SUGAR: Simulating MEMS

Transcription

1 SUGAR: Simulating MEMS David Bindel UC Berkeley, CS Division SUGAR: Simulating MEMS p.1/30

2 Outline SUGAR group and research goals Microsystems overview Simulation methodology Software architecture Research directions Concluding thoughts SUGAR: Simulating MEMS p.2/30

3 SUGAR: System simulation Goal: Be SPICE to the MEMS world Fast enough for early design stages Simple enough to attract users Capable of simulating interesting coupled physics SUGAR: Simulating MEMS p.3/30

4 SUGAR group Faculty Grad students A. Agogino D. Bindel Z. Bai J.V. Clark J. Demmel D. Garmire S. Govindjee R. Kamalian K.S.J. Pister S. Lakshmin J. Nie SUGAR: Simulating MEMS p.4/30

5 Microsystem applications Multi-domain micromachines made with IC fab technology. Inertial sensors: accelerometers, gyros Fluidics: ink jet printers, biolab chips Optics: optical switches, projectors Pressure sensors: industrial, medical, auto RF devices: cell phone, radar components Other: microrelays, sensors, disk heads (List from Microsystem Design by S. Senturia) SUGAR: Simulating MEMS p.5/30

6 Microscale physics Surface area / volume ratio is large (compared to most macroscopic structures) Gravitational forces negligible Electrostatic forces substantial Frictional forces (particularly stiction ) important Air behaves like a very viscous fluid (Re << 1) Still classical (vs. nanosystems) SUGAR: Simulating MEMS p.6/30

7 Simulation approaches What? Systems vs devices vs TCAD. Why? Brainstorming, tuning, design verification,... How? Solve continuum equations (finite elements, finite differences, boundary elements) Solve simplified equations of beam and plate theory Solve network equations These approaches are not mutually exclusive! SUGAR: Simulating MEMS p.7/30

8 Modeling approach Similar to circuit and structure simulators; systems modelers Add multiphysics: electro-thermo-mechanical coupling, damping interactions Use balance laws + element models: LRC elements, sources Beams, rigid connectors, plates, point masses, forces Gaps and combs SUGAR: Simulating MEMS p.8/30

9 What can we model? SUGAR: Simulating MEMS p.9/30

10 Of PDEs and ODEs Get ODEs from spatial discretization of PDEs. Simple example is a Hookean rod: ρau tt + EAu xx = F (x, t) and u(0, t) = 0, u(x, 0) = 0 Rewrite PDE in weak form : for any weight w, L 0 w(x, t) EAu xx (x, t) dx = L 0 w F (x, t) dx Assume u(x, t) = û(t) x/l and w(x, t) = αx/l to get Mû tt (t) + Kû(t) = ˆF (t) SUGAR: Simulating MEMS p.10/30

11 Balance laws Local element relations are assembled based on global balance principles: Circuits: KCL and KVL Mechanics: force balance and continuity Similar principles in other domains Software structure above the element level is very generic. SUGAR: Simulating MEMS p.11/30

12 SUGAR architecture Netlist Solvers System assembly Models Results Transient analysis Steady state analysis Static analysis Sensitivity analysis Matlab Web Library Interfaces SUGAR: Simulating MEMS p.12/30

13 Device description language Based on the Lua scripting language Basic ingredients: nodes, materials, elements Node positions can be explicit or implicitly determined User-defined components (subnets) with named parameters for heirarchical design Accept externally defined parameters SUGAR: Simulating MEMS p.13/30

14 Hello world: a cantilever use mumps.net use stdlib.net anchor {node substrate, p1; l=10u, w=10u} beam3d {node substrate, node tip, p1; l=100u, w=2u} f3d {node tip ; F=2u, oz = 90} SUGAR: Simulating MEMS p.14/30

15 Hello world: a cantilever x Y vertical [m] X horizontal [m] x 10 5 SUGAR: Simulating MEMS p.15/30

16 Element routines Standard element interfaces for both Matlab and C/C++ Unused element cases have reasonable defaults Basic tasks: Initialize element data Output element data Display element Declare node and branch variables of interest Compute element forces/currents and tangents Declare boundary conditions SUGAR: Simulating MEMS p.16/30

17 Global analyses Standard analyses on assembled system: Transient response Static equilibrium (DC analysis) Steady-state small-signal response Mode shape determination Treat assembled systems with standard solver technology (e.g. SuperLU, LAPACK, and ARPACK). Can also assemble system in Matlab and use Matlab analysis routines. SUGAR: Simulating MEMS p.17/30

18 Using the Matlab interface 0 x x Y vertical [m] dq = []; for k=1:12 end param.v = k; X horizontal [m] x 10 4 net = cho_load( beamgap2b.net, param); dq = cho_dc(net, dq); tip(k) = cho_dq_view(dq, net, c, y ); SUGAR: Simulating MEMS p.18/30

19 M&MEMS: SUGAR on the Web SUGAR: Simulating MEMS p.19/30

20 Notes on overall architecture Lesser artists borrow; great artists steal. Stravinsky Trying to integrate state of the art from several fields Integration a challenge, even with modular design Continues to evolve: 3.5 is C++ based with automatically generated interfaces for mixed language management SUGAR: Simulating MEMS p.20/30

21 Research directions Software design, integration, and test Model development Measurement feedback Design synthesis, optimization, and sensitivity Model reduction Parameter-dependent eigencomputations + bifurcation analysis What designers need! SUGAR: Simulating MEMS p.21/30

22 Model development Incorporation of anisotropic effects Improved damping models Continued development of multiphysics approximations Microfluidic modeling Extraction from more detailed simulation SUGAR: Simulating MEMS p.22/30

23 Measurement feedback Integrate measurements from probe stations, interferometric systems, Doppler vibrometers Compare to simulation in real time to guide experiments Use results to extract material properties or tune models SUGAR: Simulating MEMS p.23/30

24 Measurement feedback Movie of interferometric recording SUGAR: Simulating MEMS p.24/30

25 Design optimization and synthesis Genetic algorithms and simulated annealing to optimize topology of designs Uses SUGAR as a black box to evaluate objective General issues: Design rule checking and model feasibility Identifying model limits Optimization of continuous parameters Design sensitivity SUGAR: Simulating MEMS p.25/30

26 Model reduction Used to create macromodels from detailed device simulations Also used to reduce large system models Need to handle nonlinear effects SUGAR: Simulating MEMS p.26/30

27 Model reduction 140 Bode plot 120 Gain (db) Frequency (Hz) 200 phase(degree) Frequency (Hz) SUGAR: Simulating MEMS p.27/30

28 Model reduction SUGAR: Simulating MEMS p.28/30

29 Parametric eigencomputations 0.9 hw = e Value = 5.08E+07 Hz Can track resonant modes as geometry changes Track eigenvalues of linearized system to analyze stability of equilibria and bifurcation behavior Close relation to model reduction SUGAR: Simulating MEMS p.29/30

30 Concluding notes Lots of pieces we don t yet touch (control laws, contact models, fluids,...) Trying to remain relevant to current BSAC research Expect some intersection in aims (and SW engineering challenges!) with programs like Ptolemy SUGAR: Simulating MEMS p.30/30