nanoHUB.org online simulations and more

Nano 101 Quantum Dots WHAT?

Gerhard Klimeck Technical Director Network for Computational Nanotechnology (NCN)

Network for Computational Nanotechnology nanoHUB.org Presentation Outline online simulations and more • Classical Systems . Particles . Propagating Waves . Standing Waves . Chromatography • Strange Experimental Results => The Advent of Quantum Mechanics . Discrete Optical Spectra . Photoelectric Effect . Particle-Wave Duality • Quantum Dots . What is a Quantum Dot . Experimental Examples . Applications • NEMO 3-D - Nanoelectronic Modeling . Multimillion Atom Simulations . Artificial Atoms and Artificial Molecules

Network for Computational Nanotechnology nanoHUB.org Classical Macroscopic Particles online simulations and more Properties: • Have a finite extent •continuous (ignoring atomic granularity) • Have a finite weight •continuous (ignoring atomic granularity) • Are countable with integers •discrete

Laws of Motion • Classical Newtonian Mechanics

Interactions with other particles • Energy continuity • Momentum continuity

Example • Billiard balls

Network for Computational Nanotechnology nanoHUB.org Propagating Plane Waves online simulations and more "t Properties: x = k • Have infinite extent • Have finite wavelength • Have a finite frequency ! " 2u " 2 x Laws of Motion # c 2 = 0 • Wave equation "t 2 "x 2 • One solution u u sin kx t c " f = 0 ( "# ) = ± k = ±# Interactions with other waves / environment • Cohe!re nt superposition => interference, constructive and destructive http://www.qmw.ac.uk/~zgap118/5/ => o!ne wave can cancel out !an other • Huygens principle: one plane wave made up by many circular waves => diffraction => waves go around corners

http://farside.ph.utexas.edu/teaching/ 302l/lectures/node135.html

Network for Computational Nanotechnology nanoHUB.org Huygens’ Principle online simulations and more • All waves can be represented by point sources

• This animation shows an example of a single point source

http://id.mind.net/~zona/mstm/physics/waves/propagatio

Network for Computational Nanotechnology nanoHUB.org Huygens’ Principle online simulations and more • All waves can be represented by point sources

• This animation shows an example of multiple single point sources creating a wavefront.

http://id.mind.net/~zona/mstm/physics/waves/propagatio

Network for Computational Nanotechnology nanoHUB.org Propagating Plane Waves online simulations and more Light is an Electromagnetic Wave Properties: • Have infinite extent • Not countable • Have finite wavelength • Continuous • Have a finite frequency • Continuous " 2u " 2 x Laws of Motion # c 2 = 0 • Wave equation "t 2 "x 2 Double Slit Experiment • One solution u u sin kx t c " f = 0 ( "# ) = ± k = ±# Interactions with other waves / environment • Cohe!re nt superposition => interference, constructive and destructive => o!ne wave can cancel out !an other http://en.wikipedia.org/wiki/Double-slit_experiment • Huygens principle: one plane wave made up by many circular waves => diffraction => light goes around corners

Accepted Proof: • Light is an electromagnetic wave

http://www.qmw.ac.uk/~zgap118/2/

Network for Computational Nanotechnology nanoHUB.org Standing Waves online simulations and more Properties: • Have finite extent • Countable in 1/2 wavelength " = L /2 • Have discrete wavelengths • Integer multiples 1 • Integer fractions • Have discrete frequencies "2 = L 2 2 " u 2 " x Laws of Motion # c = 0 L! t 2 x 2 • Wave equation " " $ ! • One solution u0 sin(kx "#t); 0 ' x ' L " u = % k j = j • Quantized momentum kj & 0; x < 0;x > L L ! Interactions with other waves / environment • Cohe!re nt superposition => e.g. sounds add in an instrument • A standing wave is a resonator ! • one! re sonator can couple to another => e.g. string <=> guitar => energy is transferred between resonators => energy conservation • resonators must be “in-tune” => momentum conservation

Network for Computational Nanotechnology nanoHUB.org Frequency Content of Light online simulations and more

http://en.wikipedia.org/wiki/Prism_%28optics%29

• “White” light consists of a broad spectrum of colors • Each individual color is associated with a particular frequency of wave • A prism can dissect white light into its frequency components

• Is there some information in this kind of frequency spectrum? => chromatography

Network for Computational Nanotechnology nanoHUB.org Presentation Outline online simulations and more • Classical Systems http://en.wikipedia.org/wiki/Prism_%28optics%29 . Particles "1 = L /2 . Propagating Waves " = L . Standing Waves 2 . Chromatography L! • Strange Experimental Results =>! The Advent of Quantum Mechanics . Discrete Optical Spectra ! . Photoelectric Effect . Particle-Wave Duality • Quantum Dots . What is a Quantum Dot . Experimental Examples . Applications • NEMO 3-D - Nanoelectronic Modeling . Multimillion Atom Simulations . Artificial Atoms and Artificial Molecules

Network for Computational Nanotechnology nanoHUB.org Strange Experimental Observations online simulations and more The Advent of Quantum Mechanics Discrete light spectrum: • Light emitted from hot elemental materials has a discrete spectrum

• The spectrum is characteristic for the material (fingerprint) Images from: http://en.wikipedia.org • E.g.: H spectrum http://en.wikipedia.org/wiki/Prism_%28optics%29

• E.g.: Iron spectrum

• E.g. application - bright yellow Na lamps => lot of excitation energy converted into single frequency

Development of atomic models • Bohr atom model - electrons in looping orbits • Quantum mechanical model

•

=> electrons are standing waves bound to a core => discrete transition energies lead to discrete spectra

Network for Computational Nanotechnology nanoHUB.org Strange Experimental Observations online simulations and more The Advent of Quantum Mechanics Photoelectric Effect: E • Light can eject electrons from a clean metal kinetic • Observed by many researchers but not explained for 55 years: EVacuum = 0 1839, 1873, 1887, 1899, 1901 E Binding see details: http://en.wikipedia.org/wiki/Photoelectric_effect Unexplained problems: ! • Electrons emitted immediately, no time lag ! • Increasing light intensity increases number of electrons but not their e!ne rgy • Red light will not cause emission, no matter what intensity • Weak violet light will eject few electrons with high energy => Light had to have a minimum frequency / color to excite electrons fm • => Emitted electrons have light dependent energy

http://en.wikipedia.org/wiki/Photoelectric_effect "E #( f $ fm ) The solution in 1905 (Nobel prize for Einstein in 1921) E = hf Light consists of particles ! • Light can be described by discrete particles of discrete energy Photons ! • Planck’s constant - h • Light energy is not divisible ! • Have to have minimum energy to kick out an electron from the bound state E hf Binding = m E kinetic = E light " E Binding = h( flight " f m ) # 0

Network for Computational Nanotechnology

! ! nanoHUB.org Wave - Particle Duality online simulations and more All particles have a wave property •Can interfere •Can diffract •Can form standing waves

All waves have particle properties •Have momentum •Have an energy •Can be created and destroyed

Typical descriptions: •Energy E, frequency f, Momentum k •A set of discrete quantum numbers

•Choose wave/particle description according to problem

Network for Computational Nanotechnology nanoHUB.org More Mind Games online simulations and more •Electrons in atoms are attracted / confined by the atomic core => electrons are .Quantized in energy .Located in orbitals

•What if we could: .Confine electrons to a small, man-made space? .Make sure the material is “clean”

•Sounds like an “artificial atom”

=> Quantum Dot

Network for Computational Nanotechnology nanoHUB.org Presentation Outline online simulations and more • Classical Systems . Particles . Propagating Waves . Standing Waves . Chromatography • Strange Experimental Results => The Advent of Quantum Mechanics . Discrete Optical Spectra . Photoelectric Effect . Particle-Wave Duality • Quantum Dots Pain Pointer . What is a Quantum Dot? . Experimental Examples . Applications • NEMO 3-D - Nanoelectronic Modeling . Multimillion Atom Simulations . Artificial Atoms and Artificial Molecules

Network for Computational Nanotechnology nanoHUB.org What is a Quantum Dot ? online simulations and more Basic Application Mechanisms Physical Structure: • Well conducting / low energy domain surrounded in all 3 dim. by low conducting / high energy region(s) • Domain size on the nanometer scale Electronic structure: • Electron energy may be quantized -> artificial atoms (coupled QD->molecule) • Contains a countable number of electrons

Photon Photon Tunneling/Transport Absorption Emission Occupancy of states

Detectors/ Lasers/ Logic / Memory Input Output

Quantum dots are artificial atoms that can be custom designed for a variety of applications

Network for Computational Nanotechnology nanoHUB.org QD Example Implementations online simulations and more

Self-assembled , InGaAs on GaAs. Colloidal, CdSe, ZnSe Pyramidal or dome shaped

R.Leon,JPL(1998)

http://www.research.ibm.com/journal/rd/451

Electrostatic Gates, GaAs, Si, Ge Create electron puddles Fluorescence induced by exposure to ultraviolet light in vials containing various sized cadmium

Source: http://www.spectrum.ieee.org/WEBONLY/wonews/aug04/0804ndot.html selenide (CdSe) quantum dots. Source: http://en.wikipedia.org/wiki/Fluorescent ß

Network for Computational Nanotechnology nanoHUB.org Quantum Dot Applications online simulations and more

• Memory: Store discrete charge in potential wells. • Transistors: Use discreteness of channel conduction. • Logic: Lent, Porod @ Notre Dame: Quantum Use electrostatically coupled Cellular automata, electrostatically quantum dots. coupled quantum dots.

Chou @ Princeton Room Temp. Single Electron Memory

Hitachi: 128Mbit Integration Harris @ Stanford: Room demonstrated temperature single electron transistor

Network for Computational Nanotechnology nanoHUB.org Quantum Dot Applications 2 online simulations and more

• Medical Markers: Inject body with optical markers that are attached / adsorbed to particular tissue • Quantum Computing: Process coherent states of charge, spin, or optical interactions Colloidal Dots can be used • Infrared Detectors: as implantet optical markers Can absorb light at all angles

Quantum Dots: Absorption has QDs for Quantum Computing weak incidence angle dependence

Network for Computational Nanotechnology nanoHUB.org Quantum Dots as Optical Detectors online simulations and more

• Problem: Quantum wells are “blind” to light impinging orthogonal to the detector surface. • Standard Solution: Need gratings to turn the light • New Approach: Quantum dots have a built-in anisotropy and state quantization Quantum Wells: Absorption has in all three dimensions strong incidence angle dependence -> absorption at all angles Electromagnetic Modeling

Standard Solution: electric field models Grating

optimized Quantum Dots: Absorption has light coupling weak incidence angle dependence Network for Computational Nanotechnology nanoHUB.org Lighting online simulations and more

• Quantum-dot LEDs . Seem to be key to advances in the fields of full-color, flat-panel displays and backlighting • QD emits a color based on its size . Smaller dots emit shorter wavelengths, such as blue, which, in the past, has been difficult to attain Fluorescence induced by exposure . Larger dots emit longer wavelengths, like to ultraviolet light in vials red containing various sized cadmium selenide (CdSe) quantum dots. Source: http://en.wikipedia.org/wiki/Fluorescent

Network for Computational Nanotechnology nanoHUB.org Quantum Dots and online simulations and more Single Electronics

Moore’s Law (loosely formulated): • Overall device performance doubles every 18 months • Historically true for over 20 years • Technically achieved by • Making device features ever smaller => devices become faster • Making wafer ever larger => reducing or maintainig the overall cost per chip

SIA Roadmap 100 e2 m) kT >> ! CMOS ( DRAM 2-D 2C Devices Lithography -1 feature Size 10 h CMOS Devices 1-D t

with Quantum Effects w o

Feature feature 10-2 r G Quantum Devices 5-100 Å e2 kT << 2C Minimum 10-3 1980 1990 2000 2010 2020 Year

Network for Computational Nanotechnology nanoHUB.org Presentation Outline online simulations and more • Classical Systems . Particles . Propagating Waves . Standing Waves . Chromatography • Strange Experimental Results => The Advent of Quantum Mechanics . Discrete Optical Spectra . Photoelectric Effect . Particle-Wave Duality • Quantum Dots . What is a Quantum Dot . Experimental Examples . Applications • NEMO 3-D - Nanoelectronic Modeling Pain Pointer . Multimillion Atom Simulations . Artificial Atoms and Artificial Molecules

Network for Computational Nanotechnology nanoHUB.org NEMO 3-D Technical Approach online simulations and more

Designed Optical Transitions Sensors

Quantum Dot Array s Atomic Orbitals Structure Nanoscale Quantum States Computing size: 0.2nm Millions of atoms (Artificial Atoms, size 20nm) Problem: Approach: Nanoscale device simulation requirements: • Use local orbital description for individual atoms • Cannot use bulk / jellium descriptions, need in arbitrary crystal / bonding configuration description of the material atom by atom • Use s, p, and d orbitals. => use pseudo-potential or local orbitals • Use genetic algorithm to determine • Consider finite extend, not infinitely periodic material parameter fitting => local orbital approach • Compute mechanical strain in the system. • Need to include about one million atoms. • Develop efficient parallel algorithms to generate => need massively parallel computers eigenvalues/vectors of very large matrices (N=40million for a 2 million atom system). • The design space is huge: choice of materials, • Develop prototype for a graphical user interface compositions, doping, size, shape. based nanoelectronic modeling tool (NEMO-3D) => need a design tool Realistic material description at the atomic level enables simulation of realistic nanoelectronic devices.

Network for Computational Nanotechnology nanoHUB.org Atomistic Tight-Binding Hamiltonian online simulations and more

orbitals Wavefunction Basis l "i, j,k = #Ci, j,k$l l ! = s, p3, d 5 l s ! p3

5 Crystalline Structure d

Network for Computational Nanotechnology nanoHUB.org Nearest-Neighbor sp3d5s* Model online simulations and more

- Realistic zinc-blende lattice - Each atom has 10 spin-degenerate orbitals (sp3d5s*) - Each atom has 4 nearest neighbors - TB parameters found by fitting of bulk band structure to experiment

) 20 4nn 20 20 H c+ c t c+ c = # #" R! R! R! + # # # # R! ,R'! ' R! R'! ' atoms R ! =1 atoms R atoms R'=1 ! =1 ! '=1 bands bands bands

Systems with up to 21 million atoms

Matrix order: 4x108 Lanczos Diagonalization

Network for Computational Nanotechnology nanoHUB.org Parallelization and Methods online simulations and more

• Divide Simulation domain into slices. • Electronic structure needs eigenvalues and • Communication only from one slice to the eigenvectors. Matrix is Hermitian next (nearest neighbor) • NEMO 3-D methods: • Communication overhead across the • Standard 2-pass Lanczos surfaces of the slices. • PARPACK about 10x slower • Folded Spectrum Method (Zunger), also • Limiting operation: typically slower than Lanczos complex sparse matrix-vector multiplication • Enable Hamiltonian storage or re-computation on the fly.

Network for Computational Nanotechnology nanoHUB.org From Beowulf Concept (JPL, Tom Sterling) online simulations and more to Commodity Products in 4 Generations

NewYork (2002) 66 Xserve G4 1GHz 1GB RAM per node A Pluto (2001) 33 GB total 64 Pentium IIIs 800MHz

60 GB Disc per node f dual CPUs 2 TB total f 2 GB RAM per node 100 Mb/s ethernet crossbar o Nimrod (1999) 64 GB total MAC OS X, MPI 32 Pentium IIIs 450MHz 10 GB Disc per node r

495GFlops d Hyglac (1997) 512 MB RAM per node 320 GB total 16 Pentium Pros 200MHz 16 GB total 2 Gb/s Myricom crossbar a 128 MB RAM per node 8GB Disc per node Linux, MPI 2 GB total 256 GB total 51.2 GFlops b 5GB Disc per node f o

100 Mb/s ethernet crossbar l

80 GB total Linux, MPI e 100 Mb/s ethernet crossbar 14.4 GFlops r

Linux, MPI S 3.2GFlops ~ $ u Gordon Bell Prize 1997 1 p 0 e 0 r c k o m p u t e r

Network for Computational Nanotechnology nanoHUB.org Parallelization Benchmark online simulations and more Apple G5

G5 Apple cluster: a 32 node G5 Xserver Apple cluster at JPL, with nodes consisting of dual 2GHz PowerPC G5, 2GB RAM, Dual Gigabit Ethernet.

Electronics scale well

Network for Computational Nanotechnology nanoHUB.org Some Wavefunctions of a online simulations and more Pyramidal Quantum Dto

Network for Computational Nanotechnology nanoHUB.org HPC and Visualization online simulations and more NEMO 3-D: Electronic structure for tens of Million Atoms d NCN Objective: i r g

• Engage computational scientists a r e

• Deploy new community codes T

• Advance the state-of-the-art in nano F S N

simulation through HPC n o

Approach: d

• Identify a numerically challenging e m r

nano simulation problem o f r

• Multidisciplinary team: ECE, CS, ITaP: e 2 fac, 2 s/w prof, 1 post-doc,5 students P Nano-Problem: Result / Demonstrations / Impact: • Atomistic quantum dot simulations • Algorithm, performance and memory Computational Problem utilization improvements • Conjugate grad. real O(3x108) 100Ma • Developed 3D volume rendering tool • Interior eigenvect comlx O(4x108) 20Ma • 64 Ma strain, O(1.8x108),vol (110nm)3 • Efficient parallelization • 21 Ma electronics - value and vector Status one year ago: O(4.2x108), (78nm)3 or 15x178x178nm3 • Strain 16Ma - O(4.8x107) • Studied long range strain • Eigenvalues: 9Ma - O(1.8x107) • Studied coupled quantum dots • Eigenvectors: 0.1Ma - O(2x106) • New details through visualizations 3 Computed Electronic in a realistic struNcetwuorrk efor oComf p(u7tat8ionalm Nan)ote cvhnoololguy me nanoHUB.org Proof of Concept online simulations and more Extraction of Targeted Interior Eigenstates

N states N~2mln

P ~40 eV ~10 meV S

Network for Computational Nanotechnology nanoHUB.org Proof of Concept online simulations and more Extraction of Targeted Interior Eigenstates

11.3 nm 33.9 nm 50.9 nm 22.6 nm 67.8 nm

101.7 nm

N states N~2mln

P S

Unique and targeted eigenstates of correct symmetry can be computed in all electronic computational domains Network for Computational Nanotechnology nanoHUB.org Presentation Outline online simulations and more • Classical Systems . Particles . Propagating Waves . Standing Waves . Chromatography • Strange Experimental Results => The Advent of Quantum Mechanics . Discrete Optical Spectra . Photoelectric Effect . Particle-Wave Duality • Quantum Dots . What is a Quantum Dot . Experimental Examples . Applications • NEMO 3-D - Nanoelectronic Modeling . Multimillion Atom Simulations . Artificial Atoms and Artificial Molecules Pain Pointer

Network for Computational Nanotechnology nanoHUB.org Vertically Coupled Two-Dot online simulations and more Molecule

ELECTRONIC QUANTUM- MOLECULAR ENERGIES

1.36

1.35 +H ORBITALS OF 1.34

) UNCOUPLED DOTS

1V .33 e P ( H = 2.83 nm

1y .32

R = 6.5 nm g

1 r 1.31 R2 = 6.96 nm e n D IS A PARAMETER 1.30 E

1.29 1.28 S E2 40 60 80 100 120 140 BONDING ORBITAL Interdot distance D (A) E2

ANTIBONDING ORBITAL E1 E1

Network for Computational Nanotechnology nanoHUB.org Vertically Coupled Seven-Dot Molecule online simulations and more Identical dots • Application in lasers • Strain: 44.7 Ma m m n n

6 • Electronics: 6.1 Ma 5 9 2 . . 3 2 6 = 1 D • 7 Identical dots, without strain m n

=> symmetric miniband 3 8 13.0 nm . with 7 states 2 55.4 nm • Can derive this analytically 84.8 nm from 1 dot simulations

E1 E2 E3

E4

E7 E6 E5

Network for Computational Nanotechnology nanoHUB.org Vertically Coupled Seven-Dot Molecule online simulations and more Growth asymmetry => Non-identical dots 18.43 nm • Application in lasers • Strain: 44.7 Ma m m n n

6 • Electronics: 6.1 Ma 5 9 2 . . 3 2 = 6 1 D • Non-identical dots, higher dots m n

have larger diameter 3 8 13.0 nm . • Miniband broken 2 55.4 nm • Ground state in the BOTTOM! 84.8 nm • Cannot derive this analytically!

EE11 EE22 EE33

EE44

Modeling capability E7 E6 E7 E6 EE55 absolutely unique!!

Network for Computational Nanotechnology nanoHUB.org VolQD online simulations and more Million Atom Volume Rendering on a single GPU Objective/Problem - Requirements: Result / Demonstrations / Impact: • Interactive volume data rendering • Visualization of 21 million atom • Realistic crystals wavefunction on single PC • Crystal is not a space-filling mesh • Interactive tool • Analyze composition of wavefunction • Need to drill down into data contributions • Would like to work on single CPU • Provided new physical insights Approach: Authors: • Utilize Graphics Processing Unit-GPU • Wei Qiao (CS), David Ebert (ECE), • Develop a visualization tool-box Marek Korkusinski, Gerhard Klimeck

Publication was just accepted at premier IEEE Visualization conf.-88 of 268 accepted

Network for Computational Nanotechnology nanoHUB.org VolQD online simulations and more Drilling down into 3-D Volume Data

First excited state (a) Volume data (b-d) 2-D slices through data

Statistical Analysis: Contributions in various orbitals vary spatially

Network for Computational Nanotechnology nanoHUB.org VolQD online simulations and more Discovery of Surprising Nodal Symmetries

s + s* orbitals p + d orbitals

Second excited state • Different orbital symmetries in (s+s*) versus (p+d) • Discovery really enabled by visualization!

• Prompted additional investigations

all orbitalsNetwork for Computational Nanotechnology nanoHUB.org Presentation Outline online simulations and more

• Classical Systems http://en.wikipedia.org/wiki/Prism_%28optics%29 . Particles . Propagating Waves . Standing Waves . Chromatography • Strange Experimental Results => The Advent of Quantum Mechanics . Discrete Optical Spectra . Photoelectric Effect . Particle-Wave Duality • Quantum Dots . What is a Quantum Dot . Experimental Examples . Applications • NEMO 3-D - Nanoelectronic Modeling . Multimillion Atom Simulations . Artificial Atoms and Artificial Molecules

Network for Computational Nanotechnology nanoHUB.org Alloy Disorder in Quantum Dots online simulations and more

AxB(1-x)C Dot

• Compositional Alloys • Engineer dot size and energy spectrum • Engineer confinement potential

• Atomistic Simulation • Include disorder effects explicitly • Test validity of virtual crystal approximations

Network for Computational Nanotechnology