Transcript Network for Computational Nanotechnology (NCN) Purdue, Norfolk State, Northwestern, MIT, Molecular Foundry, UC Berkeley, Univ.

Network for Computational Nanotechnology (NCN)
Purdue, Norfolk State, Northwestern, MIT, Molecular Foundry, UC Berkeley, Univ. of Illinois, UTEP
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
[email protected]
Building block for quantum computing device
•Quantum dot (QD)
n=3
» Confinement (particle-in-a-box)
» s- p- d- like orbitals (“artificial atom”)
n=2
n=1
•Optical applications (LED/PD)
Light absorption
QDOT Lab @nanoHUB.org
•Applications for quantum
computers (QC)
6~7 ionized P in Si
» Carry electron/nucleus spin info.
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Hanson and Awschalom,
Nature 453, 2008
M. Füchsle et.al.,
Nature Nanotechnology, 2010
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
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QD images adopted with permission from Simmons’ group
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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)
Modeling Si:P QD : Need for atomistic modeling
Si
SiGe
150 nm
•Predicting valley splitting in Si
Si SiGe
16 nm
SiGe
10 nm
Alloy disorder
» (First excited state) – (GND state)
» Important measure in QC
» 10 ueV ~ 1 meV
Rough steps
•Random alloy disorder
» Sample variation (Error bars)
» ex) disorders in the 2D Si:P layer,
published in PRB
Kharche et al. Appl. Phys. Lett. 90, 092109 (2007)
•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)
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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
Modeling Si:P QD : NEMO3D-peta
•Solving an eigenvalue problem
NEMO3D (physics)
(Schrödinger solver)
Localized orbital basis
(sp3d5s*)
» Atomistic grid
» 𝐻Ψ = 𝐸Ψ
» dim 𝐻 = (106~107) (atoms)
X (10~20) (basis/atom)
= 107~108 !!
Atomistic structure
(~106 atoms)
•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
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Parallelization engine in NEMO3D-peta
•Why do we need “better” parallel computing?
 To reduce simulation time even more!
NEMO3D: 1D slices
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NEMO3D-peta: 2D/3D slices
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𝐻=
time
NEMO3D : single shot
eigenvalue problem
NEMO3D-peta: Selfconsistent simulation !!
(10~30 iterations)
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# procs.
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.)
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NEMO3D-peta for QD simulation
NEMO3D-peta development
NEMO3D (physics)
(Schrödinger solver)
3D spatial parallelization
Localized orbital basis
(sp3d5s*)
Atomistic structure
(~106 atoms)
Potential-charge
self-consistency
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QD
Device modeling
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 !!
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Modeling: Domain
•Domain
3D schematic
» Doping plane 2D (n++ doped)
» 3D distribution of charge
δ-doping plane
56 nm
Top view
G2
D
360 nm
S
[001]
G1
p-type substrate (1015cm-3)
[1-10]
[110]
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Modeling: Background potential
Device geometry (top view)
G2
•Semi-classical calculation
Semi-classical
region
» Background potential
» WITHOUT impurity QD
•Leads
» (n++) doping region, ND=1021 (cm-3)
DRN
SRC
•Background doping (p-)
[1-10]
» NA=1015(cm-3)
G1
[110]
•VSD = 0
•VG1=VG2=VG
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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. Rahman @ Nat. Phys.)
» “D+” state
• Single electron filled QD
» QD potential “screened”
 Shallower potential
» Self-consistent calculation
» Next ground state “floats up”
» “D0” state
QD changes shape
with electron filling !!
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Modeling: Potential profile
•Superposition
» Background potential
» QD potential
Equilibrium potential profile
[110] (nm)
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Modeling: Charge filling (Ack: H. Ryu)
Device geometry (top view)
•Quantum region
» Channel region
» 12x60x20 (nm3)
G2
DRN
SRC
Quantum
region
[1-10]
•Compute ground eigenstate at
each Vg
•Determine charge filling
G1
» Does Ground state hit EF(SRC)?
[110]
D+
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Modeling: Charge filling (Ack: H. Ryu)
•VDS = 0 V, sweep VG
•Plot
D+
» Ground state eigenvalue (1s(A))
» EF
•VG = 0.0 V
» Channel empty (D+)
-5
[110] (nm)
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-5
- (nm)
[110]
Ground eigenstate
Acknowledgment: Dr. Hoon Ryu 17
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Modeling: Charge filling (Ack: H. Ryu)
•VDS = 0 V, sweep VG
•Plot
D+
» Ground state eigenvalue (1s(A))
» EF
•VG = 0.2 V
» Channel empty (D+)
-5
[110] (nm)
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-5
- (nm)
[110]
Ground eigenstate
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Modeling: Charge filling (Ack: H. Ryu)
•VDS = 0 V, sweep VG
•Plot
D+
» Ground state eigenvalue (1s(A))
» EF
•VG ≈ 0.45 V
» 1s(A) hits EF
» D+  D0 transition
» Screened QD ! (impose D0 potential)
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-5
[110] (nm)
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-5
- (nm)
[110]
Ground eigenstate
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Modeling: Charge filling (Ack: H. Ryu)
•VDS = 0 V, sweep VG
•Plot
D0
» Ground state eigenvalue (1s(A))
» EF
•VG ≈ 0.55 V
» Channel filled by one electron (D0)
-5
[110] (nm)
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-5
- (nm)
[110]
Ground eigenstate
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Modeling: Charge filling (Ack: H. Ryu)
•VDS = 0 V, sweep VG
•Plot
D0
» Ground state eigenvalue (1s(A))
» EF
•VG ≈ 0.72 V
» 1s(A) hits EF
» D0  D- transition
-5
[110] (nm)
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-5
- (nm)
[110]
Ground eigenstate
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Modeling: Charge filling (Ack: H. Ryu)
•Simulation vs. Experiment: How close are we ?
3. EC = 46.3 meV
D+
-5
[110] (nm)
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-5
- (nm)
[110]
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1e
0e
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
0.11
0.15
4. Gate Lever-arm
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Modeling: Coulomb diamond (Ack: Y.H.M. Tan)
•Extract results from NEMO3D-peta
Lead DOS profiles
» Channel states
» Lead DOS profiles
•Rate equation tool
Methodology, S. Lee, PRB 2011
Si:P wire, H. Ryu, PhD dissertation, 2011
B. Weber, Science 2011
 Transition points (
0.42, 0.72V)
 Charging energy (Ec = 46.3 meV)
 Gate controllability (slope a = 0.15)
 Lead DOS profiles (streaks)
Channel states, EF
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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
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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
0.11
0.15
4. Gate Lever-arm
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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
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Double Quantum Dot
Acknowledgment
• Committee members
» 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 …
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List of publications
1. 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
2. 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
3. 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
4. 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
5. 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
6. 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
7. 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
8. 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
9. 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,” https://nanohub.org/resources/5203, Sep. 2008 (Now replaced by NEMO 5)
10. 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, 84 205309, 2011
11. 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
12. Three other publications ready for submission, one in preparation
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Result 4 : Coulomb diamond
Basic Features
Ground + excited states
Ground states
Coupling DOS in leads
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]
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[110]
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
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Method
•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
[1-10]
[110]
» Output 1: VP
» Output 2: VS
[001]
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[110]
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
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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 spectrum @ N electron
regime
» Compare VS with SiGe-Si-SiGe QD
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