Introduction to COMSOL Multiphysics San Diego CA September

Introduction to COMSOL Multiphysics San Diego, CA September 20, 2005 Mina Sierou, Ph. D. Comsol Inc.

Contents Morning Session • • Introduction Demonstration of the modeling procedure • Workshop: Electro-thermal analysis of semiconductor device – 3 D stationary – 3 D parametric • Workshop: Mesh Control Afternoon Session • Hands-on modeling workshops: – Flow over a Backstep – Electric Impedance Center – Thermal Stresses in a Layered Plate – MEMS Thermal Bilayer Valve – Using Interpolation Function – Using Mapped Meshes

COMSOL – The company • Founded 1986 • Development of FEMLAB® /COMSOL Multiphysics (in Sweden) • Business: software, support, courses, consulting • Today, 120 employees worldwide. Offices in US (Boston, L. A. ), UK, Germany, France, Sweden, Finland, Norway, and Denmark • Distributor network covering the rest of the world

Highlights of COMSOL Multiphysics • General purpose Multiphysics FEA code • MATLAB/COMSOL Script integration – COMSOL Multiphysics can be run stand-alone – or with MATLAB for richer set of functions – Can use MATLAB or COMSOL Script as a scripting language • Easy to learn and use • Extremely adaptable and extensible

The COMSOL Multiphysics Product Line And introducing…

COMSOL Script

CAD import module + Mesh import • In 3. 2 we can import IGES, STEP, SAT, X_T, Pro/E, CATIA, Inventor, VDA files with: – More than 1000 faces – Sliver faces, spikes, short edges and other errors

COMSOL Multiphysics Users • • • Rice, Texas A & M, UH UT Austin, UT Arlington Stanford, Caltech, JPL UC’s, UW MIT, Harvard, Princeton… Y NL – Y=LA, LL, LB, PN, Sandia • NASA research centers • NIST, NREL, USGS, SWRI • NIH • • • • Shell, Exxon Mobil Schlumberger, Dow Chemicals Northrop-Grumman, Raytheon Applied Materials, Agilent Boeing, Lockheed-Martin GE, 3 M Merck, Roche Procter and Gamble, Gillette Energizer, Eveready Hewlett-Packard, Microsoft, Intel Nissan, Sony, Toshiba ABB, Volkswagen, Glaxo. Smith. Kline Philip-Morris

Mathematical Modeling • Mathematical description of physical phenomena translates into equations • Description of changes in space and time results in Partial Differential Equations (PDE’s) • Complex geometries and phenomena require modeling with complex equations and boundary conditions • Resulting PDEs rarely have analytical solutions Numerical tools are necessary

Material Balances Material balances are usually described by an equation of the form where j is the flux vector and F a source term

General PDE Form inside domain on domain boundary Example: For Poisson’s equation, the corresponding general form implies All other coefficients are 0. (For later, note: )

Coefficient Form PDE If equation is linear, the general form can be expanded into a coefficient form: transforms into inside subdomain on boundary Example: Poisson’s equation inside subdomain on subdomain boundary (Implies c=f=h=1 and all other coefficients are 0. )

Multiphysics Capabilities • Very different physical phenomena can be described with the same general equations • Coupling of different physical formulations (multiphysics) is thus straightforward in COMSOL Multiphysics • Resulting systems of equations can be solved sequentially or in a fully-coupled formulation • Extended Multiphysics: Physics in different geometries can be easily combined • Coupling variables can also be used to link different physics or geometries

Support & Knowledgebase • • support@comsol. com www. comsol. com/support/knowledgebase

Worked Example – A Simple Fin

Purpose of the model • Explain the modeling procedure in COMSOL Multiphysics • Show the use of pre-defined application modes in physics mode • Introduce some very useful features for control of modeling results

Problem definition • Heat transfer by conduction (Heat Conduction application mode) • Linear equation, stationary solution • Different thermal conductivities can be defined in different subdomains

Problem Definition Step 1 symmetry Step 2

Modeling, Simulation and Analysis • • Draw geometry Define Boundary conditions PDE specification/material parameters Generate mesh Solve (initial conditions, solver parameters) Visualize solution, animation Parametric analysis Optional COMSOL Scripts/MATLAB interface (Optimization, postprocessing, batch jobs etc)

Results

Example: Thermal effects in an electric conductor

Introduction Purpose: Introduce you to the general concepts of multiphysics modeling methodology in COMSOL Multiphysics • The phenomena in this example involve the coupling of thermal and electronic current balances. • The ohmic losses due to the device’s limited conductivity generate heat, which increases the conductor’s temperature and thus also changes the material’s conductivity. This implies that a 2 -way multiphysics coupling is in play. • Parameterization to study temperature as function of different electrode potentials

Problem definition Conductive film Copper conductor Solder joints

Problem definition Heat balance: Current balance: - ·( V) = 0

Second Example: Mesh Control • Automated mesh generator – Suitable for some problems – But not always optimal • How can you to create a non-uniform mesh? – Mesh parameters menu – Mesh Quality • Thin Geometries – Scale problem / mesh / Unscale • Workshop Exercise: Mesh Control – Mesh parameters menu – Displaying Mesh Quality

Lunch Break • Back in 1 hour

Interpolation functions • Interpolation of measured data is commonly necessary when analytical expressions for material properties are not available • New feature in 3. 1 • You can use interpolation function directly in the GUI (without the need for MATLAB) • Data can be entered from a table (for 1 D interpolation) or from a text file (for multidimensional interpolation) • Example: Thermal conductivity as a function of temperature

Example: Flow over a backstep

Thermal Flow over a Backstep • Single physics – Fluid dynamics • Multiphysics – You could add heat transfer and establish temperature profiles • Aim of the model – To give an overview of the modeling process in COMSOL Multiphysics – Standard CFD benchmark – Use both regular triangular and mapped meshes and compare the solution for various mesh densities

Problem definition Step 1: Flow field (note form of input velocity) Step 2: Heat transfer 300 330

Results: Stationary velocity profile

Results: Transient temperature profile t=5 t=10 t=15 t=20

Concluding remarks • The model is simple to define and solve in COMSOL Multiphysics. • The applications can be solved simultaneusly or sequentially and for stationary or time dependent problems. • Different Reynolds numbers can be easily sampled

Example: Electric Impedance Sensor

Introduction • Electric impedance measurement techniques are used for imaging and detection – Geophysical imaging – Non-destructive testing – Medical imaging (Electrical Impedance Tomography) • Applying voltage to an object or a matrix containing different materials and measuring the resulting potentials or current densities • Frequency range: 1 Hz < f < 1 GHz

Main points • Use of Electromagnetics Module, Small Currents Application Mode • Different Subdomains with different physical properties • Logical expressions can be used to modify the geometry

Geometry Electrode Air Ground Conductive medium • We will study how the lateral position of the air-filled cavity affects the measured impedance

Domain Equation • Modelled with Small In-Plane Currents application in COMSOL Multiphysics – Valid for AC problems where inductive effects are negligible – The skin depth must be large compared to the object size • Equation of continuity • Electric field • Displacement

Equations and boundary conditions

Results: Current distribution [on a d. B scale]

Impedance defined as Cavity position

Results: Impedance phase angle Cavity position

Example: Thermal Stresses in a Layered Plate

Geometry coating substrate carrier 1. The coating is deposited on the substrate, at 800 °C 2. The temperature is lowered to 150 °C -> thermal stresses in the coating/substrate assembly. 3. The coating/substrate assembly is epoxied to a carrier plate. 4. The temperature is lowered down to 20 °C.

Model Definition • No motion in the z-direction (2 D Plane Strain application) • Thermal loads are introduced according to: Constitutive relations

Results: First step • Result after depositing the coating on the substrate and lowering the temperature to 150 °C • The figure shows the stress in the x direction

Results: Final step The stress in the x direction after attaching the carrier and lowering the temperature to 20 °C

Example: Rapid thermal annealing

Rapid Thermal Anneal –the device • Important process step in semiconductor processing • Rapidly heat up Silicon wafer to 1000 degrees C for 10 seconds

Rapid Thermal Anneal –model geometry • Modeling question: what is the difference in signal from an IR detector and a thermoresist? Silicon wafer Detector Heater

Rapid Thermal Anneal –COMSOL Multiphysics model • Transient temperature behaviour is modeled with the General Heat Transfer application mode • Radiative Heat Transfer is determined by Surface-to-surface radiation (included in General Heat)

Rapid Thermal Anneal –results T-lamp T-wafer IR detector signal Thermoresist signal => IR detector gives better signal!

Example: MEMs Thermal Bilayer Valve

Thermal Bilayer Valve • Layered material with different thermal expansion coefficients • Layers undergoing different expansion induces curvatures which can be used to close a switch, operate a valve, etc.

Thermal Bilayer Valve • Structural deformation from thermal expansion • Structural buckling • Thermal conduction • Heat source: Joule heating • Current from DC conductive – Axisymmetric • Meshing Thin Layers

Using Mapped Meshes • Feature introduced in FEMLAB 3. 1 • 2 D quadrilateral elements can be generated by using a mapping technique (defined on a unit square) • Best suited for fairly regular domains (connected, at least four boundary segments, no isolated vertices) but irregular geometry can also often be modified/divided in smaller regular ones • 2 D mesh can then extruded/revolved to generate 3 D brick elements

Example: Printed Circuit Board

Printed Circuit Board • Two 3 D geometries, one for the board and one for the circuits • Geometries are meshed and extruded separately • Identity coupling variables are used to link the two geometries back together