1. 1 Nanoscale Modeling and Computational Infrastructure ___________________________ Ananth Grama Professor of Computer Science, Associate Director, PRISM Center for Prediction of Reliability, Integrity, and Survivability of Microsystems Purdue University ayg@cs.purdue.edu, http://www.cs.purdue.edu/homes/ayg ayg@cs.purdue.edu

2. 2 PRISM Model Device

3. 3 PRISM Modeling Paradigms Key Challenge: Scaling from femtosecond bond activity to predictions of billion-cycle performance DFT for atomistic resolution Reactive Molecular Dynamics for surface chemistry Molecular dynamics for materials properties Material Point Methods for bulk materials Finite Volume Methods for fluid damping

4. 4 Input Experiments: Surface roughness, composition, defect densities, grain size and texture Atomistics PRISM Device simulation MPM & FVM Validation Experiments: Microstructure evolution, device performance & reliability Predictions Defect nucleation & mobility in dielectric Dislocation and vacancy nucleation & mobility in metal Fluid-solid interactions Thermal & electrical conductivity Electronic processes Micromechanics Fluid dynamics Thermal and mass transport Trapped charges in dielectric Elastic, plastic deformation, failure Fluid damping Temperature and species PRISM Multi-physics Integration

5. 5 Develop first principles-based constitutive relationships and provide atomic level insight for coarse grain models Atomistic Simulations in PRISM Identify and quantify the molecular level mechanisms that govern performance, reliability and failure of PRISM device using: Ab initio simulations Large-scale MD simulations

6. 6 Atomistic Modeling of Contact Physics How: Reactive/Classical MD with ab initio-based potentials Size: 200 M to 1.5 B atoms Time scales: nanoseconds Mechanical response: Force-separation relationships (history dependent) Generation of defects in metal & roughness evolution Generation of defects in dielectric (dielectric charging) Electronic properties: Thermal role of electrons in metals Current crowding and Joule Heating Chemistry: Surface chemical reactions Predictions: Role of initial microstructure & surface roughness, moisture and impact velocity on: Main Challenges Interatomic potentials Implicit description of electrons

7. 7 Atomistic modeling of Contact Physics Mobility of dislocations in metal, Interactions with other defects Link to phase fields Defects in semiconductor Mobility and recombination Role of electric charging Surface chemical reactions Reactive MD using ReaxFF Fluid-solid interaction: Interaction of single gas molecule with surface (accommodation coefficients) for rarefied gas regime Smaller scale (0.5 – 2 M atom) and longer time (100 ns) simulations to uncover specific physics:

8. 8 Obtaining Surface Separation-Force Relationships Contact closing and opening simulation 200 M to 1.5 billion atoms – nanoseconds (1 billion atom for 1 nanosecond ~ 1 day on a petascale computer) Characterize effect of: Impact velocities Moisture Applied force and stress Surface roughness Peak to peak distance and RMS Presence of a grain boundary

9. 9 Upscaling MD to: Fluid Dynamics Given a distribution of incident momenta characterize the distribution of reflected momenta (accomodation coefficients) pipi Fluid FVM models use accommodation coefficients from MD and predict incident distribution Role of temperature and surface moisture on accommodation coefficients

10. 10 Upscaling MD to Electronic Processes Defect formation energies Equilibrium concentration Formation rates if temperature increases Impact generated defects Characterize their energy and mobility as a function of temperature Predict the distribution non-equilibrium defects Characterize energy level of defects

11. 11 Upscaling MD to Micromechanics Elastic constants Vacancy formation energy and mobility Bulk and grain boundaries Dislocation core energies Screw and edge Dislocation nucleation energies At grain boundaries, metal/oxide interface Nucleation under non-equilibrium conditions (impact) Dislocation mobility and cross slip Interaction of dislocations with defects Solute atoms and grain boundaries Upscaling MD to Thermals Thermal conductivity of each component Interfacial thermal resistivity Role of closing force, moisture and temperature

12. 12 Computational Challenges Development of effective algorithms for constitutive modeling paradigms Reactive MD, classical MD Effective solvers for sparse linear systems Coupling and information transfer (upscaling, fluid- structure interaction, etc.

13. 13 Bond Order Interaction Bond order for C-C bond Uncorrected bond order: where  is for  and  bonds  The total uncorrected bond order is sum of three types of bonds Bond order requires correction to account for the correct valency

14. 14 Bond Order : Choline

15. 15 Bond Order : Benzene

16. 16 Parallel Performance Reactive and non-reactive MD on 131K BG/L processors. Total execution time per MD step as a function of the number of atoms for 3 algorithms: QMMD, ReaxFF,conventional MD [Goddard, Vashistha, Grama]

17. 17 Parallel Performance Total execution (circles) and communication (squares) times per MD time for the ReaxFF MD with scaled workloads—36,288 x p atom RDX systems (p = 1,..,1920).

18. 18 A1A1 A2A2 A3A3 A4A4 B1B1 C2C2 C3C3 C4C4 B2B2 B3B3 x1x1 x4x4 x3x3 x2x2 f1f1 f4f4 f3f3 f2f2 = Ax = f A = D  S D = diag (A 1, A 2, A 3, A 4 ) (i) Solve Dy = f (ii) Solve Sx = y Next Generation Sparse Solvers: The SPIKE Algorithm

19. 19 N k p Observed Model 5, 000, 000 35 128 2.78 2.64 5, 000, 000 25 128 1.55 1.49 5, 000, 000 15 128 0.70 0.66 5, 000, 000 35 256 1.49 1.33 5, 000, 000 25 256 0.79 0.75 5, 000, 000 15 256 0.35 0.33 5, 000, 000 35 512 0.67 0.67 5, 000, 000 25 512 0.38 0.38 5, 000, 000 15 512 0.20 0.17 5, 000, 000 35 1, 024 0.37 0.35 5, 000, 000 25 1, 024 0.21 0.20 5, 000, 000 15 1, 024 0.10 0.09 SPIKE: Excellent Predictable Performance! Benchmarks on TACC Ranger Sun Constellation Cluster.

20. 20 Summary Highly innovative algorithms and parallel formulations for supporting next generation of nanoscale modeling challenges