cb7f77b9827a2951a2026307308df9b3.ppt

- Количество слайдов: 27

Lecture 6 This lecture covers aspects related to: - More on Scaling effects - Simulation of MEMS Dan O. Popa, EE 5349 Microsystems, Summer 2015

Multiphysics in MST • Many coupled effects have been exploited at the microscale: - Electrostatics+Elasticity – accelerometers, resonators, actuators, electrostriction - Magnetodynamics+Elasticity – Voice coils, magnetic levitation, magnetostriction - Electrostatics+ Fluidics – Electrophoresis, electrorheological fluidic actuators. - Piezoelectricity – Actuators, energy scavengers - Thermal+Elasticity – Actuators (bimorph, shape-memory), sensors - For scaling effects summary see Table 9. 3 Madou text. - Modern MEMS modeling software includes multiphysics analysis based on Finite Element Analysis, Nodal Analysis, or Lumped Model Approximations. - Breakdown in continuum assumptions occurs in all cases, but usually at sub micron scale. - Many coupled effects remain to be exploited or understood. - Propose or exploit scaling of physical phenomena and make a microdevice in your class project! Dan O. Popa, EE 5349 Microsystems, Summer 2015

Summary of Multiphysics in MST • Heat – PDE with T(t, x, y, z) and conduction, convection, or radiation B. C. – Conservation of Heat Energy – Constitutive assumption: volumetric heat flux proportional with temperature gradient: Fourier’s Law – BC: Newton’s cooling law (heat conduction): heat flux through a surface proportional to temperature change across the surface – Coefficients: k – conduction coeff. , h – heat transfer coeff • Elasticity – Navier’s equations: PDE with U(t, x, y, z) (displacement) – Conservation of momentum (F=ma) in differential format – Constitutive assumptions: stress/strain tensors are proportional: Hooke’s Law – Euler-Lagrange equations: ODE with U(x, y, z) displacement to determine steady-state deformation using minimization of energy – Add body forces produced by thermal expansion to Navier’s equation for thermoelasticity. – Coefficients: , – Lame coeff. E, – Young’s Modulus, Poisson’s Ratio, I – area moment of inertia, - coeff. of thermal expansion. Dan O. Popa, EE 5349 Microsystems, Summer 2015

Summary of Multiphysics in MST • Fluids – Navier-Stokes PDEs with U(t, x, y, z) fluid velocity, and slip/tension B. C. – Conservation of mass and conservation of momentum equations. – Constitutive assumption: stress in fluid proportional with pressure and flow velocity. – Coefficients: – Lame dynamic viscosity coeff. – kinematic viscosity, Re – Reynold’s number, Kn – Knudsen’s number • Electromagnetism – Maxwell’s equations: PDE with E, B vector fields. – Conservation of EM energy, and EM induction equations (Gauss, Ampere, Faraday). – Constitutive assumptions: magnetic and electric fields related to flux densities through permitivity and permeability tensors. – Lorentz force, Biot-Savart Law, Poisson, conservation of charge are all consequences of Maxwell’s equations. – Permanent and temporary EM effects in materials – Coefficients: - permitivity (dielectric) constant, - permeability, c – speed of light. Dan O. Popa, EE 5349 Microsystems, Summer 2015

Additional Effects • Coupled effects – – – – Piezo-electric Electro-fluidic Magneto-fluidic Electro-elastic Magneto-elastic Molecular diffusion Dan O. Popa, EE 5349 Microsystems, Summer 2015

Scaling in Electrostatics Capacitor scaling Energy: Capacitance: Breakdown voltage: Fz Dielectric - Higher breakdown voltages due to Paschen effect Large changes in capacitance used for sensing position Fairly large forces for actuators by scaling the plate gap and increasing the plate area Must deal with “pull-down” effects (e. g. prevent metal structures from direct contact). Dan O. Popa, EE 5349 Microsystems, Summer 2015 A=L² Fx Force: Electrostatics is favorable to scaling down: + V - D

Scaling in Electromagnetics Wire Forces on electrical charges placed in magnetic field B Force on charged particle (Lorenz): Force on current carying wire (Laplace): Magnetic field around a wire (Ampere): Circular coil Magnetic field: Inductance: Current I B Wire length L, radius r Fz Small magnet w/ magnetization M Stored Energy: Force to another loop: D Bcenter I Force to small magnet Magnetism is not favorable to scaling down: - Scaling to higher dimensional power Increase in current density to compensate creates Joule heating Fixes: increase in permanent magnetization, use of multiple coils (e. g. solenoid) or superconductivity Dan O. Popa, EE 5349 Microsystems, Summer 2015 Repelling force Fz

Scaling of Elastic Strength • Stiffness of cantilever beams – – – – E – Young’s Modulus (N/m) L – Beam Length (m) t – Beam thickness and width (m) I – Area Moment of Inertia (m 4) w(x) – beam weight per unit length (kgf/m) u(x) – beam deflection (m) x – distance from fixed point u/ x – slope of beam σ=EI 2 u/ x 2 – bending moment EI 3 u/ x 3 – shear force F – force applied at end of beam y – beam tip vertical displacement k – beam vertical stiffness - resonant frequency of beam Dan O. Popa, EE 5349 Microsystems, Summer 2015 Euler-Bernoulli equation F y

Dan O. Popa, EE 5349 Microsystems, Summer 2015

Summary of Scaling Effects • Physics of scaling laws is dominated by surface effects, instead of volumetric effects. • Microfluidic fluid flow is dominated by viscous forces. Reynolds numbers are very small (<<1). • Small fluid-fluid interfaces have large energy, resulting in dominant surface tension forces forming bubbles and menisci. • Electrostatic surface charges can exert large forces at small scales. Magnetic effects are much weaker at the miscoscale. • Heat diffusion of small objects is very fast, and conduction cooling through the surface dominates. Ohmic (Joule) heating cannot be neglected. • Small structures become very stiff compared to their weight. They become fragile to external concentrated forces and can easily break. Their natural frequencies of vibration increase as size decreases. Inertial effects at small scales can often times be neglected. Dan O. Popa, EE 5349 Microsystems, Summer 2015

MATLAB Simulations • Type “help graphics, help graph 2 D, help graph 3 D” at the command prompt. Use plot, plot 3 D, xlabel, ylabel, rectangle, etc commands to plot graphs and draw objects. • Download MEMS simulation tool Sugar 2. 0, or Sugar 3. 0 from. L http: //www-bsac. eecs. berkeley. edu/cadtools/sugar/ • Locate the manuals and follow instructions for installation (set your path in MATLAB to the download and unzip folder and its subfolders). • Go through the demo examples, especially the cantilever demo and see if you can run it. • Let me know if you have any difficulties. Dan O. Popa, EE 5349 Microsystems, Summer 2015

MEMS Modeling • Mask Layout Tools • 3 D solid modeling tools. • Meshing and Finite Element Analysis: electro-mechanothermal-fluidic. • Lumped model approximation from physical principles. • Nodal analysis: Dynamic reduced order modeling. • Simulation tools are connected to foundry processes. DRC – built in to many tools. • Examples: – – – – LASI (Layout Editor), L-Edit COMSOL (Former FEMLAB) – Multiphysics Simulation ANSYS – Multiphysics Simulation MEMS Nodal Analysis: Sugar (BSAC), NODASV (CMU) Samples - (Sandia MEMS Design and Simulation) Intellisuite (MEMS Design and Simulation) MEMSPro (MEMS Design and Simulation) Coventorware (MEMS Design and Simulation) Dan O. Popa, EE 5349 Microsystems, Summer 2015

MEMS Layout Terminology Anchor: A point at which part of a MEMS device is secured to the substrate to prevent part from moving. Tether: An anchor which can be broken to release a MEMS part. Dimple: A small feature or bump, typically a raised square on the surface of a MEMS device. Dimple can be used as mechanical stops. e. g. to control the touch down in a high aspect ratio device. Pad: A rectangular area metalllzed and used as an electrical interconnect. Etch Hole: A rectangular area etched out to provide an added release flow channel. Cell: A design repeated across the wafer. EDA: Electronic Design Automation. EDA is to an electronic engineer what CAE is to a mechanical engineer. Traditional EDA software providers are Cadence & Mentor Graphics. DRC: Design Rule Checking: A process, typically fully automated by the layout EDA software that check a layout for fabrication feasibility based on a built in knowledge base. CIF File: ASCII based 2 -D layout file format used to transfer layout information between EDA tools, by Foundry to generate fabrications masks. DXF: The Auto. DEsk Drawing e. Xchange Format: A drawing format that is commonly used to transfer layout information between EDA tools, and by the Foundry to generate fabrications masks. GDS II: 2 -D mask layout Binary file format used to transfer layout information between EDA tool, and by the Foundry to generate fabrications masks. There are two flavors, "Manhattan" where devices have edges composed of straight line, and "Boston" where devices can have true curves. HARM: High Aspect Ratio MEMS manufacturing techniques including surface micromachining that result in high aspect ratio geometry. HDL: Hardware Description Language. Similar to SPICE, an efficient method of reduced order modeling electronic components and systems. HDL-A applies to Analog circuits. Lumped Parameters: Simple parameters describing a device such as a mass, spring constant, damping factor that can be used as an analytical representation of the real device. The parameters used in reduced order modeling. Dan O. Popa, EE 5349 Microsystems, Summer 2015

L-Edit – VLSI – Layout Tool • • • L-Edit is an easy to learn draw type LAYOUT EDITOR from Tanner Research. While it is primarily a VLSI design tool, it is also flexible enough to do micromachining design, printed circuit board layout, and other CAD work. The multipass display is particularly powerful (layers can be semitransparent; where two layers overlap, a third color is produced), as is the hierarchy of cells and layers. Changes to a cell (or group) are propagated to all instances and arrays of that cell. The drawing tool pallet includes standard tools and supports right angle, 45 degree, and all angles modes. L-Edit/DRC is L-Edit with a built in Design Rule Checker. DRC is to layout what a spelling checker is to a word processor--it indicates where your design may be faulty. It allows user programmable rules for automatic checking of widths, spacing, and overlaps. www. tanner. com Dan O. Popa, EE 5349 Microsystems, Summer 2015

MEMSPro - MEMSCAP • Standard MEMS Layout and Simulation Package, tailored to MEMSCAP’s foundry processes: Poly. MUMPS, SOIMUMPS, Metal. MUMPS. • ANSYS FEA Engine • www. memscap. com • www. softmems. com Dan O. Popa, EE 5349 Microsystems, Summer 2015

Coventor. Ware – 3 D • Coventor's Process Access Kits are available for the following standard processes: – – – INTEGRAM – Qineti. Q’s Metal Nitride Surface Micromachining (MPK) - CMOS compatible INTEGRAM - Qineti. Q’s Deep Etch Silicon. On-Oxide Process (DPK) - CMOS compatible INTEGRAM - Qineti. Q’s 2 -Layer Polysilicon (PPK) Poly. MUMPS – MEMSCAP’s 3 -Layer Polysilicon Surface Micromachining SOIMUMPS - MEMSCAP’s Silicon-On. Oxide Metal. MUMPS - MEMSCAP’s Nickel Electroplating Tronics - 60 um HARM (High Aspect Ratio Mircomachining) SOI with wafer caping Multi. MEMS – Senso. Nor Infinion Technologies’ Bull Silicon-Glass Micromachining for piezoresistive sensors IMEPKU - Polysilicon (BETA version) HBSRI - Wafer Dissolved Process (BETA version) SIMIT- Process for capacitive MEMS (BETA version) Micro. Fabrica 's EFAB - Multiple stack electroplating (BETA version) Dan O. Popa, EE 5349 Microsystems, Summer 2015 www. coventor. com

Intellisuite – www. intellisense. com Dan O. Popa, EE 5349 Microsystems, Summer 2015

ANSYS Multiphysics Dan O. Popa, EE 5349 Microsystems, Summer 2015

COMSOL - Multiphysics • http: //www. comsol. com/products/tutorials/ Dan O. Popa, EE 5349 Microsystems, Summer 2015

LASI – Free Layout Editor • • LASI 7. 0 files are written in XML (Extensible Markup Language) Format. Free download from: http: //lasihomesite. com/ TLC (Transportable Layout Cell) is a form of LASI cell data that is used for drawing cell data storage and interchange. TLC files are sequential text files written in a well documented format. The information in a TLC file is "line oriented text", that is, you can write it with a text editor and you can read it in a simple line input procedure. This makes these files easily readable by programming languages including Virtual Basic and C/C++. It also makes them very tolerant to catastrophic errors since data can be fairly easily recovered or repaired by a text editor. TLC is convenient for writing special programs to be used with LASI such as drawing transformation utilities or converters from other drawing systems. (CIF 2 TLC 7. EXE, GDS 2 TLC 7. EXE and LASIFLAT 7. EXE are examples. ) A TLC file contains information about the basic objects (boxes, paths, text and cells) in a larger cell. It does not contain information on how to make any cells that may be used within a cell. To build a complete drawing you need a COMPLETE set of TLC files or a TLD file. TLD (Transportable Layout Drawing) is an extended TLC file format. It contains a cell reference table, a layer table and the various other records of ALL the cells needed to make a particular cell. Since TLD can pack one or more complete cells it is intended for archiving and transporting complete drawings. A TLD of a particular cell is called a "packed cell". Cell files in TLC or TLD always have the extension ". tlc" or ". tld" respectively. Masks will be converted to GDS. Converters to CIF or DXF also available. Dan O. Popa, EE 5349 Microsystems, Summer 2015

TLC XML Format Cell Object Record: =C{nl} or **{nl} Layer of Box{sp}X of Left Side{sp}Y of Bottom Side{sp}X of Right Side{sp}Y of Top Side{nl} **{nl} (omit in original TLC) Path/Poly Object Record: =P{nl} or

{nl} Layer of Path/Poly{sp}Width{sp}Number of Vertices{nl} (Width in basic units) X 1{sp}Y 1{sp}X 2{sp}Y 2{sp}X 3{sp}Y 3{sp}X 4{sp}Y 4{sp}X 5{sp}Y 5{nl} . . . . Xn-1{sp}Yn-1{sp}Xn{sp}Yn{nl}

{nl} (omit in original TLC) Dan O. Popa, EE 5349 Microsystems, Summer 2015 TLC Tags Example: =L 3 STRUCT 2 NOTE 10 WAFER 20 =H JAMMER 1 7. 0. 1. 2 100 um 02/18/04 10: 45: 57 2 -35000 -36800 20750 40000 15 15 709 2 =C CROSS 0 -35000 40000 0 =B 2 -5900 -36800 0 -34000 =P 2 0 7 -20000 13407 -20000 20300 18750 20300 -18750 17343 -19050 16900 -19050 14050 -20000 13407LASI MUMPS Die Layout Source: Zyvex Dan O. Popa, EE 5349 Microsystems, Summer 2015 Lasi 7 Editor

SUGAR – Free MEMS Sim • • • SUGAR is a MATLAB toolbox for basic simulation of MEMS, V 0. 5 -V 3. 1 Devices are described by text netlists. Can be parameterized and heirarchical. Lists of elements connected together at nodes. Similar to SPICE or finite element netlists. Can include files via a uses statement Numbers can have metric suffixes (e. g. 2 u for two micrometers) Comments begin with %, extend to end of line Can form simple numerical expressions, Matlab-like syntax for operations Example: Demo_cantilever – – • Load and display device description – – • dq = cho_dc(net); cho_display(net, dq) Analyze and display static displacement – • net = cho_load(’cantilever. net’); cho_display(net); dy = dqval(net, dq, ’tip’, ’y’) Get y-displacement of tip Dan O. Popa, EE 5349 Microsystems, Summer 2015

Sugar Architecture Mumps. net process poly = [ Poisson = 0. 3 thermcond = 2. 33 e-6/C viscosity = 1. 78 e-5 fluid = 2 e-6 density = 2300 Youngsmodulus = 165 e 9 permittivity = 8. 854 e-12 sheetresistance = 20 stress = 0 straingradient=0 thermalexpansion=0 ambienttemperature=0 ] %Poisson's Ratio = 0. 3 %Thermal conductivity Si = %Viscosity (of air) = 1, 78 e-5 % Between the device and the substrate. %Material density = 2300 kg/m^3 %Young's modulus = 1. 65 e 11 N/m^2 %permittivity: C^2/(u. N. um^2)=(C. s)^2/kg. um^3; %Poly-Si sheet resistance [ohm/square] process p 1 : poly = [ h = 2 e-6 meters ] %Layer height of mcnc poly 1 process p 2 : poly = [ h = 1. 5 e-6 meters ] %Layer height of mcnc poly 2 process d 2 : poly = [ fluid = 0. 75 e-6 ] Dan O. Popa, EE 5349 Microsystems, Summer 2015 %Fluid layer thickness p 1: p 2 = 0. 75 e-6 meters.

Example: Multibeam. net % This demonstration netlist describes an oddly-shaped % structure consisting of % % - An anchor at node 'substrate' in the first poly. Si layer % - A 100 micron beam from 'substrate' to 'A' in the same layer % - Two 50 micron beams extending from 'A' at 45 degree angles to % the default orientation, where the rotation is about the z axis. % In the default orientation, the direction from the first to second % node is the positive x direction. % - An arm sticking up at an angle out of the x-y plane, extending % from the end of one of the arms of the Y-shaped structure. % - A one nano-Newton-meter moment applied at D uses mumps. net anchor p 1 [substrate] [l=10 u w=10 u] beam 3 d p 1 [substrate A] [l=100 u w=2 u oz=0] beam 3 d p 1 [A B] [l=50 u w=4 u oz=pi/4] beam 3 d p 1 [A C] [l=50 u w=4 u oz=-pi/4] beam 3 d p 1 [C D] [l=50 u w=4 u oy=-pi/4] f 3 d * [D] [M=5 n oy=-pi/2] Sugar Intro 1 Sugar Intro 2 Sugar Intro 3 Dan O. Popa, EE 5349 Microsystems, Summer 2015 Sugar 1, 2, 3

Need for system-level simulation tools • Motivation: – A significant number of designers use a common set of components, so they should be reused. • Simple Actuators: Thermal bimorph / Comb drive / Bank of bimorphs / XY Bimorph banks / XY stage / Rotary drive / Snap connector / Gripper • Complex systems: Multi DOF micro-robot / Large numbers of micro-robots. – Lumped-model approximations are good for parametric designs, while full fledged FEA analyses take too long. Design optimization based on iterative methods requires fast computation of mechanism kinematics and dynamics. – FEA offers diminishing returns as the number of components or time steps increase. – Lumped model solver has O(N³) complexity, where N is the number of beams. Improved solvers are needed for large N. • Difficulty: – Simulation of large number of micro-robots performing a task cooperatively or in parallel is complicated by large numbers of so called closed-loops, and by intermittent constraints. • Approach: – Use physical principle models & experimental data to derive simple models for the basic actuators – Use reduced order models for complex MEMS structures by linking together simple building blocks – Use efficient (linear in the number of DOFs) algorithms for simulation of complex systems, allowing for design iteration – Use reduced order models for optimization, open-loop input shaping, and closed-loop control Dan O. Popa, EE 5349 Microsystems, Summer 2015

Readings for Weeks 1 -3 • • HW 1 posted – requires reading! Guidelines for term project posted Chapters 2, 3 from Pelesko Text Chapter 9 – Madou Text Dan O. Popa, EE 5349 Microsystems, Summer 2015