Status of the Nanoelectronic Modeling tool (NEMO 1-D and 3-D) and its planned extension to Spintronics

1
Status of the Nanoelectronic Modeling tool (NEMO
1-D and 3-D) and its planned extension to
Spintronics

• Gerhard Klimeck, Fabiano Oyafuso, Timothy B.
  Boykin, and R. Chris Bowen
• Jet Propulsion Laboratory, California Institute
  of Technology
• University of Alabama in Huntsville
• Email gekco_at_jpl.nasa.gov
• Web http//hpc.jpl.nasa.gov/PEP/gekco

• Outline
• Atomistic modeling agenda
• Tight binding parameter fitting
• Parallel eigenvalue solver
• Parallel strain calculation

• Alloy disorder calculation
• AlGaAs bulk
• InGaAs quantum dot
• Planned Extensions

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High Performance Computing at JPL

• JPL is the Lead Center for Robotic Space
  Exploration
• Deep Space Missions
• Earth Observing Missions

• JPL Builds Observational Systems for Remote
  Sensing
• Imaging instruments across all wavelengths
• Spectroscopic and in-situ instruments for
  planetary investigation
• Fundamental technology development for new
  instruments

http//mars.jpl.nasa.gov
http//www-misr.jpl.nasa.gov

• JPL High Performance Computing is a Key
  Technology
• Modeling and simulation of devices and
  instruments
• Rapid data reduction and analysis
• Advanced software design, implementation and
  application
• Integrated Design, Optimization and Synthesis

3
Progressive Spacecraft Miniaturization
Cassini
1000 kg
Mars Pathfinder
Clark
Lewis
Solar Probe
NEAR
Pluto/Kuiper Express
Mars 98 Lander/Orbiter
100 kg
Spacecraft Mass
Europa Orbiter
Stardust
10 kg
Microspacecraft
Past
Present
Future
Low weight, low power and high efficiency Have a
special meaning to NASA
4
Limit of Military Interest
Limit of Commercial Interest
NASA radiation and temperature requirements are
outside commercial and military interest
5
Quantum Dot Simulation forRevolutionary
Computing and Sensing
DesignedOptical Transitions Sensors
Quantum Dot Arrays Computing
Atomic Orbitals size 0.2nm
Structure

• Opportunity
• Nanoscale electronic structures can be built!gt
  Artificial Atoms / Molecules
• Problem
• The design space is huge choice of materials,
  compositions, doping, size, shape.
• Approach
• Deliver a 3-D atomistic simulation tool
• Enable analysis of arbitrary crystal structures,
  atom compositions and bond/structure
  configurations.

6
Quantum Dot Simulation forRevolutionary
Computing and Sensing
DesignedOptical Transitions Sensors
Quantum Dot Arrays Computing
Atomic Orbitals size 0.2nm
Structure

• Approach
• Use local orbital description for individual
  atoms in arbitrary crystal / bonding
  configuration
• Use s, p, and d orbitals Use genetic algorithm
  to determine material parameter fitting
• Compute mechanical strain in the system.
• Develop efficient parallel algorithms to generate
  eigenvalues/vectors of very large matrices
  (N40million for a 2 million atom system).
• Develop prototype GUI for (NEMO-3D)

• Problem
• Nanoscale device simulation requirements
• Cannot use bulk / jellium descriptions, need
  description of the material atom by atom gt use
  pseudo-potential or local orbitals
• Consider finite extent/transport, not infinitely
  periodic gt local orbital approach
• Need to include about one million atoms. gt need
  massively parallel computers
• The design space is huge choice of materials,
  compositions, doping, size, shape. gt need a
  design tool

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Leverage NEMO 1-DA User-friendly Quantum Device
Design Tool

• NEMO was developed under a government contract to
  Texas Instruments and Raytheon from 1993-97
• gt50,000 person hours of RD
• 250,000 lines of code in C, FORTRAN and F90
• Based on Non-Equilibrium Green function formalism
  (Datta, Lake, Klimeck).
• NEMO in THE state-of-the-art heterostructure
  design tool.
• Used at Intel, Motorola, HP, Texas Instruments,
  and gt10 Universities.

Transport/ Engineering
Quantum Mechanics / Physics
Testmatrix
8
Mapping of Orbitals to Bulk Bandstructure

• Bulk Semiconductors are described by
• Conduction and valence bands, bandgaps (direct,
  indirect), effective masses
• 10-30 physically measurable quantities

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Semiconductor Compoundscation In, Ga,
Alanion Sb, As, P
In
Ga
Al
Sb

• Match experimental data in various electron
  transport areas of the Brillouin zone
• Effective masses of electrons at G, X and L
• Effective masses of holes at G
• Bandedges at G, X and L

As

• Each individual material poses a 15 dimensional
  fitting problem.

P
10
Eigenvalue Solver for 108x108 MatricesHermitian
and Non-Hermitian Matrices
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Parallelization of NEMO 3-D

• Divide Simulation domain into slices.
• Communication only from one slice to the next
  (nearest neighbor)
• Communication overhead across the surfaces of the
  slices.
• Limiting operation sparse matrix-vector
  multiplication
• Enable Hamiltonian storage or re-computation on
  the fly.

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Parallel Eigenvalue Solver on a Beowulf(32 node,
dual CPU Pentium III, 800MHz, Linux)

• Eigenvalue computation ranging from 1/4 to 16
  million atoms
• Large problems are too big for a single CPU
  (memory requirements)
• sp3s basis set , Matrix sizes up to 1.6 108x1.6
  108
• Recompute Hamiltonian matrix on the fly.
• Measure time for 30 Lanczos iterations, Full
  problem 1000-5000 iterations
• 1million atoms 5000 iteration 1 CPU 48 hours
  20 CPUs 3.4 hours
• Computation time linear in system size.

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Atomistic strain calculationfollowed by sp3sd5
tight binding eigenvalue solution

• Dot Formation Due to Strain
• Self-Assembly induced by strain in GaAs/InAs and
  Si/Ge material systems.
• Bond length and orientation distortion

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Parallelization of Strain Calculation

• Problem (1million atoms)
• Serial strain computation 43 min.
• Serial electronic structure calculation (1000
  iterations) 9.6 hours
• Parallel electronic structure computation on 20
  CPUs41 min.
• Solution
• Parallelize strain calculation as well

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Alloy Disorder in Quantum Dots

• Results
• Simulated 50 dots with random cation
  distributions.
• Inhomogeneous broadening factor of 5meV due to
  alloy disorder.
• Impact
• Fundamental uniformity limit for ensemble of
  alloy-based quantum dots.

• Problem
• Cations are randomly distributed in alloy dots.
• Does alloy disorder limit electronic structure
  uniformity for dot ensembles?
• Approach
• Simulate a statistical ensemble of alloyed dots.
• Requires atomistic simulation tool.

In0.6Ga0.4As Lense Shaped Dot
Diameter30nm,Height5nm, GaAs embedded
1,000,000 Atom Simulation, sp3s basis
In and Ga atoms are randomly distributed
Inhomegenious Broadening?
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3-D Random Alloy Simulation ofAlGaAs Band Gap

• sp3s tight binding model
• VCA derived from pure GaAs and AlAs results in an
  wrong bandgap (parameter averaging)
• Perform 3-D alloy simulation of the bandedges.
• Represent each individual atom in the chunk of
  material
• 3-D random alloy simulation matches experimental
  data well.

• Some questions to be addressed
• What is the noise in such a system?
• How large is the configuration noise?
• How large is the concentration noise?
• How many atoms need to be included in the
  simulation?
• What is the dependence of the noise on the Al
  concentration?
• What is the effect of clustering?

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Configuration Noise

• The actual placement of the Al atoms in the 3-D
  domain differs in each sample-gt configuration
  noise
• For a system containing 1000 atoms with the exact
  concentration, the variation is about 2-5 meV
• Conduction band noise increases at the G-X
  transition at Al0.45
• Valence band dependence is much smoother.

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Configuration and Concentration Noise

• Concentration may vary stochastically as well.
• Concentration noise is larger than configuration
  noise.
• For a system containing 1000 atoms, the variation
  is about 10-15 meV
• Conduction band noise shows a significant feature
  at the G-X transition (Al0.45)
• Valence band dependence is much smoother.
• What do the distributions look like?

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Configuration NoiseDistribution Functions at
Al0.2

• 3000 atoms
• 2800 samples
• x0.2, s0 Configuration noise only
• Valence band edge shows some asymmetry
• Conduction band symmetric
• Band gap has asymmetry due to valence band
  asymmetry.

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Configuration and Concentration
NoiseDistribution Functions at Al0.2

• 3000 atoms
• 2800 samples
• Concentration noise dominating the configuration
  noise.
• Valence and conduction band have symmetric
  distributions

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Configuration and Concentration
NoiseDistribution Functions at Al0.2

• Configuration noise uncorrelated Ec and Ev
• Concentration noise correlated Ec and Ev.

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Size Dependence of Bandedge and Deviation

• Configuration noise only.
• 1 million atom simulations !
• Standard deviation decreases approximately as
  N-1/2

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Alloy Disorder in Quantum Dots

• Results
• Simulated 1000 dots with random cation
  distributions.
• Inhomogeneous broadening factor of 5meV due to
  alloy disorder.
• Impact
• Fundamental uniformity limit for ensemble of
  alloy-based quantum dots.

• Problem
• Cations are randomly distributed in alloy dots.
• Does alloy disorder limit electronic structure
  uniformity for dot ensembles?
• Approach
• Simulate a statistical ensemble of alloyed dots.
• Requires atomistic simulation tool.

In0.6Ga0.4As Lense Shaped Dot
Diameter30nm,Height5nm, GaAs embedded
1,000,000 Atom Simulation, sp3s basis
In and Ga atoms are randomly distributed
Inhomegenious Broadening?
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InGaAs Bond Length Distribution

• VCA on the bond length is incorrect.
• InAs and GaAs maintain their bondlength character
  - gt proper strain treatment

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Local Bandstructure in an Alloyed QD

• In-As bonds compressed in x-y
• -gt Ec raised from bulk value of 0.58eV to
  1.2eV
• -gt Ev HH raised from bulk value of 0.22eV to
  0.3eV
• Ga-As bonds compressed in x-y and stretched in z
  inside dot
• -gt Ec raised from bulk value of 1.42eV to
  1.55eV
• -gt Ev raised from bulk value of 0eV to 0.1eV

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Spatial Irregularity in the Hole Ground State

• VCA / no Disorder Disorder Sample 1 Disorder
  Sample 2

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Spatial Irregularity in the Hole States
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Spatial Irregularity in the Electron States
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gt1000 Alloyed Quantum Dot Samples

• Atomistic granularity
• s 2.3meV

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gt1000 Alloyed Quantum Dot Samples

• Atomistic granularity
• s 2.3meV
• Cell granularity
• s 4.5meV

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gt1000 Alloyed Quantum Dot Samples

• Atomistic granularity
• s 2.3meV
• Cell granularity
• s 4.5meV
• Ec and Ev strongly correlated
• Ec and x weakly corelated

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NEMO 3-D Conclusion / Future Vision
Quantum Dots

• Atomistic Simulation (NEMO 3-D)
• Fitting tight binding sp3s,sp3d5s
• General structure input
• Several million atom solutions
• Parallel eigenvalue solvers
• Strain simulations
• Spin is explicitly included in the basis.

Grading
Atomistic Simulation
Abrupt
Graded
gt Quantum Computing
End of SIA Roadmap

• Extension of NEMO 3-D to Spintronics
• Arbitrary magnetic fields
• Magnetic impurities
• Many-body interactions (electrons, phonons,
  photons)
• Open boundary conditions
• Extension of NEMO 1-D to Spintronics
• DC Spin transport RTD-like structures
• Time dependent spin - transport

Dopant Fluctuations in Ultra-scaled CMOS
Electron Transport in Exotic Dielectrics
(Ba,Sr)TiO3
TiO2