Quantum Dots: Artificial Atoms & Molecules in the Solid-State
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1 Network for Computational Nanotechnology (NCN) Purdue, Norfolk State, Northwestern, UC Berkeley, Univ. of Illinois, UTEP Quantum Dots: Artificial Atoms & Molecules in the Solid-State Network for Computational Nanotechnology Purdue University
2 Bulk Semiconductors Bulk semiconductors: Periodic in 3D GaAs band structure (Energy-momentum (E-k) diagram)
3 Semiconductors under confinement Bulk (3D periodic) Quantum Well (2D periodic) Lz Nanowire (1D periodic) Lx, Ly, Lz long E-k relation 3D (kx, ky, kz) Quantum Dots (0D-Not periodic) Lx Ly Ly, Lz long, Lx small E-k relation 2D (ky, kz) Lz long, Lx, Ly small E-k relation 1D (kz) Lx, Ly, Lz small No E-k relation: 0D discrete energy levels, Localized states Lz
4 Semiconductors under confinement
5 Quantum Dots Defined by Geometry QDs for optoelectronics (hetero-structure) (LEDs, Lasers, Solar Cells, Photo detectors) Nano crystal QD photo-detectors
6 Gate Defined Quantum Dots Two gate defined quantum dots for Quantum Computing. Tracy et. al., APL 97, (2010)
7 Hydrogen Atom Coulomb potential of nuclear charge: V= 1/r Schrodinger Equation (Quantum Mechanics) Energy conservation: Kinetic + potential = total Energy Electrons are not point particles, but probability distributions (shapes) : Ψ(r) 2 Quantum numbers: Discreteness (quanta) n, l, m
8 Hydrogen Atom: Wavefunctions s orbital (l=0) p orbital (l=1) d orbital (l=2) f orbital (l=3)
9 Hydrogen Atom: Quantum Numbers Features of the H atom: Quantum numbers n, l, m, s Shell structure: n=1,2,3 Orbitals /sub-shells (l): s(0), p(1), d(2), f(3) Magnetic field responses: m, s No. of electrons per shell: 2n 2 Rules: n=1,2,3,. l=0,, n-1 m=-l,, +l, s=+/-1/2 (up/down) n l m s Type /-1/2 s /-1/2 2s /-1/2 2p (x) /-1/2 2p (y) /-1/2 2p (z) Energy levels in atoms are defined by quantum numbers.
10 Multi-electron Atoms e-e interactions: Coulomb, exchange, correlation
11 Simplest QD: Particle in a box V= V=0 V= 0 L Quantum number n Energy E n =n 2 (h 2 /8mL 2 ) In 3D, (nx, ny, nz) Energy E n =(nx 2 +ny 2 +nz 2 )*(h 2 /8mL 2 ) GS: (1, 1,1) 1 states ES1: (1,2,1), (2,1,1), (1,1,2) 3 states Spin: +/- ½ 2 states Wave function: Sin (n*π*x/l)
12 QD model: Quantum Harmonic Oscillator V=0.5mω 2 x 2 Quantum number n=0,1,2,3 E n =(n+1/2)*hω/(2π) Energy splitting depends on confinement In 2D, E n =(nx+ny+1) *hω/(2π) Wavefunctions Probability Densities GS: n=(0,0) 1 x 2 ES1: n=(1,0), (0,1) 2 x 2 ES2: 3 x 2
13 Evidence of atom-like structure: Shell filling in QDs Shell structure in atoms Shell structure in a GaAs QD No. of electrons per shell: 2n 2 No. of electrons per shell: 2, 4, 6 (2D QHO) Reimann & Manninen, Rev. Modern Physics 74, 1283 (2002).
14 QDs are customized atoms Natural atoms: fixed properties QDs: Tunable (size, shape, material, voltage) Energy, wavefunction, various QM properties Designed atoms
15 Multiple QDs: Artificial Molecules H2 Molecule Double Quantum Dot Molecule Two Si QDs 20 nm apart (NEMO) Si DQD: Maune et al (Nature 2012) Molecular Properties Accessible in QDs
16 Applications of QDs: Light-Emitting Diodes/Lasers Light Emitting Diodes (LED) TV Displays Lighting
17 Applications of QDs: Solar Cells/Photo detectors Quantum Dot Photo Detectors Scanning Imaging
18 Applications of QDs: Quantum Computing Idea: Encode information in quantum states. Classical Computing: 0> or 1> Quantum Computing: a 0> + b 1> Can quantum states be manipulated in semiconductor devices? Advantages: Quantum parallelism (speed) Algorithms: Quantum search, Fourier Transform, Prime Factoring Applications: cryptography, simulations, factoring, database search, etc. Quantum Computing
19 electron QD Applications of QDs: Logic Devices Majority Gate Quantum Dot Cellular Automata
20 Applications of QDs: Biology Biology/Medicine Biology: Cell imaging and drug delivery
21 QD Modeling with NEMO S G1 D 1 D 2 G2 D III-V QDs for optoelectronics M. Usman. et. al. IEEE TRANSACTIONS ON NANOTECHNOLOGY, VOL. 8, NO. 3, MAY 2009
22 Electron Transport: Measurement of current-voltage TFET Device On (1) QD Current-Voltage Off (0) Rev. Mod. Phys. 79, 1217 (2007)
23 QDs: Coulomb Diamond Electron Transport: QD V_sd Vg No current Results from Coulomb Blockade Single atom transistor, Nature Nano 7, 242 (2012)
24 Device Schematic Source Dot Drain I DS Potential V DS =0 Landscape V G =0 V DS =0 >0 V G =0 >0 V G E F E F 1) Apply V DS bias 2) Apply V G bias 3) First electron 4) First + second electron 5) First electron trapped 6) First + second electron trapped
25 Device Schematic Source Dot Drain I DS Potential V DS =0 Landscape V G =0 V DS =0 >0 V G =0 >0 G V G V G E F V DS E F V D S G V G
26 Device Schematic Source Dot Drain V D S 1 1 G Potential V DS =0 Landscape V G =0 V DS =0 V G = V G E F E F Charge Stability Diagram The I-V curve of atomic transistors Plots conductance G vs. V DS and V G 1 = Transistor on (current flow) 0 = Transistor off (no current flow)
27 From Theory to Reality Source Dot Drain V D S G V G 1 1 V D S A single-atom transistor, M. Fuechsle et.al. Nature Nanotechnology, 2012 V G
28 From theory to reality: Simulation Ingredients Single P impurity potential D 0 D - Ground States Only V DS V G Ground + Excited States V DS Density of States Fluctuations V DS V G V G
29 Summary Quantum Dots act like artificial atoms and molecules with discrete energy levels. Quantum Dots can be designed to suit the application requirements. Variety of applications: LEDs, Quantum Computing, Photo-detectors, Biology, Logic. Current flow is significantly different in QDs than transistors. NEMO can be used to model and investigate quantum dots in detail.
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