1. 1 Panel Discussion on V&V/UQ N. R. Aluru

2. 2 V&V Challenges Approach: Identify key phenomena and rank their importance; Verification using tier-1 (single physics), tier-2 (coupled physics), and tier-3 (system level) Challenges: Lack of modules/codes/analytical expressions for some physical phenomena; Verification can be challenging for tier-2 and tier-3 Verification Approach: Identify key phenomena and rank their importance; Validation using tier-1 (single physics), tier-2 (coupled physics), and tier-3 (system level); Use experimental data from literature, Sandia and in-house experiments Challenges: Lack of data for some physical phenomena; Validation can be challenging for many examples Validation

3. 3 UQ Challenges Questions: What input uncertainties are the most important? How does uncertainty in microstructure affect macroscopic membrane response? Uncertainty in dimensions? How does uncertainty in microstructure propagate into the force-history response and thus into structural response? Criterion for success: Comparison to uncertainty experiments Challenges: Propagating uncertainty across scales and physics, computational size and cost, careful control of number of uncertain variables Young’s modulus for polysilicon as measured by various research group over the years [J. V. Clark, Ph.D. thesis, 2005].

4. 4 Verification Techniques Structural-Thermal-Electrostatics Structural-Thermal-ElectrostaticsCoupling Tier III Example FVM + MPM Solver: domain discretization; solution algorithms; time-marching ANSYS: domain discretization; solution algorithm; time-marching Verification: Define criteria structure Assumptions a. specified geometry; b. specified boundary conditions; c. specified applied voltage d. linear elastic material e. heat generation in metal Electrostatic field

5. 5 Validation Techniques PhenomenaSource of Validation Data Tier 3 (System-Level Validation) 1.Electro-mechanical response with dielectric charging and environmental effects 2.Shock response 3.Materials characterization and surface roughness evolution 1.Purdue experiments with actual RF MEMS in the range of 25-125C and different humidity levels 2.Purdue experiments on actual RF MEMS structures for a range of accelerations and temperatures from -55C to 75C. 3.Purdue experiments with TEM and AFM on evolution of grain size, orientation, defects, and surface roughness

6. 6 UQ Techniques Generalized Polynomial Chaos Stochastic Collocation Methods + Easy to implement + Minor changes to code ─ Not as efficient as Galerkin ─ Harder to implement ─ Significant changes to code + More efficient than collocation Choice of inputs from collocation Solver Stochastic Galerkin Methods Solver  Good solution for LAMMPS  Good starting point for other codes  Better for FVM / MPM codes  Optimization beyond collocation realizations

7. 7 How we will use V&V and UQ to guide and set priorities for research activities  Identifying key phenomena and ranking their importance is largely driven by V&V and UQ  Sensitivity/UQ will determine what inputs are important to models – example: role of accomodation coefficients in rarefied gas damping Modeled PhenomenaAlgorithm or Solver Test Problems Tier I (Individual) 1. Drift diffusion charge transport 2. Atomistic-level computation of mechanics FVM MD/LAMMPS Analytic solutions for drift -diffusion for known potential field Comparison of wire/beam bending with in-house MD codes, GRASP Tier II (Coupled) 1. Electrostatics+linear mech. response 2. Fluid-structure interaction FVM+MPM Published solutions (44 - 47) Comparison with ADINA Modeled PhenomenaImportanceModel Adequacy Comments 1. ElectrostaticsHighAdequateLarge microelectronics literature and adequate data 2. Stiction: a. Roughness evolution b. Capillary condensation High Inadequate Few detailed models or simulations for roughness evolution, condensation. 3. Electro-thermo-mech. response: a. Linear b. Nonlinear High Adequate Inadequate Classical electro-mech. response well understood Interaction of microstruct with continuum not well understood.

8. 8 Far-Reaching V&V/UQ Issues  Electrostatic pull-in in MEMS leads to discontinuities in the random domain; Need to develop efficient stochastic algorithms for non-smooth functions in the random domain  Explore easier ways of implementing UQ  New software paradigms for automating UQ implementation  Extensive experimental data is needed for UQ /Validation  Education, teaching and training new generation of students in V&V/UQ