COMSOL MultiphysicsThe MEMS Module

Jarmo RitolaCOMSOL

3. June 2008

• What is the MEMS Module?

• What is MEMS?

• Application areas of the the MEMS Module

• Physics and application modes covered by the MEMS Module

• What can you do, and how do you work with the MEMS Module application modes?

Contents

FSI sensor

What is the MEMS Module?

• The MEMS Module is an add-on to COMSOL Multiphysics

• Collection of additional tools for modeling MEMS devices,microfluidics systems, and physics phenomena common to MEMS

• Collection of MEMS-specific modeling examples

• The MEMS Module seamlessly integrates with all other COMSOL products

– COMSOL Multiphysics and all other modules – Material Library– COMSOL Script (incl. Signals and Systems Lab, Optimization Lab)– Reaction Engineering Lab– CAD Import module

What is MEMS?

• MEMS is short for – Micro: in the microscale– Electro: electromagnetic phenomena– Mechanical: moving or deforming parts– Systems: all in the same device

• MEMS in COMSOL Multiphysics– Modeling of microscale devices and physics that affect their operation– Structural mechanics – Piezoelectric effects – Electrostatic fields– Microfluidics with electrokinetic effects and reactions

Applications From Single Physics …

Structural

ElectricalFluid flow

… to Multiphysics Applications

Structural

ElectricalFluid flow

ThermalTransport

MEMS Module Application Fields

• Electro-mechanical– Electrostatic actuation– Piezoelectric effect– Piezoresistive effect

• Electro-thermal– Resistive heating– Temperature dependent electric

material properties

• Thermo-mechanical– Thermal expansion– Thermo-elastic damping

• Electro-thermo-mechanical

• Fluid-structure– Solid-fluid interaction– Solid-pressure coupling

• Fluid-thermal– Buoyancy, temperature dependent

material properties

• Electrokinetic– Electroosmosis, electrophoresis,

dielectrophoresis, …

• Fluid-chemical– Surface reactions

• Electro-thermo-mechano-fluidic

• Structural mechanics, Electrical fields, Microfluidics

Work Flow

• Model Navigator

• Geometry

• Physics settings

• Solve the model

• Post processing

Add several modes to the modelSpace dimension

Application mode andanalysis type

Geometry Modeling

• Use the built-in CAD tool of the COMSOL Multiphysics

• Import your CAD-files into the model

• Use SolidWorks Live Interface

• Use COMSOL Script to automate geometry generation

• Details of the geometry form the basis for successful analysis

Subdomain Settings

Material models

Coordinate systemsMaterial library

• Define material with application specific user interfaces

Boundary, Edge and Point Settings

• Define settings on all domain levels with application specific user interfaces

Constraint condition

Boundary selection

Define groups

Properties and Settings

• Application mode properties– Tune application mode operation

• Coupling variables– Integration, multigeometry couplings, …

• Global equations– ODEs, import Spice net list, control equations, …

• Solver settings– Tune solver operation for best operation in multiphysics applications

Postprocessing and Visualization

The Inkjet model

The MEMS Module Application Modes

Structural Mechanics Application Modes

• Continuum Mechanics – No simplifying assumptions– Stress strain relation applied directly

to the material– Plane Stress, Plane Strain,

Axial symmetry and 3D formulations

• Several Material models available– Isotropic, orthotropic, anisotropic, elastoplastic– hyperelastic, nearly incompressible formulation

• Coordinate systems define material orientation • Thermal expansion, Loads• Initial stress and strain effects• Large deformation (geometrical nonlinearity), stress stiffening

Structural Mechanics Application Modes

• Several analysis types available– Static, Frequency response,

eigenfrequency, parametric, ….– You can run several tests on the model

by simply changing the analysis type

• Structural damping– time dependent, frequency response,

damped eigenfrequency

• Contact and friction analysis• Follower loads• Perfectly Matched Layers (PMLs)

Model: Prestressed Micromirror

Introduction

• During the manufacturing process materials may gain either compressive or tensile residual stress, which will affect the operation of any MEMS Device

• Residual stress can also be an intended property

• Using a parametric analysis this model studies the deformation of amicromirror for different prestress levels

Model Definition

Fixed

Fixed

Tensile stress (blue)

Compressive stress (red)

Physics SettingsCompressive stress

Solver Parameters Sweep variable andthe parameter list

Results

Film Damping Application Mode

• The modified Reynolds equation modelsthe damping effect of a thin gas film that surrounds a vibrating object.

• Formulation for slide film damping and squeezes film damping

• Special relative flow rate coefficients allow modeling of applications where continuum assumption does not hold

• Time dependent and Frequency response analysis

• Predefined coupling: Structural with film damping.

Model: MEMS Gyroscope

Introduction

• This is a 3D model of a MEMS gyroscope.• The quantity of interest is the “Q factor”, which is a measure of the

ratio of stored energy to energy lost per cycle.• To calculate the Q factor, the eigenfrequency solver is used. The Q

factor can be calculated from the eigenvalue according to:

Model Definition

Fixed

Applied load in x-direction

Fluid damping on underside of device

Physics Settings

Work with predefinedgroups

Results

• A sharp resonance peak is observed at 4.338x105Hz.

Results

• Plot of total displacement for the third eigenvalue.

Piezoelectric Application Modes

• Fully coupled piezoelectric equations for linear piezoelectricity

• Direct and inverse effects

• Stress-Charge and Strain-charge formulations

• Several analysis types– Static, time dependent analysis, frequency response, eigenfrequency and

damped eigenfrequency

• Structural damping

Piezoelectric Application Modes

• Piezo-component modeling– Piezoelectric material– Decoupled isotropic and anisotropic structural and electrical material

• Static and time-harmonic electric fields

• Floating potential boundary condition for floating electrodes

• Compatibility with Structural Mechanics and AC/DC Module application modes

• Applications: BAW and SAW resonators, ultrasonic transducers, piezoelectric actuators and sensors, …

Model: Piezoelectric Effects

Introduction

• This is a 3D model of a piezoelectric transducer.• Piezoelectric materials have a strong two-way coupling between

electrostatics and structural mechanics.• The model allows us to determine the eigenfrequencies of the

structure.• Extruded meshes are used to keep the number of degrees of

freedom to a minimum.

Model Definition

Piezoelectric material

Aluminum (blue)

Adhesive (green)

Ground0.5V

Use Material model todefine Piezoelectric or Decoupled material

Physics Settings

Results

• Plot of mechanical displacement at a frequency of 1.06e5Hz.

Results

• Plot of the absolute value of thesusceptance of the transducer.

• Peaks indicate theeigenfrequencies.

Electrostatics Application Mode

• Solves the electric field and electric potential distribution in non-conducting media

• Three constitutive formulations

• Infinite elements allow approximation of infinite domains

• Electromagnetic force and torque calculations

• Several boundary conditions, with– Port boundary condition to compute the capacitance matrix– Floating potential condition for floating conductors (electrodes)

Model: ALE Cantilever Beam

Introduction

• This is a 3D model of a cantilever beam.• The model uses electrostatics, structural mechanics and moving

mesh application modes.• A potential difference is applied between a ground plate and a

beam.• This creates an electrostatic force on the beam which leads to

deformation of the structure.• The moving mesh application mode is used to track the

deformation.

Model Definition

Air box (red)

Polysilicon beam (blue)

Ground56V

Electrostatic force cause the deflection of the beam.

Physics Settings

Results

• The arrows indicate the electric field, the boundary shows the total displacement of the beam.

• The beam deflection is approximately half its thickness for an applied voltage of 45V.

Conductive Media CD

• Solves the electric current and electricpotential distribution in conductive materials: solids or fluids

• Infinite elements allow approximation of infinite domains

• Resistive heating and temperature dependent conductivity

• Several boundary conditions with:– Port condition to compute the impedance matrix– Floating potential for floating electrodes– Circuit terminal for easier connection to Spice network– Periodic condition

Model: Microresistor Beam

Model Geometry

Upper surfaces are ”free”

Surface attached to the base of the device

Problem Definition, Electric Current

DC current balance forconductive media

Fixed potentials to generate a potential difference ∆V

Physics Settings

Temperature dependentconductivity

Problem Definition, Thermal Analysis

Inside the material:Thermal flux balance with the electric heating as source: Q = s|ÑV|2

Fixed temperature T0

Convection conditionsflux out:h*(T-Tamb)

Physics Settings

Resistive heating

Problem Definition, Structural Analysis

Force balance with the thermally induced stress as volume load

Fixed to the base plate

Physics Settings

Thermal expansion

Results, Electric Potential Distribution

Potential profile [V]

Results, Temperature Field

Maximum temperature

Results, Deformation

Fluid Flow Modeling, Single Phase, Laminar

• Several application modes formodeling of laminar flow

• Navier-Stokes and Stokes equations• Incompressible and weakly compressible

formulations• Microscale effects

– Electroosmotic flow – Viscous slip (viscous non-continuum effect)– Thermal creeping flow– Laminar inflow/outflow

• Artificial Diffusion methods – improved convergence – Allows linear-element multigrid hierarchy for large models

Model: Electroosmotic Micropump

Model Definition

Gel anode (salt bridge)

Gel cathode (salt bridge)

One wide channel

800 µm

+

-

+

-

+

-

Modeled geometry

Stack of thin channels

OutletInlet

Subdomain Settings

Boundary Settings

Results

Fluid Flow Modeling, Two-phase Flow

• The Level Set method– Solves the interface between two fluids

• Fully integrated with all laminar flow application modes

– Level Set Two-Phase Flow, Laminar

• Applications– capillary flow, droplets ink-jets, self

assembly of microparts, …

Model: Capillary Flow

Model Definition

• This model investigates how the surface tension drives the fluid up into the vertical capillary

Water

Air

Wetting angle, θ

θ

Axial symmetry, r = 0

Physics Settings

• Define properties for the two fluids

Results

Transport Modeling

• Transport of diluted species within fluid flow

– Convection and Diffusion– Flow with Species Transport, predefined

coupling for easier flow and transport modeling

• Transport of charged particles under applied electric field and fluid flow

– Electrokinetic Flow

• Connection to the Reaction Engineering Lab– Design the reaction equations in the Reaction Engineering Lab– Export equations to COMSOL Multiphysics– Solve the transport problem in the true geometry

Model: Separation in Micro H-cell

Model Definition

• Coupled flow and mass transfer

• This model studies transport of species with different diffusivity

– Separation of species– Transport from inlet A to Outlet B

Inlet A, c = c0

Outlet B

Outlet A

Inlet B, c = 0

Physics Settings

Fluid velocity

Concentration dependent viscosity

Results

Predefined Couplings

• Structural with Film damping

• Structural with Thermal expansion

• Fluid-Structure interaction

• Electroosmotic flow

• Flow with species transport

• Joule heating

• Each module provides additional predefined couplings

• You can couple any application modes with each other

MEMS Related Features

• COMSOL: Deformed Mesh (ALE)– Geometry effects in electrostatic fields (capacitance, pull-in), fluid-structure

interaction, …

• COMSOL: Heat transfer by conduction– Thermal effects in solids, thermoelastic damping, resistive heating effects, …

• COMSOL: Heat transfer by convection and conduction– Joule heating, thermo-electrokinetic effects, …

• AC/DC Module: Time harmonic electric currents– Time harmonic electric fields in electrolytes: AC-electoosmosis,

dielectrophoresis, …

• COMSOL Script– Save your model as m-file and run parametric analyses of geometry, material

parameters, …

Thank You!