1. Development of a Massively Parallel Nano-electronic Modeling Tool and its Application to Quantum Computing Devices
Sunhee Lee
Network for Computational Nanotechnology
Electrical and Computer Engineering

2. Building block for quantum computing device
Quantum dot (QD)
Confinement (particle-in-a-box)
s- p- d- like orbitals (“artificial atom”)
Optical applications (LED/PD)
Applications for quantum computers (QC)
Carry electron/nucleus spin info.
n=1
n=2
n=3
QDOT
Light absorption
6~7 ionized P in Si
M. Füchsle et.al.,
Nature Nanotechnology, 2010
Hanson and Awschalom, Nature 453, 2008

3. Phosphorus quantum dot in Si
Ionized P impurity QD
Phosphorus quantum dot in Si
Promising candidate for QC device
Long spin coherence times
Naturally uniform
Store electron/nucleus spin info.
Fabrication challenges
First single donor QD system !!
STM+MBE technology
2D dopant patterning
QD images adopted with permission from Simmons’ group 1 2 3 4 5 3

4. Single Donor Quantum Dot: Experiment
Experimental Work (UNSW): a single donor QD !
Questions: is this real??
How can we explain the coupling of the channel donor to the Si:P leads ?
Can we quantify the controllability of plane Si:P leads on the channel confinement ?
Why are there the conductance streaks at the Coulomb diamond edges ?
Prove it is real! (Purdue) 4

5. Modeling Si:P QD : Need for atomistic modeling
150 nm
16 nm
10 nm
15 nm Si
SiGe
Kharche et al. Appl. Phys. Lett. 90, (2007)
Alloy disorder
Rough steps
Predicting valley splitting in Si
(First excited state) – (GND state)
Important measure in QC
10 ueV ~ 1 meV
Random alloy disorder
Sample variation (Error bars)
ex) disorders in the 2D Si:P layer, published in PRB
Individual dopant spectrum
Single impurity QD in finFET
Atomistic treatment with localized basis set
sp3d5s* atomistic tight-binding
Lansbergen et al. Nat. Phys. 4, 656 (2008)

6. Modeling Si:P QD : Experience
Modeling Work (Purdue): Single Donor QD system
Strength
Single impurity physics (R. Rahman & S. Rogge)
Realistic modeling of Si:P contacts
Strong connections to experiment
Single electron charging energy, transition points, gate controllability & Coulomb diamond 6

7. Modeling Si:P QD : NEMO3D-peta
Localized orbital basis
(sp3d5s*)
Atomistic structure
(~106 atoms)
NEMO3D (physics)
(Schrödinger solver)
Solving an eigenvalue problem
Atomistic grid
𝐻Ψ=𝐸Ψ
dim 𝐻 = (106~107) (atoms)
X (10~20) (basis/atom)
= 107~108 !!
NEMO3D-peta (2008~)
Atomistic tight-binding, million atom simulation tool
For QD-like simulations
Inherits the physics aspect of NEMO3D
Schrödinger-Poisson self-consistency module
3D spatial parallelization
Useful in self-consistent simulations
NEMO3D-peta
(Schrödinger-Poisson solver) +
NEMO3D

8. Parallelization engine in NEMO3D-peta
Why do we need “better” parallel computing?
 To reduce simulation time even more!
NEMO3D: 1D slices
NEMO3D-peta: 2D/3D slices 𝐻= 1 2 4 8 16
Bent’s work
NEMO3D : single shot eigenvalue problem
NEMO3D-peta: Self-consistent simulation !! (10~30 iterations)
time
# procs.

9. NEMO3D-peta Highlights (2008~present)
90,000+ lines of code (from scratch!!)
3.5+ years of development
~8 applications implemented
Expandable and maintainable
15,000,000 compute hours awarded
Capable of utilizing 32,000 processors
Released to Intel (2010)
Top of the Barrier / bandstructure app.
1 nanoHUB tool
1d-hetero
15 Publications in line
9 journal and conference papers (3 experimental)
2 journal publication accepted (1 B. Weber et al. Science)
4 journal publications ready for submission (1 M. Fuechsle et al.)

10. NEMO3D-peta for QD simulation
NEMO3D-peta development
Localized orbital basis
(sp3d5s*)
Atomistic structure
(~106 atoms)
NEMO3D (physics)
(Schrödinger solver)
3D spatial parallelization QD
Device modeling
Potential-charge
self-consistency

11. Single Donor Quantum Dot: Questions
Experimental Work (UNSW): a single donor QD !
Questions: is this real??
How can we explain the coupling of the channel donor to the Si:P leads ?
Can we quantify the controllability of plane Si:P leads on the channel confinement ?
Why are there the conductance streaks at the Coulomb diamond edges ?
Prove it is real !! 11

12. Modeling: Domain Domain 3D schematic Top view
Doping plane 2D (n++ doped)
3D distribution of charge
3D schematic
p-type substrate (1015cm-3)
56 nm
128 nm
360 nm
δ-doping plane S D G1 G2
Top view
[001]
[1-10]
[110]

13. Modeling: Background potential
Semi-classical calculation
Background potential
WITHOUT impurity QD
Leads
(n++) doping region, ND=1021 (cm-3)
Background doping (p-)
NA=1015(cm-3)
VSD = 0
VG1=VG2=VG
Device geometry (top view)
Semi-classical
region
[110]
[1-10]
SRC
DRN G1 G2

14. Modeling: Impurity QD potential
Empty QD (ionized donor QD)
Binding energy data of P in Si
(Rep. Prog. Phys., Vol. 44, 1981)
Coulombic (1/r) + TB param. fitting
(Work by R. Nat. Phys.)
“D+” state
QD changes shape with electron filling !!
Single electron filled QD
QD potential “screened”
 Shallower potential
Self-consistent calculation
Next ground state “floats up”
“D0” state
Before applying gate bias

15. Modeling: Potential profile
Superposition
Background potential
QD potential
Equilibrium potential profile
[110] (nm) 15

16. Modeling: Charge filling (Ack: H. Ryu)
Device geometry (top view)
Quantum region
[110]
[1-10]
SRC
DRN G1 G2
Quantum region
Channel region
12x60x20 (nm3)
Compute ground eigenstate at each Vg
Determine charge filling
Does Ground state hit EF(SRC)? D+

17. Modeling: Charge filling (Ack: H. Ryu)
VDS = 0 V, sweep VG
Plot
Ground state eigenvalue (1s(A)) EF
VG = 0.0 V
Channel empty (D+) D+ -5 5 - -5 5
[110] (nm)
[110] (nm)
Ground eigenstate
Acknowledgment: Dr. Hoon Ryu

18. Modeling: Charge filling (Ack: H. Ryu)
VDS = 0 V, sweep VG
Plot
Ground state eigenvalue (1s(A)) EF
VG = 0.2 V
Channel empty (D+) D+ -5 5 - -5 5
[110] (nm)
[110] (nm)
Ground eigenstate

19. Modeling: Charge filling (Ack: H. Ryu)
VDS = 0 V, sweep VG
Plot
Ground state eigenvalue (1s(A)) EF
VG ≈ 0.45 V
1s(A) hits EF
D+  D0 transition
Screened QD ! (impose D0 potential) D+ -5 5 - -5 5
[110] (nm)
[110] (nm)
Ground eigenstate

20. Modeling: Charge filling (Ack: H. Ryu)
VDS = 0 V, sweep VG
Plot
Ground state eigenvalue (1s(A)) EF
VG ≈ 0.55 V
Channel filled by one electron (D0) D0 -5 5 - -5 5
[110] (nm)
[110] (nm)
Ground eigenstate

21. Modeling: Charge filling (Ack: H. Ryu)
VDS = 0 V, sweep VG
Plot
Ground state eigenvalue (1s(A)) EF
VG ≈ 0.72 V
1s(A) hits EF
D0  D- transition D0 -5 5 - -5 5
[110] (nm)
[110] (nm)
Ground eigenstate

22. Modeling: Charge filling (Ack: H. Ryu)
Simulation vs. Experiment: How close are we ?
3. EC = 46.3 meV
[110] (nm) 5 -5 - D+ 0e 1e
Experiment
Theory
1. 0e  1e Transition VG (V)
0.40
0.45
2. 1e  2e Transition VG (V)
0.80
0.72
3. Charging energy EC (meV)
47 ± 2
46.3
4. Gate Lever-arm
0.11
0.15

23. Modeling: Coulomb diamond (Ack: Y.H.M. Tan)
Lead DOS profiles
Methodology, S. Lee, PRB 2011
Si:P wire, H. Ryu, PhD dissertation, 2011
B. Weber, Science 2011
Extract results from NEMO3D-peta
Channel states
Lead DOS profiles
Rate equation tool
Transition points ( , 0.72V)
Charging energy (Ec = 46.3 meV)
Gate controllability (slope a = 0.15)
 Lead DOS profiles (streaks)
Channel states, EF

24. Single Donor Quantum Dot: Answers
Experimental Work (UNSW): a single donor QD !
How can we explain the coupling of the channel donor to the Si:P leads ?
Semi-classical treatment of gate biasing
No stark effect (parallel shift of ground state)
Can we quantify the controllability of plane Si:P leads on the channel confinement ?
Transition points / Charging energy
Why are there the conductance streaks at the Coulomb diamond edges ?
Excited states + DOS of the leads 24

25. Quantitative match with experiment
Conclusion
Quantitative match with experiment
Transition point / charging energy / in-plane gate modulation
 A strong support for single impurity QD
Methodology applicable for future Si:P QD devices
Experiment
Theory
1. 0e  1e Transition VG (V)
0.40
0.45
2. 1e  2e Transition VG (V)
0.80
0.72
3. Charging energy EC (meV)
47 ± 2
46.3
4. Gate Lever-arm
0.11
0.15

26. Focused on the electrostatic modeling of single donor QD
Summary
Focused on the electrostatic modeling of single donor QD
Gate modulation and charge filling
A quantitative match with the experimental results
Methodology can be extended to future Si:P QD system
Transition phase (Y.H.M Tan)
Double Donor QD (D-168)
Understanding the two-electron operations in multiple QD systems
Find new methods to efficiently model QDs
Double Quantum Dot

27. Acknowledgment Committee members Special thanks to … Thanks to …
Prof. Gerhard Klimeck
Prof. Mark Lundstrom, Prof. Leonid Rokhinson, Prof. Alejandro Strachan & Prof. Michelle Simmons
Special thanks to …
Dr. Hoon Ryu
Matthias Tan, Zhengping Jiang & Junzhe Geng
Dr. Abhijeet Paul
Changwook Jeong, Seokmin Hong & Jayoung Park
Thanks to …
Dr. Mathieu Luisier, Dr. Honghyun Park, Dr. Jim Fonseca & Dr. Michael Povolotskyi
Sunggeun Kim, Parijat Sengupta, Mehdi Salmani, Saumitra Mehrotra & Yahua Tan
Quantum dot subgroup
CQC2T Collaborators
Dr. Lloyd Hollenberg
Dr. Suddhasatta Mahapatra, Dr. Jill Miwa, Dr. Martin Fuechsle and Bent Weber
Cheryl Haines & Vicki Johnson
Funding agencies: NSF, ARO, MSD, SRC …

28. List of publications
S. Lee, H. Ryu, Z. Jiang, and G. Klimeck, “Million atom electronic structure and device calculations on peta-scale computers,” in 13th International Workshop on Computational Electronics, 2009 (IWCE '09), May 2009
H. Ryu, S. Lee, and G. Klimeck, “A study of temperature-dependent properties of n-type delta-doped Si band-structures in equilibrium,” in 13th International Workshop on Computational Electronics, 2009 (IWCE '09), May 2009
S. Lee, H. Ryu, G. Klimeck, H. Campbell, S. Mahapatra, M. Y. Simmons, and L. C. L. Hollenberg, “Equilibrium bandstructure of a phosphorus delta-doped layer in silicon using a tight-binding approach,” IEEE Proceedings of NANO 2010, 2010
H. Ryu, S. Lee, B. Weber, S. Mahapatra, M. Simmons, L. Hollenberg, and G. Klimeck, “Quantum transport in ultra-scaled phosphorous-doped silicon nanowires,” in Silicon Nanoelectronics Workshop (SNW), Jun. 2010
B. Weber, S. Mahapatra, W. R. Clarke, R. H., L. S., G. Klimeck, L. C. L. Hollenberg, and M. Y. Simmons, “Quantum transport in atomic-scale silicon nanowires,” in Silicon Nanoelectronics Workshop (SNW), Jun. 2010
G. Tettamanzi, A. Paul, G. Lansbergen, J. Verduijn, S. Lee, N. Collaert, S. Biesemans, G. Klimeck, and S. Rogge, “Thermionic emission as a tool to study transport in undoped n-FinFETs,” IEEE Electron Device Letters, vol. 31, Feb. 2010
G. Tettamanzi, A. Paul, S. Lee, S. Mehrotra, N. Collaert, S. Biesemans, G. Klimeck, and S. Rogge, “Interface trap density metrology of state-of-the-art undoped Si n-FinFETs,” IEEE Electron Device Letters, vol. 32, Apr. 2011
A. Paul, G. C. Tettamanzi, S. Lee, S. Mehrotra, N. Colleart, S. Biesemans, S. Rogge, and G. Klimeck, “Interface trap density metrology from sub-threshold transport in highly scaled undoped Si n -FinFETs,” accepted for publication in Journal of Applied Physics 2011
A. G. Akkala, S. Steiger, J. M. D. Sellier, S. Lee, M. Povolotskyi, T. C. Kubis, H. Park, S. Agarwal, and G. Klimeck, “1d heterostructure tool,” Sep (Now replaced by NEMO 5)
S. Lee, H. Ryu, H. Campbell, L. C. L. Hollenberg, M. Y. Simmons and G. Klimeck, “Electronic structure of realistically extended atomistically resolved disordered Si:P δ-doped layers,” Physical Review B, , 2011
B. Weber, S. Mahapatra, H. Ryu, S. Lee, A. Fuhrer, T. C. G. Reusch, D. L. Thompson, W.C.T. Lee, G. Klimeck, L. C. L. Hollenberg, M.Y. Simmons, “Ohm’s law Survives to the Atomic Scale,”, accepted for publication in Science 2011
Three other publications ready for submission, one in preparation

29. Result 4 : Coulomb diamond
Basic Features
Ground states
Ground + excited states
Coupling DOS in leads

30. Electrostatically defined QD (UNSW)
Si MOS QD
Electrostatically defined QD (UNSW)
MOS fabrication technology
Dit = 5x1010 cm-2eV-1 (x 0.1~0.01)
Nelectron = 0, 1, 2, … !!
Lateral confinement
Vertical confinement
Electron charging
[001]
[110]
[110]

31. Six-valley degeneracy
Challenges
Six-valley degeneracy
Valley splitting (Δ)
= First excited eigenstate – GND state
In this QD : ~100 ueV
Questions
What are the possible factors that influence VS ?
Does our results compare experimental results ?
Typical quantum well case example

32. Self-consistent simulation
Method
[110]
[001]
[1-10]
Simulation domain
Size = 60x90x30 nm3, 8 million atoms
Self-consistent simulation
Input 1: Barrier height (VB1=VB2)
Input 2: Plunger gate size (30xWc)
Wc= 30,40,50 & 60 nm
Input 3: Assume 1 electron filled
Output 1: VP
Output 2: VS

33. Smaller dot, Large lateral barrier  Stronger confinement
Results
Small lateral barrier height
Large lateral barrier height
Weak vertical confinement
Strong vertical confinement
Smaller dot, Large lateral barrier  Stronger confinement
Eigenstates float up  Deeper vertical confinement required
VS range : 100~500 ueV (100 ueV exp.)
VS tunable but sensitive to QD geometry and lateral barrier height

34. Work is still in progress
Conclusion
VS in Si MOS QD
100~500 ueV (100 ueV exp.)
VS can be tunable
Controlling barrier height
Adjusting QD size
Sensitive to electrostatics
Work is still in progress
Excited state N electron regime
Compare VS with SiGe-Si-SiGe QD