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

2. Contents Morning Session Introduction Demonstration of the modeling procedure Workshop: Electro-thermal analysis of semiconductor device –3D stationary –3D 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

3. 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

4. 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

5. The COMSOL Multiphysics Product Line And introducing…

6. COMSOL Script

7. 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

8. 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, 3M Merck, Roche Procter and Gamble, Gillette Energizer, Eveready Hewlett-Packard, Microsoft, Intel Nissan, Sony, Toshiba ABB, Volkswagen, GlaxoSmithKline Philip-Morris

9. 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

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

11. 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: )

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

13. 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

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

15. Worked Example – A Simple Fin

16. 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

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

18. Problem Definition symmetry Step 1 Step 2

19. 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)

20. Results

21. Example: Thermal effects in an electric conductor

22. Introduction 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 Purpose: Introduce you to the general concepts of multiphysics modeling methodology in COMSOL Multiphysics

23. Problem definition Conductive film Copper conductor Solder joints

24. Problem definition Heat balance: Current balance: -  ·(   V) = 0

25. 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

26. Lunch Break Back in 1 hour

27. 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 1D interpolation) or from a text file (for multidimensional interpolation) Example: Thermal conductivity as a function of temperature

28. Example: Flow over a backstep

29. 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

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

31. Results: Stationary velocity profile

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

33. 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

34. Example: Electric Impedance Sensor

35. 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: 1Hz < f < 1GHz

36. 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

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

38. 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

39. Equations and boundary conditions

40. Results: Current distribution [on a dB scale]

41. Impedance defined as Cavity position

42. Results: Impedance phase angle Cavity position

43. Example: Thermal Stresses in a Layered Plate

44. 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.

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

46. 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

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

48. Example: Rapid thermal annealing

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

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

51. 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)

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

53. Example: MEMs Thermal Bilayer Valve

54. 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.

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

56. Using Mapped Meshes Feature introduced in FEMLAB 3.1 2D 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 2D mesh can then extruded/revolved to generate 3D brick elements

57. Example: Printed Circuit Board

58. Printed Circuit Board Two 3D 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