Evolutionary Synthesis of MEMS Design Ningning Zhou, Alice Agogino, Bo Zhu, Kris Pister*, Raffi Kamalian Department of Mechanical Engineering, *Department of Electrical Engineering and Computer Science University of California at Berkeley

Outline Introduction MEMS GA representation Genetic operations Synthesis example 1 Synthesis example 2 Conclusion and Future work

Introduction to MEMS Synthesis MEMS are extremely small (~um) mechanical elements often integrated together with electronic circuitry, manufactured in a similar way to computer microchips. MEMS synthesis: automatically generate functional and optimum solutions for MEMS design. Device design synthesis Fabrication process synthesis

Evolutionary Approach Genetic algorithms are global stochastic optimization techniques based on the adaptive mechanics of natural genetics. Robust and non-problem specific. GAs code the parameter set of the optimization problem as finite-length string. GAs start the searching from a population of random points, improve the quality of the population over time by genetic operations: selection, crossover, mutation; The best fitted solution will be evolved toward objective function.

Multi-objective Genetic Algorithms (MOGAs) Deal with multiple, often competing, objectives. Present a set of pareto-optimal solutions: A(1) B(1) D(1) G(2) H(2) I(3) f1 f2 A solution x is pareto- optimal if there doesn’t exist any other solutions that dominate x. equally good; non- dominated;

Evolutionary MEMS Synthesis Approach Done Pareto ranking Rank-based fitness assignment Design specifications MEMS simulation (SUGAR or other tools ) Create initial designs Yes No New generation of designs Random immigrants Pe%Pe% Elitism Pi%Pi% 1 - P e % - P i % Performance values Meet specifications Genetic operations: selection,crossover mutation

MEMS GA Representation A MEMS device is decomposed into parameterized MEMS GA building blocks. Basic or primitive elements: anchors, beams etc. Clusters: springs(several beams), comb-drive etc. Represented by subnets in SUGAR. A rooted acyclic tree of building components. Acyclic: open-chain structure. Rooted: A reference node.

GA Building Blocks Block type A number is assignment to represent one type; Block ports (nodes) Nodes connected to other building blocks ; Variable Parameters

MEMS GA Representation (cont.) Anchor + spring1 Mass (a)MEMS resonator with four meandering springs Anchor + spring2 Anchor + comb1 Anchor + comb2 Spring3 + anchor Spring4 + anchor (b) GA Building blocks and their connectivity Center mass Serpentine spring Comb drive anchor beam a y x

Genetic Operations: Selection Fitness assignment for each individual: f f is proportional to performance; Roulette wheel selection p1p1 p2p2 p3p3 p4p4 pipi …… Pointer

Genetic Operation: Crossover Cut and splice crossover Analogous to the traditional one-point crossover Cut each parent into two pieces and exchange; Achieve configuration evolution. Parametric Crossover Analogous to the traditional uniform crossover Arithmetical crossover for selected building block parameters: c=λp1 + (1-λ)p2 Achieve building block parameter evolution.

Crossover (cont.) AnchorSpring 2Spring 1 AnchorMassSpring 1Spring 2Anchor Parent 1: Parent 2: L2 L1 L2 Anchor Spring 2 Spring 1 Mass Anchor MassSpring 1Spring 2 Anchor Child 1: Child 2: Mass Arithmetical crossover

Mutation Uniform mutation Each design variable is replaced by a random number within boundaries Each design variable is mutated independently according to the mutation probability (very small).

Example 1: Meandering Spring Concept design: one anchor and N beams connected subsequently; Design goal: generate a mechanical spring with designated K x, K y. Design variables: number of beams N, length of beams L, width of beams w, angle of beams theta; Design Constraint: 2um < w <20um, w < L < 400um, -pi/2 < theta <pi/2

Example 1: Parameter Coding type node variables [anchor] [1] [beam] [1 2] [L1 w1 theta1] [beam] [2 3] [L2 w2 theta2] [beam] [3 4] [L3 w3 theta3] …………

Example1: Crossover parent 2 N 2 =3 parent 1 N 1 =5 child 2 child 1 child 2 child 1 Parameter crossover for the first N min rows Cut and splice

Example 1: Results N = 2 K x = 2.00 N/m K y = 2.00 N/m Solution 1 N = 3 K x = 2.00 N/m K y = 2.00 N/m Solution 2 Objectives: K x = 2.00 N/m K y = 2.00 N/m

Example 1: Results (cont.) Solution 5 N = 5 K x = 1.92 N/m K y = 2.00 N/m N = 5 K x = 1.99 N/m K y = 1.98 N/m Solution 6 Solution 4 N = 3 K x = 1.99 N/m K y = 2.03 N/m Objectives: K x = 2.00 N/m K y = 2.00 N/m

Example 2: Meandering resonator Concept design: four meandering spring and one center mass; Design goal: generate a resonator with designated lowest resonant frequency f, stiffness K x, K y. Design variables: parameters of each spring and the mass. Design Constraint: 2um < w <20um, w < L < 400um, -pi/2 < theta <pi/2

Example 2: parameter coding type node variables [mass] [ ] [L W] [spring1] [1] [L1 w1 theta1….] [spring2] [2] [L1 w1 theta1….] [spring3] [3] [L1 w1 theta1….] [spring4] [4] [L1 w1 theta1….]

Example 2: schematic Building block 1 (Anchor + spring) center mass Building block 2 (spring + anchor) Building block 4 (Anchor + spring) Building block 3 (spring + anchor)

Example 2: results Solution 1 f = Hz K x = 1.80 N/m K y = N/m f = Hz K x = 2.00 N/m K y = N/m Solution 3 Objectives: f=93723 Hz, K x = 1.90 N/m, K y = 0.56 N/m

Example 2: results f = Hz K x = 1.90 N/m K y = 0.52 N/m Solution 6 f = Hz K x = 1.84 N/m K y = 0.59 N/m Solution 5 Objectives: f=93723 Hz, K x = 1.90 N/m, K y = 0.56 N/m

Example 2: convergence curves Iterations (generations) The lowest natural frequency (rad/s) Stiffness in y direction (N/m) Iterations (generations) Average performance value in the pareto-set in each generation Objective performance value

Example 2: convergence curves Stiffness in x direction (N/m) Iterations (generations) Average performance value in rank 1 in each generation Objective performance value

Conclusion A representation of MEMS designs with a rooted acyclic tree of MEMS GA building blocks is proposed and shown to be effective and extensible for GA MEMS synthesis. A crossover operator, with emphasis both on configuration and variable parameter searching, is developed and shown to be feasible. Multi-objective genetic algorithms (MOGAs) were successfully applied to MEMS device design synthesis to produce results not previously envisioned by human designers.

Future Work Feedback from fabrication and testing on final Pareto set. Develop heuristic rules to ensure valid geometrical, functional & producible designs. Compare simulated annealing to genetic algorithms for MEMS device synthesis. Develop library of MEMS devices (indexed by function, materials, etc.) with useful GA building blocks (clusters & primitives). Develop knowledge-based and case-based reasoning tools help to choose an initial concept design for MOGA.

Proposed MEMS Synthesis Architecture Devices (indexed by function, materials, etc.) Building Blocks (clusters & primitives) Case Library Input Specifications Obtain & Select Configurations Optimize & Simulate Layout & Fabrication Add to Case Library Test & Evaluate

Current MEMS Libraries None are indexed databases. All existing libraries relatively small and not compatible with Sugar. CaMEL (Consolidated Micromechanical Element Library) Non-Parametrized (springs, hinges, sliders, actuators, accelerometers, gear trains, test structures, etc.) Parametrized (comb drive, side drive, bearings, springs, test structures, etc.) Commercial CAD tool libraries (e.g., MEMSCAP, Tanner, Coventor)