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Mathieu Luisier, Sascha Brück, Mauro Calderara, and Jean M. Favre* Integrated Systems Laboratory, ETH Zürich, Switzerland
*CSCS, Lugano, Switzerland
Thursday 19 November 15 1 NVIDIA Booth Presentation, SC15, November 2015
GPU-Enabled Simulation and Visualization of Nanoelectronic Devices
Thursday 19 November 15 2
• Nanoelectronic Device Simulations From Moore’s Law to TCAD
• Ab-initio Simulation Approach Models and scalability
• Visualization of internal quantities Nanoscale current trajectories
• Outlook and Conclusion Advanced Device Simulations
Overview
Thursday 19 November 15 3
• Nanoelectronic Device Simulations From Moore’s Law to TCAD
• Ab-initio Simulation Approach Models and scalability
• Visualization of internal quantities Nanoscale current trajectories
• Outlook and Conclusion Advanced Device Simulations
Overview
4
Motivation: Future of Moore’s Scaling Law
65nm (2005)
45nm (2007)
32nm (2009)
22nm (2011)
The transistor evolution is governed by Moore’s Scaling Law
Thursday 19 November 15
XXnm (202X)
??? Every 18-24 months, 30% dimension scaling. ⇒ area is divided by 2.
Breakthrough: 2D->3D
New Structures
Next Generation Devices
Thursday 19 November 15 5
New Materials
Next Generation Devices
Thursday 19 November 15 6
New Concepts
Advanced Design Tool(s) Required
Next Generation Devices
Thursday 19 November 15 7
• 3D Quantum Transport Solver • Accurate Representation of the
Material Properties • Atomistic Description of Devices
• Multi-Physics Modeling OMEN
Physical Models Device Engineering
Efficient Parallel Computing
GAA NW
Electron Density
Id-Vgs
• Industrial-Strength Nano-electronic Device Simulator
• Multi-Geometry Capabilities • Explore, Understand, Predict,
Optimize Novel Designs
TCAD Tool Requirements
Three different perspectives: EE+PHYS+HPC
• Accelerate Simulation Time • Investigate New Phenomena
at the Nanometer Scale • Move Hero Experiments to a
Day-to-Day Basis
8 Thursday 19 November 15
Thursday 19 November 15 9
• Nanoelectronic Device Simulations From Moore’s Law to TCAD
• Ab-initio Simulation Approach Models and scalability
• Visualization of internal quantities Nanoscale current trajectories
• Outlook and Conclusion Advanced Device Simulations
Overview
10 Thursday 19 November 15
Computational Approach
H (k) ⋅Ψ(k) = E(k) ⋅Ψ(k)
What is needed: solution of Schrödinger equation
Computational Goal: wave function ψ(k) and energy E(k)
Device Simulation: open system (NEGF)
Key Component of NEGF equations
H (r,k)
(E −H (k)−ΣR (E,k)) ⋅GR (E,k) = IG<(E,k) =GR (E,k) ⋅ Σ<(E,k) ⋅GA (E,k)
: Hamiltonian matrix in selected basis (EMA, TB, DFT)
Ab-initio Quantum Transport Simulations
Thursday 19 November 15 11
Coupling of OMEN with a density-functional theory (DFT) tool: CP2K
1. Hamiltonian H and overlap S matrices created in CP2K and transferred in OMEN 2. Ab-initio transport simulations in OMEN with DFT instead of tight-binding basis
Step 2
Step 1
Collaboration with the group of Prof. J. VandeVondele (ETH Zurich)
NEGF Solution of Schrödinger Equation
Thursday 19 November 15 12
Open Boundary Conditions § Generalized Eigenvalue Problem
§ Difficult to parallelize 1 core ~1.8 hrs (on Cray XC30)
Run
time
[s]
Matrix Inversion § Recursive Green’s Function algorithm
§ Inherently sequential
4820
1290
0
1000
2000
3000
4000
5000
6000
NEGF
rGF OBC
(E ⋅SCP2K −HCP2K − ΣRB) ⋅GR(E) = I
Nanowire Transistor
Equation to solve:
for each energy E ~10000 atoms
Accelerating DFT+NEGF QT Simulations (1)
Thursday 19 November 15 13
Step 1: Moving from NEGF to QTBM
(E ⋅SCP2K −HCP2K − ΣRB) ⋅GR(E) = I
(E ⋅SCP2K −HCP2K − ΣRB) ⋅ Ψ(E) = Inj(E)
Run
time
[s]
0
1000
2000
3000
4000
5000
6000
NEGF QTBM
Boundary
Schrödinger Eq.
MUMPS on 16 cores: 48x faster than RGF on 1 core
Step 2: FEAST for OBCs
Run
time
[s]
0
200
400
600
800
1000
1200
1400
SI FEAST FEAST+
Boundary
Schrödinger Eq.
FEAST on 32 cores: 43x faster than shift-and-invert on 1 core
Solve generalized EV problem through contour integration
Thursday 19 November 15 14
Accelerating DFT+NEGF QT Simulations (2)
Step 3: SplitSolve Algorithm
Trick: interleave computation of on CPUs and GPU solution of
(E ⋅SCP2K −HCP2K − ΣRB) ⋅ Ψ(E) = Inj(E)
0
20
40
60
80
100
120
140
FEAST & MUMPS
FEAST & SplitSolv
Schrödinger Eq.
Boundary
Run
time
[s]
Strong scaling on Titan @ ORNL
15 PFlop/s on 18564 Hybrid Nodes
Gordon Bell Prize Finalist 2015
ΣRB(E)
Solution time: Time to compute OBCs on CPUs Speedup: >5x
Thursday 19 November 15 15
• Nanoelectronic Device Simulations From Moore’s Law to TCAD
• Ab-initio Simulation Approach Models and scalability
• Visualization of internal quantities Nanoscale current trajectories
• Outlook and Conclusion Advanced Device Simulations
Overview
Current Flow through Nanodevices
Thursday 19 November 15 16
K. Storm et al., NL 12, 1-6 (2012)
GAA Nanowire Transistor
Source
Gate Drain
Atomic-scale filament
A. Emboras et al., arXiv:1508.07748
Memristor
Visualization Techniques
Thursday 19 November 15 17
Software: VTK from Kitware
New OpenGL2 access for better visualization
2015 marks great milestones by the Kitware team, enabling
much improved Molecular Support, pushing a great deal of
geometry creation and rendering on the GPU:
§ Improved Molecular Rendering
§ Improved Glyphing
§ Improved Point Sprites
Thursday 19 November 15 18
• Nanoelectronic Device Simulations From Moore’s Law to TCAD
• Ab-initio Simulation Approach Models and scalability
• Visualization of internal quantities Nanoscale current trajectories
• Outlook and Conclusion Advanced Device Simulations
Overview
19 Thursday 19 November 15
Conclusion
• Next-Generation Nano-Devices TCAD to accelerate process innovation
• Proposed Simulation Approach Dedicated to large variety of nanoscale devices GPU as computation and visualization enabler Excellent scalability on petascale machines
• Future Work and Challenges Establish multi-scale coupling DFT->TB->DD Work more closely with experimental groups
Thursday 19 November 15 20
Acknowledgments
We are deeply grateful to the following persons/organizations:
• Joost VandeVondele (ETH Zürich)
• Jack Wells and his team (ORNL)
• Peter Messmer (NVIDIA)
• Ichitaro Yamazaki (MAGMA)