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.

INDUSTRY SPECIFIC EXPERTISE – INJECTION MOLDING

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.

COUPLED FIELD MEMS SIMULATIONS

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)• …

PIEZORESISTIVE-STRUCTURAL

PIEZORESISTIVE-STRUCTURAL

PIEZORESISTIVE-STRUCTURAL

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

DESIGN OPTIMIZATION

BUILDING DIFFERENT WORKFLOWS

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.

DIFFERENT DOE’S FOR DIFFERENT PURPOSES

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

MEMS OPTIMIZATION CASE STUDY

• 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

ROBUST DESIGN OPTIMIZATION - WORKFLOW

Stochastic Inputs

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

OPTIMIZATION STEP BY STEP

Stay Ahead During Challenging Times

• To purchase software or for consulting• ANSYS• modeFRONTIER• MEMSPro

please contact us: info@ozeninc.com(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) 732-4665info@ozeninc.comwww.ozeninc.com