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Nanoscale Modeling and Computational Infrastructure___________________________Ananth GramaProfessor of Computer Science, Associate Director, PRISM Center for Prediction of Reliability, Integrity, and Survivability of MicrosystemsPurdue University

ayg@cs.purdue.edu, http://www.cs.purdue.edu/homes/ayg

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PRISM Model Device

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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

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Input Experiments:Surface roughness, composition, defect densities, grain size and texture

Atomistics

PRISM Device simulation

MPM & FVM

Validation Experiments:Microstructure evolution,

device performance & reliability

Predi

ctio

ns

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

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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

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Atomistic Modeling of Contact PhysicsHow: Reactive/Classical MD with ab initio-based potentialsSize: 200 M to 1.5 B atomsTime scales: nanoseconds

Mechanical response:Force-separation relationships (history dependent)Generation of defects in metal & roughness evolutionGeneration of defects in dielectric (dielectric charging)

Electronic properties:Thermal role of electrons in metalsCurrent 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

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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:

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Obtaining Surface Separation-Force Relationships

Contact closing and opening simulation200 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

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Upscaling MD to: Fluid Dynamics

Given a distribution of incident momenta characterize the distribution of reflected momenta (accomodation coefficients)

pi

Fluid FVM models use accommodation coefficients from MD and predict incident distribution

Role of temperature and surface moisture on accommodation coefficients

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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

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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

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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.

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Bond Order Interaction

Bond order for C-C bond

BOij '(rij ) exp a

rijr0

b

• Uncorrected bond order:

where is for andbonds

• The total uncorrected bond order is sum of three types of bonds

• Bond order requires correction to account for the correct valency

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Bond Order : Choline

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Bond Order : Benzene

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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]

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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).

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A1

A2

A3

A4

B1C2

C3

C4

B2

B3

x1

x4

x3

x2

f1

f4

f3

f2

=

Ax = f

A = D SD = diag (A1, A2, A3, A4)

(i) Solve Dy = f

(ii) Solve Sx = y

Next Generation Sparse Solvers: The SPIKE Algorithm

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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.

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Summary

• Highly innovative algorithms and parallel formulations for supporting next generation of nanoscale modeling challenges