COUPLED FIELD MEMS SIMULATIONS
Tuesday, March 18th, 2014
Metin Ozen, Ph.D., ASME Fellow
OZEN ENGINEERING, INC.
www.ozeninc.com
WHAT DO WE DO?
• Ozen Engineering, Inc. helps solve challenging and multidisciplinary engineering problems with
industry leading computational simulation technologies
• We provide advanced
• Multi-Physics FEA
• Computational Fluid Dynamics (CFD) simulations
THE CAE TOOLS
• ANSYS CHANNEL PARTNER, ANSYS Distributor in California
• Provide sales, marketing, training, technical support and consulting services in California for ANSYS software products
INJECTION MOLDING
INDUSTRY SPECIFIC EXPERTISE - SEMICONDUCTOR
Example of analysis we can perform:
• Multi-physics simulations of Semiconductor chambers
• Ball Grid Array Solder Joint Reliability Optimization
• Thermal-Stress
• Seismic vibration of chamber design
MEMS Ball Grid ArraysSemiconductor Chambers
INDUSTRY SPECIFIC EXPERTISE – SOLAR INDUSTRY
Example of analysis we can perform:
• Multi-physics simulations of solar panel and support
• Electrical, thermal, mechanical and structural analysis
• Solar panel design optimization
• Modal analysis
• Virtual Prototyping
Example of case studies:
- Maximize the solar flux through a surface
- Structural optimization of the pole mount supports of a solar panel in a wind load case study
- Hail Impact on a solar panel
Solar Panel Fluid Structural Analysis
Solar Panel Model
INDUSTRY SPECIFIC EXPERTISE – DESIGN OPTIMIZATION
Capabilities:
•Parametric Exploration
•Mono and Multi-Objective Design Optimization (MDO)
•Process Integration
•Sensitivity Analysis
•Robust Design
•Decision Making Criteria and Tools
BGA OPTIMIZATION
INDUSTRY SPECIFIC EXPERTISE – ELECTRONICS
System Level SimulationBoard Level SimulationChip Level Simulation
Example of analysis we can perform:
• BGA Solder Joint Reliability
• Theta Jc Thermal Characterization
• Thermal-Stress
• Fracture Mechanics & Fatigue
• Board & System Level CHT
INDUSTRY SPECIFIC EXPERTISE – CONSUMER PRODUCTS
Example of analysis we can perform:
• Drop test
• Impact analysis
• Injection Molding• Failure Analysis
• Reliability Simulation
• Fatigue Analysis
Example of case studies:
- Drop test for cell phones- Car crash
Smart Phone Drop Test
INDUSTRY SPECIFIC EXPERTISE – BIOMEDICAL INDUSTRY
Capabilities:
• Simulating how the human body performs when interacting with the environment
• Model the body, but also the objects it interfaces with
• Optimization of movement patterns
• Implant virtual prototyping
• Analysis of working movements and postures, scale results to population or subject anthropometric data
• Virtually assessing the exertion requirements of a new product or process
• Perform computational assessments and quantitatively investigate ergonomic consequences related to changes in design parameters.
COUPLED FIELD MEMS SIMULATIONS
FIELD COUPLING:
• Structural Thermal• Piezoresistive• Electroelastic• Piezoelectric• Thermal-Electric• Structural Thermoelectric• Thermal-Piezoelectric• Structural-Diffusion• Thermal-Diffusion• Structural-Thermal-Diffusion• Structural-Electric• Acoustic-Structural• Electromagnetic• Electromigration• …
COUPLED FIELD MEMS SIMULATIONS
ADVANTAGES OF DIRECT COUPLED FIELD ELEMENTS:
• Allows for solutions to problems otherwise not possible with usual finite elements.
• Simplifies modeling of coupled-field problems by permitting one element type to be used in a single analysis pass.
COUPLED FIELD MEMS SIMULATIONS
DISADVANTAGES OF DIRECT COUPLED FIELD ELEMENTS:
• Increases problem size (unless a segregated solver is used).
• Inefficient matrix reformulation (if a section of a matrix associated with one phenomena is reformed, the entire matrix will be reformed).
• Larger storage requirements.
COUPLED FIELD MEMS SIMULATIONS
COUPLING METHODS:1. Strong (also matrix, simultaneous, or full) coupling - where the matrix equation is of the form:
and the coupled effect is accounted for by the presence of the off-diagonal submatrices [K12] and [K21]. This method provides for a coupled response in the solution after one iteration.
2. Weak (also load vector or sequential) coupling - where the coupling in the matrix equation is shown in the most general form:
and the coupled effect is accounted for in the dependency of [K11] and {F1} on {X2} as well as [K22] and {F2} on {X1}. At least two iterations are required to achieve a coupled response.
BASIC GEOMETRIC NONLINEARITIES
• Many MEMS devices undergo large rotation
- Switches
- Micro mirrors
- Gyroscopes
• Switches are usually constrained at both ends, and undergo lateral deflection
• Both of these situations introduce geometric nonlinear effects into the finite element simulation. Without proper treatment, solution results can have significant error.
BASIC GEOMETRIC NONLINEARITIES
• Consider two phenomena associated with geometric nonlinearities:
1. If an element’s orientation changes (rotation), the transformation of its local stiffness into global components will change.
- This is referred to as “LARGE DEFLECTION”
X
Y
BASIC GEOMETRIC NONLINEARITIES
2. If an element’s strains produce a significant in-plane stress state (membrane stresses), the out-of-plane stiffness can be significantly affected.
As the vertical deflection increases (UY), significant membrane stresses (SX) lead to a stiffening response.
This is referred to as LARGE DEFLECTION WITH STRESS STIFFENING.
Many MEMS devices exhibit large deflection and stress stiffening.
X
Y F
F
UY
INITIAL STRESS
What is Initial Stress?
• Fabrication processes for MEMS structures often leave significant residual stresses in the device
• Residual stresses can significantly effect the performance characteristics of the device
- Pull-in voltage- Eigen frequencies- Deflection
• An initial stress state can be prescribed for selected finite elements to simulate residual stresses
SIMULATION OF MEMS DEVICES
• ELECTROSTATIC-STRUCTURAL• ELECTROSTATIC-STRUCTURAL-FLUIDS• PIEZORESISTIVE-STRUCTURAL (VM238)• …
OPTIMIZATION & COUPLING IN MEMS SIMULATIONS
• modeFrontier offers platforms for the optimization and coupling
• SoftMEMS offers CAD platforms for the design of systems containing MEMS
• ANSYS Offers FEA & CFD
SoftMEMS
CAD PLATFORMS
MEMS – IC Systems
MANUFACTURING
Partners
SoftMEMS-MEMS – IC
Foundry Kits
Electronics
DesignTools
MEMSElectronics
Sourc
e : M
em
scap
• Fabrication Modeling allows users to automatically create a 3D model of the geometry that can be sent to ANSYS and modeFrontier
• Models steps like etch, deposit, electroplating etc.
FABRICATION PROCESS MODELING
Input:
Material, Geometric Parameters….
Output:
Temperature, Stress, Mass, Pressure….
THE TRADITIONAL DESIGN APPROACH
Min Temperature
Stress<VM
Min Mass
Min Deformation
NOWADAYS AUTOMATIC MULTI OBJECTIVE OPTIMIZATION IS POSSIBLE
An optimization problem is a minimization or maximization problem
Min or Max the outputs
THE STARTING POINT: DESIGN OF EXPERIMENT (DOE)
• Performing an initial DOE maximizes the knowledge gained from experimental data.
• It is a strong tool to design and analyze experiments
DOEs are used for different applications:
Create samplings for sensitivity analysis - identify which input variables most affect the experiment
Generate an appropriate set of support points for Metamodel Creation
Create a set of stochastic points for robustness evaluation and reliability analysis
Provide to the optimization algorithms an initial population of designs.
Example of Optimization against two conflicting Objectives, both to be minimized
THE MULTI-OBJECTIVE OPTIMIZATION PROCESS
The smart algorithms kick in and identify
the OPTIMAL design configuration
The design space
exploration is started
An initial population of
designs is generated
(DOE)
“We live in a multi-objective
world”
Power vs consumption cycle time vs qualitylift vs drag
Each optimization technique
is qualified by its search
strategy that implies the
robustness and/or the
accuracy of the method.
DIFFERENT ALGORITHMS
• Micro mirror cell is part of a complex mirror array used for light deflectionapplications
• Due to the geometrical symmetry, one section of the mirror strip necessary for FEanalysis
• Reduced order modeling (ROM) approach has been used for the electrostaticallyactuated MEMS with multiple electrodes
THE MICRO MIRROR MODEL PROBLEM DEFINITION
• The electrostatic domain consists of three conductors,
• The nodes of the mirror itself are defined by node component COND1
• The fixed ground conductors are node components COND2 and COND3.
Parametric Model
THE MICRO MIRROR MODEL PROBLEM DEFINITION
MINIMIZE PULL-IN-VOLTAGE & COST OF THE MICRO MIRROR
Objective:
To determine the optimized geometric configuration of the Micro Mirror model when subjected to a multi objective optimization:
Minimize Pull-in-Voltage
Minimize Cost
Why to Minimize Pull-in-Voltage• Higher operating voltages exponentially decrease the operating lifetime of the switch.
Why to Minimize Cost
• Significant Cost Savings to increase Sales.
Create workflow in modeFRONTIER
• Define the Inputs and their Domains
• Set Ansys as an Application Node
• Set the Logic flow
• Set the Outputs
• Set the Objectives:
• Minimize Voltage
• Minimize Cost
Input Parameter Domain (mm)
fe_la 195 - 205
fe_br 6 - 12
fe_di 10 - 20
sp_la 950 - 1050
sp_br 200 - 300
mi_la 480 - 540
mi_br 25 - 50
po_la 60 - 100
po_br 60 - 100
fr_br20 - 40
d_ele15 - 25
MULTI- OBJECTIVE MICRO MIRROR OPTIMIZATION PROBLEM DEFINITION
Sobol as DOEMOGA-II as Scheduler
Multi Objective(functions to be maximized
or minimized)
Input variables of the parametric model
ANSYS Classic
Cost Calculation
Outputs
MULTI- OBJECTIVE MICRO MIRROR OPTIMIZATION PROBLEM DEFINITION IN MODEFRONTIER
• The electrostatic domain consists of three conductors,
• The nodes of the mirror itself are defined by node component COND1
• The fixed ground conductors are node components COND2 and COND3.
Parametric Model
THE MICRO MIRROR MODEL PROBLEM DEFINITION
• The Chart shows the inputs and its effect on the outputs
• The parameters which are in Red bars represent the direct effect where as Blue bars represent the indirect effect
SENSITIVITY ANALYSIS – INPUT/OUTPUT RELATIONS
Cost Voltage
d_elefe_br
fe_dipo_br
sp_brfe_dipo_br
fe_lami_la
mi_br
The five most important parameters on Cost and Voltage are listed.
POSTPROCESSING – BUBBLE PLOT
Bubble Plot – All Design Points
InitialDesign
71.43% Cost reduction69.82% Voltage reduction
70.31% Cost reduction77.1% Voltage reduction
70.8% Cost reduction73.9% Voltage reduction
Optimum Design69.75% Cost reduction
79.1% Voltage reduction
Cost
Vo
ltag
e
OPTIMIZATION SUMMARY
• Optimization found the optimum design achieving improvement for all the parameter specified:
• Multi-objective:
• 69.75% Cost reduction
• 79.1% Voltage reduction
OPTIMIZATION STEP BY STEP
Workflow
DOE
Metamodel
Optimization
Design Validation
Robustness Evaluation
Robust Design Optimization
Results
• Evaluation of the effects of random variability of certain parameters on the responses.
• Computing the robustness is extremely important
• Robustness can be checked by applying a systematic perturbation analysis based on randomly generated values for the variables.
WHY CHECK FOR ROBUSTNESS?
ROBUSTNESS EVALUATION FOR DESIGN ID 2019
• Verify if the design under exam is able to satisfy a Six Sigma quality standard
Estimation of the lowest acceptable displacement in a Six Sigma context, supposing that the displacement is normally distributed.
Designs
type
Displacementlowest acceptable
displacement
mean
*E-5
std. dev.
*E-7
mean – 6*std. dev.
*E-5
Real 2.2517 5.7998 1.9037
Virtual 2.2744 3.4488 2.0675
Customer Requirement: Lateral Displacement >2*10-5 mOperating temperature < 800°K
Robustness
Requirements
Virtual – MetamodelReal – FE Model
• After a robust evaluation, the optimal design 2019 shows not to be robust
Maximisation problem where the design parameters are defined by the mean and the deviation.
ROBUST DESIGN OPTIMIZATION
The BEST ROBUST solution could not be always identified with the BEST GLOBALsolution.
For these reasons we have to introduce 2 different objectives:
- Maximize the average value of the function inside the variables distribution;- Minimize the standard deviation.
We need a Multi Objective Algorithm to address the Robust Optimization Problem.
POSTPROCESSING – BUBBLE PLOT
The 3D Bubble plot shows the Robust Design Points.
• X-axis: Objective Max. Displacement
• Y-axis: Objective Min. Stress
• Bubble Diameter: Objective Min. Temperature
Yellow points are infeasible points (constraint(s) not satisfied)
Grey points are feasible points (constraints satisfied)
The 4D Bubble plot shows the Robust Design Points.
• X-axis: Objective Max. Displacement
• Y-axis: Objective Min. Stress
• Bubble Diameter: Objective Min. Temperature
• Bubble Color: Objective Min. Volume
Design ID 2036 Optimal Solution which satisfies the six sigma level
STATISTICAL ANALYSIS
-Probability
Density
Function Chart
-Cumulative
Distribution
Function Chart
-Quantile-
Quantile Plot
-Results
obtained by the
Distribution
Fitting tool
Stochastic
Variation of
the Input
Variables
OPTIMIZATION STEP BY STEP
Workflow
DOE
Metamodel
Optimization
Design Validation
Robustness Evaluation
Robust Design Optimization
Results
Stay Ahead During Challenging Times
• To purchase software or for consulting• ANSYS• modeFRONTIER• MEMSPro
please contact us: [email protected](408) 732-4665
THANK YOU FOR YOUR ATTENTION!
FOR FURTHER INFORMATION, PLEASE CONTACT:OZEN ENGINEERING, INC.1210 E. ARQUES AVE. SUITE: 207SUNNYVALE, CA 94085(408) [email protected]