¨ Arbitrary beam cross sections with multiple materials
– Multi-layered nature of surface micromachined MEMS devices
¨ Eliminates the need to mesh the volume of a complex geometry for a structural analysis– Dramatically reduces model size and computation time
¨ For structural analysis only– Static displacement – Time transient– Dynamic analysis
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Composite Resonator Example¨ Comb drive fingers & frame are modeled using
composite beams– Model consists of ~100 beam elements
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Initial Stress¨ Residual stresses: different thermal properties of each
material/layer – Sometimes used as a design feature
¨ Allows direct specification of a constant state of residual stress in each material– GUI or text file input
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Optical Grating Device Example¨ The effect of initial stress in the structural polysilicon
layer of a optical grating device– Deformation ~ 50 nm
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Systems of Units¨MKS units are not suitable for MEMS¨ ANSYS provides two systems of units suitable for
MEMS simulation:– uMKSV (micrometer, kilogram, second, volt, pico-ampere)– uMVSfA (micrometer, volt, second, femto-ampere, gram)
¨ Unit of length is in µm – Material properties are scaled
¨ Sample conversion tables
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Analysis Example: Thermal actuator¨ Beam actuated by thermal
expansion
SEM Image courtesy of Victor Bright, U Col. Boulder.
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Analysis Example: Electrostatic Mirror¨ Electrostatically actuated
mirror– Surrounding air also meshed
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Analysis Example: Accelerometer¨ Time transient analysis
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Analysis Example: Linear Resonator¨Modal analysis
Images courtesy of Russell DeAnna, NASA.
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Analysis Example: Linear Resonator¨ Electrostatic-structural analysis
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Analysis Example: Microfluidic Channel¨ Non Newtonian flow
120 µm
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Analysis Example: Microfluidic Valve¨Microfluidic valve / resonator