# Presentation: 130127

## 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@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

## High Performance Computing at JPL

- http://mars.jpl.nasa.gov

**High Performance Computing at JPL**

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

- 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

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

- 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

## Progressive Spacecraft Miniaturization

**Cassini**

**Mars**
**Pathfinder**

**Pluto/Kuiper Express**

**“****Microspacecraft”**

**1000 kg**

**100 kg**

**10 kg**

**Past**

**Present**

**Future**

**Spacecraft Mass**

**NEAR**

**Solar Probe**

**Stardust**

**Europa Orbiter**

**Lewis**

**Clark**

**Mars 98 Lander/Orbiter**

**Progressive Spacecraft Miniaturization**

***Low weight, low power and high efficiency***
***Have a special meaning to NASA***

## NASA radiation and temperature requirements are outside commercial and military interest

- Limit of
- Commercial
- Interest

- Limit of
- Military
- Interest

***NASA radiation and temperature requirements are ******outside commercial and military interest***

## Quantum Dot Simulation forRevolutionary Computing and Sensing 

- Structure

- Atomic Orbitals
- size: 0.2nm

- DesignedOptical
- Transitions
- Sensors

- Quantum Dot
- Arrays
- Computing

**Opportunity:**
- Nanoscale electronic structures can be built!=> 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.

**Quantum Dot Simulation for****Revolutionary Computing and Sensing**** **

## Quantum Dot Simulation forRevolutionary Computing and Sensing 

- Structure

- Atomic Orbitals
- size: 0.2nm

- DesignedOptical
- Transitions
- Sensors

- Quantum Dot
- Arrays
- Computing

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

**Quantum Dot Simulation for****Revolutionary Computing and Sensing**** **

**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 (N=40million for a 2 million atom system).
- Develop prototype GUI for (NEMO-3D)

## Leverage NEMO 1-D:A User-friendly Quantum Device Design Tool

- NEMO was developed under a government contract to Texas Instruments and Raytheon from 1993-97
- >50,000 person hours of R&D
- 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 >10 Universities.

- Transport/
- Engineering

- Quantum Mechanics /
- Physics

**Testmatrix**

## 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

**Mapping of Orbitals to Bulk Bandstructure**** **

## Semiconductor Compounds:cation: In, Ga, Alanion: Sb, As, P

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

- Each individual material poses a 15 dimensional fitting problem.

**P**

**As**

**Sb**

**In**

**Ga**

**Al**

## Eigenvalue Solver for 108x108 MatricesHermitian and Non-Hermitian Matrices

**Eigenvalue Solver for 10****8****x10****8**** Matrices**Hermitian and Non-Hermitian Matrices

## 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.**

## 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 10****8****x1.6 10****8**
**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.**

## Atomistic strain calculationfollowed by sp3s*d5 tight binding eigenvalue solution

**Atomistic strain calculation****followed by sp3s*d5 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

## 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 CPUs:****~41 min.**
**Solution:**
**Parallelize strain calculation as well**

## Alloy Disorder in Quantum Dots 

- Alloy Disorder in Quantum Dots

**In****0.6****Ga****0.4****As **Lense Shaped Dot

**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.

**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.

- In and Ga atoms are randomly distributed** **

- Inhomegenious Broadening?

- Diameter=30nm,Height=5nm, GaAs embedded

- ~1,000,000 Atom Simulation, sp3s* basis

## 3-D Random Alloy Simulation ofAlGaAs Band Gap 

**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?**

**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.**

## Configuration Noise

**The actual placement of the Al atoms in the 3-D domain differs in each sample****-> 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 ********-X transition at Al~0.45 **
**Valence band dependence is much smoother. **

## 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 ********-X transition (Al~0.45) **
**Valence band dependence is much smoother.**
**What do the distributions look like?   **

## Configuration NoiseDistribution Functions at Al=0.2

**3000 atoms**
**~2800 samples**
**x=0.2, ********=0    Configuration noise only**
**Valence band edge shows some asymmetry**
**Conduction band symmetric**
**Band gap has asymmetry due to valence band asymmetry.**

## Configuration and Concentration NoiseDistribution Functions at Al=0.2

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

## Configuration and Concentration NoiseDistribution Functions at Al=0.2

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

## Size Dependence of Bandedge and Deviation

**Size Dependence of Bandedge and Deviation**

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

## Alloy Disorder in Quantum Dots 

- Alloy Disorder in Quantum Dots

**In****0.6****Ga****0.4****As **Lense Shaped Dot

**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.

**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.

- In and Ga atoms are randomly distributed** **

- Inhomegenious Broadening?

- Diameter=30nm,Height=5nm, GaAs embedded

- ~1,000,000 Atom Simulation, sp3s* basis

## InGaAs Bond Length Distribution

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

## Local Bandstructure in an Alloyed QD 

**In-As bonds compressed in x-y**
**	****-> Ec raised from bulk value of ~0.58eV to ~1.2eV**
**	****-> 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**
**	****-> Ec raised from bulk value of ~1.42eV to ~1.55eV**
**	****-> Ev raised from bulk value of 0eV to ~0.1eV**

## Spatial Irregularity in the Hole Ground State 

**VCA / no Disorder****	****	**** Disorder Sample 1****	****	****Disorder Sample 2**

## Spatial Irregularity in the Hole States 

## Spatial Irregularity in the Electron States 

## >1000 Alloyed Quantum Dot Samples 

**Atomistic granularity**
** ********= 2.3meV**

## >1000 Alloyed Quantum Dot Samples 

**Atomistic granularity**
** ********= 2.3meV**
**Cell granularity**
** ********= 4.5meV**

## >1000 Alloyed Quantum Dot Samples 

**Atomistic granularity**
** ********= 2.3meV**
**Cell granularity**
** ********= 4.5meV**
**Ec and Ev strongly correlated**
**Ec and x weakly corelated**

## NEMO 3-D Conclusion / Future Vision

**NEMO 3-D Conclusion / Future Vision**

- Quantum Dots

- End of SIA Roadmap

- (Ba,Sr)TiO3

- TiO2

**Dopant **
**Fluctuations**
**in Ultra-scaled **
**CMOS**

- Electron
- Transport
- in Exotic
- Dielectrics

- Grading

- Abrupt

- Graded

- Atomistic Simulation

- 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.

- 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

- => Quantum Computing