These are the slides from the webinar hosted by NNIN @ University of Michigan on May 28, 2013. Find out more about my views on how atomic-scale modeling can help the development of nanoelectronics based on nanowires, interfaces, graphene. The special Atomistix ToolKit
1. Atomic-scale Modeling of Nanoelectronic
Devices With Atomistix ToolKit
Dr. Anders Blom
QuantumWise
If you find this webinar and other NNIN/C resources useful to your research, please acknowledge NNIN/C in your publications. Your
acknowledgement will greatly help us in furthering this endeavor of promoting research in micro/nanosystems.
2. QuantumWise Slide 2
Outline
Nanoelectronics is here. Or coming. Soon.
Some time, anyways. Maybe.
How can modeling help it become reality?
What methods are needed?
Atomistix ToolKit – a platform for atomistic
modeling of electronic devices, and other
nanoscale systems
Examples throughout the presentation
Bye!
3. QuantumWise Slide 3
”We are running out of atoms”
Paula Goldschmidt, Intel
(2007)
Nanoelectronics is here! Or...?
8. QuantumWise Slide 8
Fv
0vvF
=
Electrons move around randomly
with some average velocity
For metals like Cu, the
mean free path is about 50 nm!
This picture breaks down when
the device dimensions are
smaller than the mean free
path
Nanodevice
Small means quantum
0
5
10
15
20
25
30
35
0 150
Length [nm]
Resistance[kΩ]
Classical resistance
Quantum
resistance
~50 nm
“Feature size is approaching mean
free path of electrons in Cu”
(P. Gargini, Intel, Semicon West 2007)
9. QuantumWise Slide 9
Current = propagation of wave function
Landauer–Büttiker formalism
Current from transmission
10. QuantumWise Slide 10
Small means every atom matters
Blessing or curse?
Nanoscale devices can
derive their entire
functionality from effects
related to a few atoms
However, vacancies,
defects and dopants
become critical as device
size approaches the
nanoscale
How many dopants are
there in a 5 nm transistor
channel doped at 1019
cm-3
?
» Less than 1
”We are running out of atoms”
Paula Goldschmidt, Intel (2007)
1.2 nm SiO2
11. QuantumWise Slide 11
“Experiment simply cannot do it alone
– theory and modeling are essential.”
US National Science and Technology Council,
The Interagency Working Group on
NanoScience, Engineering and Technology
“You don’t understand it
until you can model it”
Professor J.C. Busot
Faculty of Chemical Engineering
University of San Francisco
“You don’t understand it
until you can model it”
Professor J.C. Busot
Faculty of Chemical Engineering
University of San Francisco
12. QuantumWise Slide 12
The story so far
Materials
» Bulk crystal
» Ok to simulate atomistically
• Simple boundary conditions – periodic
» Accurate description from DFT
• Small cell
» Success story: 45 degree rotated Si substrate
Device
» Well-known elements, like Si
• Described by bulk
materials parameters
» Large structures
• Simulated in continuum
» Classical physics
• Optical, mechanical, electrical properties
decoupled
» TCAD historically extremely
successful in this area
13. QuantumWise Slide 13
The game is changing!
Materials
» Interfaces, junctions
» How to simulate atomistically?
• Difficult boundary conditions
» Quantum-mechanical description
still needed
• Now: large cells
Devices
» Interfaces, junctions
• Exotic elements: graphene,
Ge, Hf, Ta, Ti, …
» Simulate atomistically?
• Continuum electrostatics?
» Quantum-mechanical?
• Optical, mechanical, electrical
properties becomes intertwined
14. QuantumWise Slide 14
Nanoscale challenges
Experimental trial-and-error is
expensive, cumbersome, and time-
consuming
» What property are we measuring?
» What system are we looking at?
» Influence of instrument?
Modeling is no picnic either
» TCAD models are falling behind – large
gap to bridge
» III-V, SiGe + Hf/Ta/Ti, …
» Quantum effects in “large” structures
15. QuantumWise Slide 15
Atomic-scale modeling as a complement
Complement TCAD
» Parameters from calculations
» Add new effects, study new devices
Complement experiments
» Screen new materials and designs before
proceeding with experiments
» Provide basic understanding
» Steer research directions
» Automate and parallelize – computers are
cheaper than people
» Fewer wafers taken from the line for
experimentation
17. QuantumWise Slide 17
Ohmic contacts on silicon-carbide
Qualitative experimental result:
» Epitaxially grown Ti3SiC2 bonds to
SiC and forms a coherent and
atomically ordered interface
Modeling (ATK) provides
quantitative insight:
» Interface can trap a layer of C
» This lowers the Schottky barrier via
large interface dipole shift, which
enhances transport by reducing the
potential drop
Wang et al.,
PRB 80, 245303 (2009)
Adv. Mat. 21, 4966 (2009)
Si/Si
Si/C/Si
“The results highlight the important
advance for merging Z-contrast
microscopy and first-principles
calculations in the atomic-scale
determination of a buried interface,
in addition to the possibility of
relating structures to properties on
a quantum level.”
18. QuantumWise Slide 18
New properties to compute – no, predict!
Conductance – not mobility
» Ballistic transport
Schottky barrier
Leakage current
Complex band structure
Contact resistance
Optimized geometries
Of course also “standard”
properties
» Effective masses
» Band gaps & alignments
» Reaction barriers
» Heat transport
» Phonon spectra
» Total energies
» Optical properties
Si (100) @ kA=kB=0
K. Stokbro, M. Engelund, A. Blom
Physical Review B 85, 165442 (2012)
19. QuantumWise Slide 19
We’re not in bulk anymore, Toto
???
???
??????
http://en.wikipedia.org/wiki/Colloidal_gold
21. QuantumWise Slide 21
Doping is bad for you
Proposition of a doping-free tin
(Sn is semi-metallic!) nanowire
field-effect transistor
L. Ansari, G. Fagas, J.-P. Colinge,
and J. C. Greer (Tyndall)
Nano Lett. 12, 2222 (2012)
22. QuantumWise Slide 22
Commonalities in new device architectures
“Exotic” materials
» And some Si, Ge etc.
Small scale – but many atoms
» Quantum effects
» Atomistic effects
The interface is the device
» Boundary conditions
» Electrostatics
Strong implications for
choices of methods and
modeling techniques
Electrostatic potential in a gated InAs p-i-n tunneling FET; 5000 atoms, computed with ATK-DFT.
24. QuantumWise Slide 24
LDA actually works well for semiconductors
Really?
Well, forces and total
energies
Example: Si 100 surface
» LDA predicts the
asymmetric dimer
state to be the energetic
minimum in the 2x1 cell
Other examples:
» Lattice constants
» Diffusion barriers
» Phonon frequencies
25. QuantumWise Slide 25
Example 2: Germanium
LDA/GGA useless
» (Semi)metallic
» Wrong masses
But Meta-GGA (TB09)!
Gaps:
» Γ—L: 0.62 eV
» Γ—Γ: 0.84 eV
Good masses at L and Γ
Very reasonable strain
dependence
♥
26. QuantumWise Slide 26
Traditional atomistic quantum-based software can model either
isolated molecules or periodic systems
Interfaces are more complex!
The interface is the … ok, you get it
• Periodic + finite (0D or 2D)
• Heterogeneous systems
• Finite bias
28. QuantumWise Slide 28
Open boundary conditions - simple example
From Wikipedia: “Rectangular potential barrier”
29. QuantumWise Slide 29
Transport boundary conditions
Scattering boundary conditions
» Electrons flow under an applied
voltage bias
» Non-equilibrium electron
distribution described using
NEGF (Non-Equilibrium Green’s
Functions, Keldysh formalism)
» Electric current =
ballistic, coherent tunneling
(Landauer formalism)
» Transmission is bias-dependent
30. QuantumWise Slide 30
Transport
• Exact description of semi-infinite electrodes via self-
energies
• Non-equilibrium electron distribution using NEGF
Electronic structure
• DFT, Extended Hückel, TB, …
HHDD
Bulk
region
Bulk
region
NEGF transport methodology
M. Brandbyge, J.-L. Mozos, P. Ordejón, J. Taylor, K. Stokbro, Physical Review B 65, 165401 (2002)
DFT device modelling, most important features
Electron current
(Landauer formalism)
Electrostatic screening
32. QuantumWise Slide 32
Advanced electrostatics
A transistor also has
gate electrode(s)
» No gate currents in
ATK, gates are
electrostatic only
» Top/bottom, gate-all-
around, multiple
dielectric regions
Can also be used to add a
transverse electric field to e.g.
nanotubes or graphene for opening
a band gap
34. QuantumWise Slide 34
The mission of QuantumWise
Help industrial
companies be more
successful through
atomic-scale
modeling
Our philosophy
To deliver modern
solutions to modern
problems in the field of
atomic-scale modeling
through strong
interaction with
customers and partners
35. QuantumWise Slide 35
Products
Nano-device simulator
Nano-device simulator with unique functionality, based on atomic-
scale modeling, which can replace/complement current TCAD
device simulators that use a continuum description
Atomic-scale modeling platform
Professional platform which integrates multiple atomic-scale
modeling techniques, that can accelerate R&D within materials
and electronics in multiple industry sectors
36. QuantumWise Slide 36
Key advantages of the QuantumWise offering
Enables users to study new
materials and problems
» Unique proprietary algorithms
» Bridge to academic methods
Makes users more productive
» Reducing time required to set
up, manage computations,
and analyze results
Integrates different software
tools & methods
Professional support
and software quality
» forum.quantumwise.com
Partner for customized
development of novel
functionality
41. QuantumWise Slide 41
Open models is the modern way
This is not a unique
problem to atomic-scale
modeling. Look around!
Let’s make an open
platform, with
“apps”/plug-ins, for
atomic-scale modeling
42. QuantumWise Slide 42
The solution
Make an open, general
toolbox with lots of
features!
Open
» Possible for users to
develop new features
» Share with other users
» Built-in features
delivered as open source
General
» Can also be used as a GUI
for other codes
43. QuantumWise Slide 43
Atomic Structure Builder
Add structures from
• File
• Database
• Template generator
Add custom buttons
to toolbar
Manipulate and combine several structures
Plug-ins,
plug-ins,
plug-ins,
plug-ins,
plug-ins,
plug-ins,
plug-ins,
plug-ins,
plug-ins,
45. QuantumWise Slide 45
GUI + Python
ATK combines a GUI with a
programming environment
Efficient
» Quick to set up even
complex geometries
» Generates ready-to-run
input files in minutes (also
for other codes)
Powerful
» Automate, scan, loop
» Compute non-standard
quantities in batch
Lowers the barrier for
explorations
Unleashes the power of data
analysis
» GUI: Add plugins for custom
plotting (also for other
codes)
» ATK: Custom modules for
advanced studies
47. QuantumWise Slide 47
ABINIT
ABINIT is fully integrated into ATK 13.8 (Python module)
» Run in parallel
» Bandstructure, TotalEnergy, etc
» Set up calculation in GUI
» Store results in NC files
» Post-SCF analysis
» Plot in VNL
48. QuantumWise Slide 48
VASP Scripter
Setup of calculations, also NEB
Creates POSCAR, INCAR, KPOINTS and POTCAR
Coming: support for plotting output data
49. QuantumWise Slide 49
Technical key points of ATK/VNL
Simple deployment –
runs on anything
(Linux/Windows), out of
the box
» Input/output files are
100% platform
compatible
High-performance 3D
graphics
Parallelized using
OpenMP/MPICH2
50. QuantumWise Slide 50
A lot more…
Nudged elastic band calculations for
reaction paths and barriers
» State-of-the-art NEB implementation
» Advanced GUI setup tools (also for
export to other software like VASP)
Thermoelectric calculations
Molecular dynamics
» Similar functionality as LAMMPS, but
with a GUI
etc, etc.
51. QuantumWise Slide 51
Try ATK yourself!
Register for atrial
licensewithin
2 weeksof the
webinar and get 2
monthsfreetrial
http://quantumwise.com/products/free-trial
(write “webinar” in the comments when applying)
QuantumWise.com
QuantumWiseTV
http://www.youtube.com/user/QuantumWiseTV
That was in 2007 – soon we are at 20 nm, going to 8 nm in <10 years
45 degree rotated Si – one of the major success stories for atomistic modeling of semiconductors
Good point to ask prospect: what is the point of doing modeling? Why do you do it?
There is a long-standing contact issue in silicon carbide devices: is it ohmic, and if so why? “ This paper presents an important step toward addressing the current contact issues in wide-band-gap electronics.” (or so they say themselves )
Transferability is also predictability
NEGF needed because non-equilibrium in central region.
Non-conservation of charge makes the self-consistent process a bit more complex than usually. Circles are not always relevant to explain (in fact, most often not).
What remains is to evaluate the conductance and here we're concerned with coherent elastic transport which is the simplest: In this case the conductance is determined simply by the quantum transmission from one electrode to the other. This is the celebrated Landauer description which states that the electronic current can be found by integrating the transmission in the energy range between the two chemical potentials. The f's are the Fermi functions. You can see the 2-e-square-over-h which is the quantum unit of conductance. For low bias you just get the conductance is this constant times the transmission at the Fermi energy. Again we can describe things in terms of the G and the self-energies with these formulas...
