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

Development of a Massively ParallelNano-electronic Modeling Tool and its

Application to Quantum Computing Devices

Sunhee LeeNetwork for Computational Nanotechnology

Electrical and Computer Engineeringsunnyleekr@purdue.edu

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Building block for quantum computing device

Hanson and Awschalom, Nature 453, 2008

• 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.

6~7 ionized P in Si

M. Füchsle et.al., Nature Nanotechnology, 2010

n=1

n=2

n=3

QDOT Lab @nanoHUB.orgLight absorption

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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

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Experimental Work (UNSW): a single donor QD !

Single Donor Quantum Dot: Experiment

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

• 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

150 nm

16 n

m 10 n

m15 nm

Si

SiGe

SiGe

Kharche et al. Appl. Phys. Lett. 90, 092109 (2007)

Si

SiG

e

Alloy disorder

Rough steps

Lansbergen et al. Nat. Phys. 4, 656 (2008)5

Modeling Work (Purdue): Single Donor QD systemStrength• 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 : Experience

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• Solving an eigenvalue problem» Atomistic grid

» (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

Modeling Si:P QD : NEMO3D-peta

Localized orbital basis(sp3d5s*)

Atomistic structure(~106 atoms)

NEMO3D (physics)(Schrödinger solver)

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!

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[¿¿¿]16

NEMO3D: 1D slices NEMO3D-peta: 2D/3D slices

time

# procs.

NEMO3D : single shot eigenvalue problemNEMO3D-peta: Self-

consistent simulation !! (10~30 iterations)

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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

Localized orbital basis(sp3d5s*)

Atomistic structure(~106 atoms)

NEMO3D (physics)(Schrödinger solver)

NEMO3D-peta development

3D spatial parallelization QDDevice modeling

Potential-chargeself-consistency

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Experimental Work (UNSW): a single donor QD !

Single Donor Quantum Dot: Questions

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» Doping plane 2D (n++ doped)» 3D distribution of charge

p-type substrate (1015cm-3)

56 nm

128 nm

360

nm

δ-doping plane

S D

G1

G2

Top view

3D schematic

[110]

[001]

[1-10]

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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-classicalregion

[110]

[1-10]

SRC DRN

G1

G2

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

18QD changes shape with electron filling !!

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• Superposition» Background potential» QD potential

[110] (nm)

Modeling: Potential profile

Equilibrium potential profile

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Modeling: Charge filling (Ack: H. Ryu)

• Quantum region» Channel region» 12x60x20 (nm3)

• Compute ground eigenstate at each Vg

• Determine charge filling» Does Ground state hit EF(SRC)?

Device geometry (top view)

Quantum region

[110]

[1-10]

SRC DRN

G1

G2

D+

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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+) [110] (nm) 5-5 5-5 [110] (nm)-

Ground eigenstate

D+

Acknowledgment: Dr. Hoon Ryu

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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+) [110] (nm) 5-5 5-5 [110] (nm)-

Ground eigenstate

D+

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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)

[110] (nm) 5-5 5-5 [110] (nm)-

Ground eigenstate

D+

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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) [110] (nm) 5-5 5-5 [110] (nm)-

Ground eigenstate

D0

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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 [110] (nm) [110] (nm)-5-5 -5 5

Ground eigenstate

D0

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Modeling: Charge filling (Ack: H. Ryu)

• Simulation vs. Experiment: How close are we ?

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

3. EC = 46.3 meV

[110] (nm) 5-5 5-5 [110] (nm)-

D+

0e 1e

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Modeling: Coulomb diamond (Ack: Y.H.M. Tan)

• Extract results from NEMO3D-peta» Channel states» Lead DOS profiles

• Rate equation tool 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

Lead DOS profiles

Methodology, S. Lee, PRB 2011Si:P wire, H. Ryu, PhD dissertation, 2011 B. Weber, Science 2011

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Experimental Work (UNSW): a single donor QD !

Single Donor Quantum Dot: Answers

• 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

4. Gate Lever-arm 0.11 0.15

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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

Double Quantum Dot

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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

Result 4 : Coulomb diamond

Ground + excited states

Ground states

Coupling DOS in leads

Basic Features

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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 confinementElectron charging

[001]

[110][110]

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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

» Output 1: VP » Output 2: VS

[110]

[001]

[110]

[1-10]

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Results

• 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

Small lateral barrier height

Large lateral barrier height

Strong vertical confinementWeak vertical confinement

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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