1. Towards parameter-free device modeling
4/16/2017
Towards parameter-free device modeling
Jesse Maassen
(Supervisor : Prof. Hong Guo)
Department of Physics, McGill University, Montreal, QC Canada
science
engineering
crash
Semi-classical device modeling
device parameters
Atomic, materials, chemistry modeling
quantum physics
device modeling < 50nm (1000 atoms)
May 4, 2011
Roberto Car’s group, Chemistry Department, Princeton
HP corporate template tutorial

2. The first electronic computer: ENIAC --- large sizes
2017/4/16
The first electronic computer: ENIAC --- large sizes
This computer is made of vacuum tubes, 17,000 of them.
People work inside the CPU of this computer.
1800 square feet
ENIAC: Electronic Numerical Integrator and Computer. It was 2400 times faster than human computing.
May 4, 2011
Roberto Car’s group, Chemistry Department, Princeton
HP corporate template tutorial

3. Today: transistors are very small
2017/4/16
Today: transistors are very small
Line of ~ 50 atoms
How to compute charge conduction in these atomic systems?
200 million transistors can fit on each of these pin head.
May 4, 2011
Roberto Car’s group, Chemistry Department, Princeton
HP corporate template tutorial

4. As the size of a device goes down, physics change
2017/4/16
As the size of a device goes down, physics change
Channel Length, L
1 mm
0.1 mm
10 µm
1 µ m
0.1 µm
10 nm
1 nm
0.1 nm
Macroscopic
dimensions
Top
Transistor L
1975
2000
2016
Bottom
Atomic dimensions
May 4, 2011
Roberto Car’s group, Chemistry Department, Princeton
HP corporate template tutorial

5. Conduction is usually studied “top down”
2017/4/16
Conduction is usually studied “top down”
V = I R or I = V G
Conductance G = 1/R
Conductivity
Mobility
Scattering time
Channel
m = ?
n = ?
“Not obvious”
May 4, 2011
Roberto Car’s group, Chemistry Department, Princeton
HP corporate template tutorial

6. What device parameters?
2017/4/16
What device parameters?
Device parameters
These parameters specify properties of each individual device.
How to obtain device parameters?
--- by experimental measurements - now;
--- by computational modeling;
May 4, 2011
Roberto Car’s group, Chemistry Department, Princeton
HP corporate template tutorial

7. Practical modeling method: need for many parameters
2017/4/16
Practical modeling method: need for many parameters
capacitance
Transconductance
diodes
Geometry scaling
More than a 400 parameters are needed.
May 4, 2011
Roberto Car’s group, Chemistry Department, Princeton
HP corporate template tutorial

8. Moore’s law for model parameters
2017/4/16
Moore’s law for model parameters
Number of parameter double every 18 months
Reflects the complexity in modern technology
103
Year of introduction
(arbitrary unit in log scale)
Implemented feature 1
102 10
1965
1980
1990
2000
Level 1
Level 2
Level 3
BSIM1
BSIM2
BSIM3v3
BSIM4
Number of parameters
parameter per feature
PSP
May 4, 2011
Roberto Car’s group, Chemistry Department, Princeton
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9. Roberto Car’s group, Chemistry Department, Princeton
2017/4/16
Different modeling method: includes quantum and discrete material properties (all parameter free, no m, n or )
Quantum:
Tunneling – cannot turn off transistor; Size quantization ; electron-phonon scattering during current flow; Quantum dissipation; Spin transport; Spin-orbital effects …
Atomistic structures:
Materials are no longer a continuous medium. Atomic simulations are useful when: more atomic species are used in nano-systems; charge transfer; interfaces, surfaces, domain boundaries; external potential drop; disorder …
It is highly desirable to develop parameter-free theory and modeling method.
May 4, 2011
Roberto Car’s group, Chemistry Department, Princeton
HP corporate template tutorial

10. Goal of nanoelectronics theory and modeling
2017/4/16
Goal of nanoelectronics theory and modeling
engineering
science
crash
large scale device modeling
device parameters
atomic simulations materials, chemistry, physics
quantum mechanics Physics
device modeling < 50nm (1000 atoms)
Nanoelectronic device physics
This is largely applied physics: it is absolutely important that our theory is not only fundamentally correct, but also practical.
May 4, 2011
Roberto Car’s group, Chemistry Department, Princeton
HP corporate template tutorial

11. Basic ingredients of a theory:
2017/4/16
Basic ingredients of a theory:
A transport model
Device Hamiltonian
Non-equilibrium Physics
Transmission
Fermi level alignment
Calculable!
Picture from: Nitzan & Ratner, Science, 300, 1384 (2003).
May 4, 2011
Roberto Car’s group, Chemistry Department, Princeton
HP corporate template tutorial

12. Theoretical transport model
2017/4/16
Theoretical transport model
A scattering region; semi-infinite leads; coherence; external potentials; coupling to other bath (the X-probe), etc.. We build an atomic model for this picture (for material specific properties).
May 4, 2011
Roberto Car’s group, Chemistry Department, Princeton
HP corporate template tutorial

13. Theoretical transport model (cont.): Landauer theory
2017/4/16
Theoretical transport model (cont.): Landauer theory
Left reservoir
empty
Under a voltage bias, electrons elastically (coherent) traverse the device from left to the right. They are “hot” electrons on the right, and some dissipation occurs and electrons end up inside the right reservoir.
Right reservoir
We compute the transmission process from left to the right.
May 4, 2011
Roberto Car’s group, Chemistry Department, Princeton
HP corporate template tutorial

14. H = Hleads + Hdevice + Hcoupling
Device Hamiltonian
The Hamiltonian determines the energy levels of the device (How to fill these levels  non-equilibrium statistics.)
What kind of H to use is an issue of accuracy (tight-binding, DFT, GW, …).
In the end, we want to compare our results with experimental data without adjusting theoretical parameters.
DFT offers a good trade-off between accuracy and speed.
H = Hleads + Hdevice + Hcoupling
May 4, 2011
Roberto Car’s group, Chemistry Department, Princeton

15. Density functional theory : Kohn-Sham Hamiltonian
Potential of ions
Potential of electrons
(Poisson equation)
Quantum/ many-body effects
Assumption : All electrons are independent
May 4, 2011
Roberto Car’s group, Chemistry Department, Princeton

16. DFT approximately solves how atoms interact :
2017/4/16
DFT approximately solves how atoms interact :
DFT for materials: put atoms in a simulation box, compute interactions between electrons and nucleus.
But, DFT solves only 2 kinds of problems: finite or periodic systems.
May 4, 2011
Roberto Car’s group, Chemistry Department, Princeton
HP corporate template tutorial

17. A device is neither finite nor periodic
2017/4/16
A device is neither finite nor periodic
For a device:
There is no periodicity.
There are infinite number of atoms because the device is hooked up to external leads…
These difficulties must be overcome in first principles modeling of transport.
May 4, 2011
Roberto Car’s group, Chemistry Department, Princeton
HP corporate template tutorial

18. Essentially, must solve two problems:
2017/4/16
Essentially, must solve two problems:
How to reduce the infinitely large system to something calculable on a computer?
Effective scattering region
Left lead
Right lead
May 4, 2011
Roberto Car’s group, Chemistry Department, Princeton
HP corporate template tutorial

19. Screening approximation --- reducing the infinitely large problem:
Within DFT, once the potential is matched at the boundary, charge density automatically goes to the bulk-electrode values at the boundaries:
Left lead
Right lead
Scattering region
Charge density
Within screen approx., we only have to worry about a finite scattering region.
May 4, 2011
Roberto Car’s group, Chemistry Department, Princeton

20. Roberto Car’s group, Chemistry Department, Princeton
Another example
Using the screening approximation and solving Poisson Equation in real space, we can deal with systems with different leads.
May 4, 2011
Roberto Car’s group, Chemistry Department, Princeton

21. Keldysh non-equilibrium Green’s function (NEGF):
2017/4/16
Keldysh non-equilibrium Green’s function (NEGF):
NEGF:
Right lead
Left lead
Effective scattering region
Correct non-equilibrium physics, correct transport boundary conditions, easiness of adding new physics (e-p).
Book of Jauho; book of Datta; Wang, Wang, Guo PRL 82, 398(1999)
May 4, 2011
Roberto Car’s group, Chemistry Department, Princeton
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22. Roberto Car’s group, Chemistry Department, Princeton
Transmission
(This is one of several ways of getting T)
May 4, 2011
Roberto Car’s group, Chemistry Department, Princeton

23. NEGF-DFT: Taylor, Guo and Wang, PRB 63, 245407 (2001).
2017/4/16
NEGF-DFT: Taylor, Guo and Wang, PRB 63, (2001).
Use density functional theory (DFT) to compute the electronic structure and all other materials properties of the open device structure;
Use Keldysh non-equilibrium Green’s function (NEGF) to populate the electronic states (non-equilibrium quantum statistics);
Use numerical techniques to deal with the open boundary conditions.
Molecular transport junctions
Solid state devices
May 4, 2011
Roberto Car’s group, Chemistry Department, Princeton
HP corporate template tutorial

24. Wide range of research has been carried out by NEGF-DFT
2017/4/16
Wide range of research has been carried out by NEGF-DFT
Leakage current in MOSFET;
Transport in semiconductor devices, photocells;
Transport in carbon nanostructures;
Resistivity of Cu interconnects;
Conductance, I-V curves of molecular transport junctions;
Computation of capacitance, diodes, inductance, current density;
TMR, spin currents, and spin injection in magnetic tunnel junctions;
Transport in nanowires, rods, films, clusters, nanotubes;
Resistance of surface, interface, grain boundaries;
STM image simulations;
Strongly correlated electrons in transport;
Transport through short peptides; ….
Recently developed modeling tool allows for:
Large-scale systems (~1000 atoms & ~10 nm).
Disorder: Surface/interface roughness, dopants, impurities.
it is a progressing field and not all is perfect yet.
May 4, 2011
Roberto Car’s group, Chemistry Department, Princeton
HP corporate template tutorial

25. Roberto Car’s group, Chemistry Department, Princeton
An example:
Graphene-metal interface
May 4, 2011
Roberto Car’s group, Chemistry Department, Princeton

26. Roberto Car’s group, Chemistry Department, Princeton
Motivation (graphene-metal interface)
Experimental studies:
Nature Nanotechnology 3, 486 (2008)
Phys. Rev. B 79, (2009)
Photocurrent
experiments
May 4, 2011
Roberto Car’s group, Chemistry Department, Princeton

27. Roberto Car’s group, Chemistry Department, Princeton
Our goal
Parameter-free transport (NEGF-DFT*) calculation of a graphene / metal interface
* Jeremy Taylor, Hong Guo and Jian Wang, PRB 63, (2001).
May 4, 2011
Roberto Car’s group, Chemistry Department, Princeton

28. Roberto Car’s group, Chemistry Department, Princeton
Atomic structure
Which metals? What configuration at the interface?
Cu, Ni and Co (111) have in-place lattice constants that almost match that of graphene.
Previous study found most stable configuration (PRL 101, (2008)).
Metal
May 4, 2011
Roberto Car’s group, Chemistry Department, Princeton

29. Roberto Car’s group, Chemistry Department, Princeton
Graphene-Cu interface
Bandstructure of hybrid
graphene | Cu(111) system
Graphene states in black
Weak hybridization
n-type graphene
Metal
Appl. Phys. Lett. 97, (2010)
May 4, 2011
Roberto Car’s group, Chemistry Department, Princeton

30. Roberto Car’s group, Chemistry Department, Princeton
Graphene-Cu interface
Transport properties: graphene-Cu(111) system
Double minimum T.
T almost perfectly described by pure graphene at TMIN.
Appl. Phys. Lett. 97, (2010)
May 4, 2011
Roberto Car’s group, Chemistry Department, Princeton

31. Roberto Car’s group, Chemistry Department, Princeton
Graphene-Cu interface
Transport properties:
graphene | Cu(111)
E = 0.2 eV
Transmission
Momentum filtering k
Nano. Lett. 11, 151 (2011) kz kx k E EF
May 4, 2011
Roberto Car’s group, Chemistry Department, Princeton

32. Roberto Car’s group, Chemistry Department, Princeton
Graphene-Cu interface
Transport properties: graphene-Cu(111) system
One Dirac point pinned, while other moves with V.
Peak in conductance  doping level of graphene
Appl. Phys. Lett. 97, (2010)
May 4, 2011
Roberto Car’s group, Chemistry Department, Princeton

33. Roberto Car’s group, Chemistry Department, Princeton
Graphene-Ni interface
Band structure : graphene-Ni(111) system
Strong hybridization with metal
Band gap opening
Graphene is spin-polarized
: A-site C(pz)
: B-site C(pz)
: Ni(dZ2)
Nano. Lett. 11, 151 (2011)
May 4, 2011
Roberto Car’s group, Chemistry Department, Princeton

34. Roberto Car’s group, Chemistry Department, Princeton
Graphene-Ni interface
Transport properties :
graphene-Ni(111) system
Nano. Lett. 11, 151 (2011)
May 4, 2011
Roberto Car’s group, Chemistry Department, Princeton

35. Roberto Car’s group, Chemistry Department, Princeton
Graphene-Ni interface
Transport properties :
graphene-Ni(111) system
Nano. Lett. 11, 151 (2011)
May 4, 2011
Roberto Car’s group, Chemistry Department, Princeton

36. Roberto Car’s group, Chemistry Department, Princeton
Graphene-Ni interface
Transport properties :
graphene-Ni(111) system
Nano. Lett. 11, 151 (2011)
May 4, 2011
Roberto Car’s group, Chemistry Department, Princeton

37. Roberto Car’s group, Chemistry Department, Princeton
Graphene-metal interface
SUMMARY
Cu merely n-dopes the graphene resulting in:
Peak in dI/dV provides doping level
Can be simply modeled assuming a n-i junction
Similar trends for Al, Ag, Au & Pt
Ni & Co create spin-dependent (pseudo-) band gaps in graphene.
Large spin injection efficiencies ~80%
May 4, 2011
Roberto Car’s group, Chemistry Department, Princeton

38. Roberto Car’s group, Chemistry Department, Princeton
4/16/2017
Conclusions
We have a first principles quantum transport theory valid at finite bias using a combination of NEGF-DFT.
Large scale parameter-free modeling tool useful for device and materials engineering.
Proper treatment of chemical bonding at interfaces and includes the effects of disorder (very important for practical calculations).
Potential to treat ~104 atoms and lengths ~10nm.
May 4, 2011
Roberto Car’s group, Chemistry Department, Princeton
HP corporate template tutorial

39. Roberto Car’s group, Chemistry Department, Princeton
4/16/2017
Take home message:
9nm
1. Quantum physics Eigler (IBM)
2. Materials physics Williams (HP)
To make quantitative predictions without phenomenological parameters, a formalism has been developed that includes these ingredients.
3. Nonequilibrium statistical physics (picture from Ratner)
May 4, 2011
Roberto Car’s group, Chemistry Department, Princeton
HP corporate template tutorial

40. Thank you ! (and to my supervisor and colleagues)
4/16/2017
Thank you !
(and to my supervisor and colleagues)
$: NSERC, FQRNT, CIFAR, DRDC; Computers :
SRC, LuXin Energy.
RQCHP,CLUMEQ
May 4, 2011
Roberto Car’s group, Chemistry Department, Princeton
HP corporate template tutorial

41. Roberto Car’s group, Chemistry Department, Princeton
Another example:
Graphene-metal interface
Ultrathin Si films
May 4, 2011
Roberto Car’s group, Chemistry Department, Princeton

42. Roberto Car’s group, Chemistry Department, Princeton
Motivation (Si nano-film)
The main motivation for our research was the experimental work by Pengpeng Zhang et al. with silicon-on-insulators.
Nature 439, 703 (2006)
Used STM to image
10 nm Si film on SiO2
Charge
traps
Surface
states
SiO2
SiO2 Si
Vacuum
May 4, 2011
Roberto Car’s group, Chemistry Department, Princeton

43. Roberto Car’s group, Chemistry Department, Princeton
2017/4/16
Our goal
Current
Electrode
Electrode
May 4, 2011
Roberto Car’s group, Chemistry Department, Princeton
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44. Roberto Car’s group, Chemistry Department, Princeton
2017/4/16
Our goal
Surface
Current
Thickness
Electrode
Electrode
Length
Doping level
(lead or channel)
Orientation
May 4, 2011
Roberto Car’s group, Chemistry Department, Princeton
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45. Roberto Car’s group, Chemistry Department, Princeton
2017/4/16
Atomic structure (surface)
Hydrogenated surface vs. clean surface
H terminated [21:H]
Clean [P(22)] H
Si (top:1)
Si (top)
Si (top:2) Si Si
May 4, 2011
Roberto Car’s group, Chemistry Department, Princeton
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46. Roberto Car’s group, Chemistry Department, Princeton
2017/4/16
Electronic structure (surface)
Atomic structure & bandstructure
H terminated [21:H]
Clean [P(22)]
|| dimers
 dimers
 dimers
|| dimers
|| dimers
 dimers
|| dimers
 dimers
Large gap ~0.7 eV
Small gap ~0.1 eV
May 4, 2011
Roberto Car’s group, Chemistry Department, Princeton
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47. Roberto Car’s group, Chemistry Department, Princeton
2017/4/16
Ultrathin Si films
n++ i H
Si (top) Si
Two-probe system
Channel : intrinsic Si
Leads : n++ doped Si
21:H surface
Periodic  to transport
L = 3.8 nm
n++ i
T = 1.7 nm
L = 19.2 nm
n++ i
May 4, 2011
Roberto Car’s group, Chemistry Department, Princeton
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48. Roberto Car’s group, Chemistry Department, Princeton
2017/4/16
Ultrathin Si films
n++ i
21:H surface
n++ i L
n++ EF VB i CB
Potential profile
Max potential varies with L
Screening length > 10nm
May 4, 2011
Roberto Car’s group, Chemistry Department, Princeton
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49. Roberto Car’s group, Chemistry Department, Princeton
4/16/2017
Ultrathin Si films
n++ i
Conductance vs. k-points ( dimers)
Shows contribution from k-points  to transport
Transport occurs near  point.
Conductance drops very rapidly 
TOP VIEW i n+ n+ 
May 4, 2011
Roberto Car’s group, Chemistry Department, Princeton
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50. Roberto Car’s group, Chemistry Department, Princeton
2017/4/16
Ultrathin Si films
n++ i
Conductance vs. k-points ( || dimers)
Largest G near  point
Conductance drops rapidly, but slower than for transport  to dimers. i
n++ 
TOP VIEW
May 4, 2011
Roberto Car’s group, Chemistry Department, Princeton
HP corporate template tutorial 50

51. Roberto Car’s group, Chemistry Department, Princeton
2017/4/16
Ultrathin Si films
n++ i
Conductance vs. Length
Conductance has exponential dependence on length, i.e. transport = tunneling.
Large difference due to orientation.
Better transport in the direction of the dimer rows.
May 4, 2011
Roberto Car’s group, Chemistry Department, Princeton
HP corporate template tutorial 51

52. Roberto Car’s group, Chemistry Department, Princeton
2017/4/16
Ultrathin Si films
n++ i
SUMMARY
Electronic structure
21:H [~0.7 eV gap]
p(22) [~0.1 eV gap]
Transport properties
Large effect of orientation in G for 21:H
More complete study to come soon!
May 4, 2011
Roberto Car’s group, Chemistry Department, Princeton
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53. Some (more) examples: Effect of dephasing on electron transport
Scattering properties of a nano-electromechanical system [Published in Phys. Rev. Lett. 105, (2010)]
Raman spectra of graphene on Cu substrate [Submitted to Phys. Rev. Lett.]
Effect of disorder and vacancies on electronic transport through a Au conductor [in progress]
Electron transport through a Si/Ge interface [in progress]

54. J. Maassen, F. Zahid and H. Guo PRB 80, 125423 (2009)
Effect of dephasing on electron transport
I(X) = 0
Phase breaking : Phenomenological model (Buttiker probe model)
Self-energy : Simple implementation
J. Maassen, F. Zahid and H. Guo PRB 80, (2009)

55. Effect of dephasing on electron transport
Al - BDT - Al
Left reservoir
Right reservoir
J. Maassen, F. Zahid and H. Guo PRB 80, (2009)

56. Effect of dephasing on electron transport
Narrow Al nanowire
V = 0.05 V
Ballistic transport independent of length
Ohm’s law behavior
J. Maassen, F. Zahid and H. Guo PRB 80, (2009)