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Sunhee Lee Network for Computational Nanotechnology Electrical and Computer Engineering

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 sunnyleekr@purdue.edu . Building block for quantum computing device. Quantum dot (QD)

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Sunhee Lee Network for Computational Nanotechnology Electrical and Computer Engineering

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  1. Development of a Massively ParallelNano-electronic Modeling Tool and its Application to Quantum Computing Devices Sunhee Lee Network for Computational Nanotechnology Electrical and Computer Engineering sunnyleekr@purdue.edu

  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=3 n=2 n=1 QDOT Lab @nanoHUB.org Light absorption 6~7 ionized P in Si Hanson and Awschalom, Nature 453, 2008 M. Füchsle et.al., Nature Nanotechnology, 2010

  3. 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 3 5 4 2

  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)

  5. SiGe Alloy disorder Si Rough steps 15 nm 10 nm SiGe Si 16 nm SiGe 150 nm 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 • Individualdopant spectrum • Single impurity QD in finFET • Atomistic treatment with localized basis set • sp3d5s* atomistic tight-binding Kharche et al. Appl. Phys. Lett. 90, 092109 (2007) Lansbergenet 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

  7. Modeling Si:P QD : NEMO3D-peta • 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 NEMO3D (physics) (Schrödinger solver) NEMO3D-peta (Schrödinger-Poisson solver) Localized orbital basis (sp3d5s*) Atomistic structure (~106 atoms) + 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 1 16 2 4 8 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 • Expandableand maintainable • 15,000,000 compute hours awarded • Capable of utilizing 32,000 processors • Released to Intel (2010) • Top of the Barrier / bandstructure app. • 1nanoHUB 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 NEMO3D (physics) (Schrödinger solver) 3D spatial parallelization Localized orbital basis (sp3d5s*) QD Device modeling Atomistic structure (~106 atoms) 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 !!

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

  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. 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 !!

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

  16. 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)? G2 DRN SRC [1-10] G1 [110] D+ Device geometry (top view) Quantum region

  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. HoonRyu

  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 1e 0e D+ - 5 5 -5 -5 [110] (nm) [110] (nm)

  23. 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) Lead DOS profiles Methodology, S. Lee, PRB 2011 Si:P wire, H. Ryu, PhD dissertation, 2011 B. Weber, Science 2011 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

  25. 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

  26. 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 • Prof. Gerhard Klimeck • Prof. Mark Lundstrom, Prof. Leonid Rokhinson, Prof. Alejandro Strachan & Prof. Michelle Simmons • Special thanks to … • Dr. HoonRyu • Matthias Tan, Zhengping Jiang & JunzheGeng • Dr. Abhijeet Paul • ChangwookJeong, Seokmin Hong & Jayoung Park • Thanks to … • Dr. Mathieu Luisier, Dr. Honghyun Park, Dr. Jim Fonseca & Dr. Michael Povolotskyi • Sunggeun Kim, ParijatSengupta, Mehdi Salmani,SaumitraMehrotra & Yahua Tan • Quantum dot subgroup • CQC2T Collaborators • Dr. Lloyd Hollenberg • Dr. SuddhasattaMahapatra, Dr. Jill Miwa, Dr. Martin Fuechsleand 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 undopedn-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 undopedSi 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,”https://nanohub.org/resources/5203, Sep. 2008 (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, 84 205309, 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. 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. 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. 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 [1-10] [110] [001] [110]

  33. Results Small lateral barrier height • 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 Large lateral barrier height Weak vertical confinement Strong vertical confinement

  34. 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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