Post on 28-Jan-2016
description
Scott DunhamUniversity of Washington
Nanotechnology ModelingEE539, Winter 2008
Nanotechnology Modeling Lab
Multiscale Materials Modeling
Scott Dunham
Professor, Electrical EngineeringAdjunct Professor, Materials Science &
EngineeringAdjunct Professor, PhysicsUniversity of Washington
Scott DunhamUniversity of Washington
Nanotechnology ModelingEE539, Winter 2008
Nanotechnology Modeling Lab
Structure Density Functional Theory (DFT) Molecular Dynamics (MD) Kinetic Monte Carlo (kMC) Continuum
Transport Tunneling Conductance Quantization Non-equilibrium Green’s Functions (NEGF)
Outline
Scott DunhamUniversity of Washington
Nanotechnology ModelingEE539, Winter 2008
Nanotechnology Modeling Lab
TCAD
ProcessSimulator
Device Simulator
ProcessSchedule
DeviceStructure
ElectricalCharacteristics
Current technology often designed via the aid of technology computer aided design (TCAD) tools
Complex trade-offs between design choices.
Many effects unmeasurable except as device behavior
Pushing the limits of materials understanding
Solution: hierarchical modeling (atomistic => continuum)
Scott DunhamUniversity of Washington
Nanotechnology ModelingEE539, Winter 2008
Nanotechnology Modeling Lab
Modeling Hierarchy
* accessible time scale within one day of calculation
ParameterInteraction
DFTQuantum
mechanics
MD Empirical potentials
KLMCMigration barriers
ContinuumReaction kinetics
Number of atoms 100 104 106 108
Length scale 1 nm 10 nm 25 nm 100 nm
Time scale* ≈ psec ≈ nsec ≈ msec ≈ sec
Scott DunhamUniversity of Washington
Nanotechnology ModelingEE539, Winter 2008
Nanotechnology Modeling Lab
Ab-initio (DFT) Modeling Approach
Model
Expt. Effect
DFT
Validation&
Predictions Critical Parameters
Parameters
Behavior
Verify Mechanism
Ab-initio Method:Density Functional Theory (DFT)
Scott DunhamUniversity of Washington
Nanotechnology ModelingEE539, Winter 2008
Nanotechnology Modeling Lab
Multi-electron Systems
Hamiltonian (KE + e-/e- + e-/Vext):
Hartree-Fock—build wave function from Slater determinants:
The good: Exact exchange
The bad: Correlation neglected Basis set scales factorially [Nk!/(Nk-N)!(N!)]
Scott DunhamUniversity of Washington
Nanotechnology ModelingEE539, Winter 2008
Nanotechnology Modeling Lab
Hohenberg-Kohn Theorem
Theorem: There is a variational functional for the ground state energy of the many electron problem in which the varied quantity is the electron density.
Hamiltonian:
N particle density:
Universal functional:
P. Hohenberg and W. Kohn,Phys. Rev. 136, B864 (1964)
Scott DunhamUniversity of Washington
Nanotechnology ModelingEE539, Winter 2008
Nanotechnology Modeling Lab
Density Functional TheoryKohn-Sham functional:
with
Different exchange functionals:
Local Density Approx. (LDA)
Local Spin Density Approx. (LSD)
Generalized Gradient Approx. (GGA)
Walter Kohn
W. Kohn and L.J. Sham, Phys. Rev. 140, A1133 (1965)
Scott DunhamUniversity of Washington
Nanotechnology ModelingEE539, Winter 2008
Nanotechnology Modeling Lab
Predictions of DFT
Atomization energy:
J.P. Perdew et al., Phys. Rev. Lett. 77, 3865 (1996)
Silicon properties:
Method Li2 C2H2 20 simple molecules(mean absolute error)
Experiment 1.04 eV 17.56 eV -
Theoretical errors:Hartree-FockLDAGGA (PW91)
-0.91 eV-0.04 eV-0.17 eV
-4.81 eV2.39 eV0.43 eV
3.09 eV1.36 eV0.35 eV
Property Experiment LDA GGA
Lattice constantBulk modulusBand gap
5.43 Å102 GPa1.17 eV
5.39 Å 96 GPa0.46 eV
5.45 Å88 GPa0.63 eV
Scott DunhamUniversity of Washington
Nanotechnology ModelingEE539, Winter 2008
Nanotechnology Modeling Lab
Implementation of DFT in VASP
VASP features:
Plane wave basis
Ultra-soft Vanderbilt type pseudopotentials
QM molecular dynamics (MD)
VASP parameters:
Exchange functional (LDA, GGA, …)
Supercell size (typically 64 Si atom cell)
Energy cut-off (size of plane waves basis)
k-point sampling (Monkhorst-Pack)
Calculation converged
Guess:
Electronic IterationSelf-consistentKS equations:
Ionic IterationDetermine ionic forcesIonic movement
Arrangement of atoms
Scott DunhamUniversity of Washington
Nanotechnology ModelingEE539, Winter 2008
Nanotechnology Modeling Lab
Sample Applications of DFT
Idea: Minimize energy of given atomic structure
Applications:
Formation energies (a)
Transitions (b)
Band structure (c)
Elastic properties (talk)
…(a) (b) (c)
Scott DunhamUniversity of Washington
Nanotechnology ModelingEE539, Winter 2008
Nanotechnology Modeling Lab
Elastic Properties of Silicon
Lattice constant: Hydrostatic:
Elastic properties: Uniaxial:
Method K [GPa] Y [GPa]
DFT (LDA) 96 117 0.297
DFT (GGA) 88 126 0.262
Literature 102 131 0.266
Method bSi [Å]
Experiment 5.43
DFT (LDA) 5.39
DFT (GGA) 5.45
Method C11 [GPa] C12 [GPa]
DFT (LDA) 156 66
DFT (GGA) 155 55
Literature 167 65
GGA
GGA
Scott DunhamUniversity of Washington
Nanotechnology ModelingEE539, Winter 2008
Nanotechnology Modeling Lab
MD Simulation
5 TC layer
1 static layer
4 x 4 x 13 cells
Initial Setup Stillinger-Weber or Tersoff Potential
Ion Implantation (1 keV)
Scott DunhamUniversity of Washington
Nanotechnology ModelingEE539, Winter 2008
Nanotechnology Modeling Lab
Recrystallization
1200K for 0.5 ns
Scott DunhamUniversity of Washington
Nanotechnology ModelingEE539, Winter 2008
Nanotechnology Modeling Lab
Kinetic Lattice Monte Carlo (KLMC)
Some problems are too complex to connect DFT directly to continuum.
Need a scalable atomistic approach.
Possible solution is KLMC.
Energies/hop rates from DFT
Much faster than MD because:
Only consider defects
Only consider transitions
Tk
EE
B
fi
2exp0
Scott DunhamUniversity of Washington
Nanotechnology ModelingEE539, Winter 2008
Nanotechnology Modeling Lab
V
Vacancy Mechanism Interstitial Mechanism
Si
Dopant
Fundamental processes are point defect hop/exchanges.
Kinetic Lattice Monte Carlo SimulationsKinetic Lattice Monte Carlo Simulations
Vacancy must move to at least 3NN distance from the dopant to complete one step of dopant diffusion in a diamond structure.
Scott DunhamUniversity of Washington
Nanotechnology ModelingEE539, Winter 2008
Nanotechnology Modeling Lab
Tk
EE
B
fi
2exp0
Simulations include As, I, V, Asi and interactions between them.
Hop/exchange rate determined by change of system energy due to the event.
Energy depends on configuration and interactions between defects with numbers from ab-initio calculation (interactions up to 9NN).Calculate rates of all possible processes.At each step, Choose a process at random, weighted by relative rates.Increment time by the inverse sum of the rates.Perform the chosen process and recalculate rates if necessary.Repeat until conditions satisfied.
Kinetic Lattice Monte Carlo Simulations
Scott DunhamUniversity of Washington
Nanotechnology ModelingEE539, Winter 2008
Nanotechnology Modeling Lab
1/4 of 40nm MOSFET (MC implant and anneal)
3D Atomistic Device Simulation
Scott DunhamUniversity of Washington
Nanotechnology ModelingEE539, Winter 2008
Nanotechnology Modeling Lab
Summary
DFT (QM) is an extremely powerful tool for: Finding reaction mechanisms Addressing experimentally difficult to access phenomena Foundation of modeling hierarchy
Limited in system size and timescale:Need to think carefully about how to apply most effectively to nanoscale systems.
Scott DunhamUniversity of Washington
Nanotechnology ModelingEE539, Winter 2008
Nanotechnology Modeling Lab
Conclusions
Advancement of semiconductor technology is pushing the limits of understanding and controlling materials (still 15 year horizon). Future challenges in VLSI technology will require
utilization of full set of tools in the modeling hierarchy (QM to continuum).
Complementary set of strengths/limitations: DFT fundamental, but small systems, time scales KLMC scalable, but limited to predefined transitions MD for disordered systems, but limited time scale
Increasing opportunities remain as computers/ tools and understanding/needs advance.
Scott DunhamUniversity of Washington
Nanotechnology ModelingEE539, Winter 2008
Nanotechnology Modeling Lab
Acknowledgements
Contributions: Milan Diebel (Intel) Pavel Fastenko (AMD) Zudian Qin (Synopsys) Joo Chul Yoon (UW) Srini Chakravarthi (Texas Instruments) G. Henkelman (UT-Austin) C.-L. Shih (UW)
Involved Collaborations: Texas Instruments SiTD, Dallas Hannes Jónsson (University of Washington)
Computing Cluster Donation by Intel
Research Funded by SRC