Fabrication / Synthesis Techniques

Transcription

1 Quantum Dots Physical properties Fabrication / Synthesis Techniques Applications Handbook of Nanoscience, Engineering, and Technology Ch.13.3 L. Kouwenhoven and C. Marcus, Physics World, June 1998, p.35 L. Kouwenhoven at el. in Mesoscopic Electron Transport edited by L.L. Sohn, L.P. Kouwenhoven S. Reimann and M. Manninen, Rev. Mod. Phys. 74 (00) 183 Y. Alhassid, Rev. Mod. Phys. 7 (000) 895

2 Confinement in 0D How small needs to be a structure in order to be 0D? Compare Thermal energy k B T with quantization of energy levels in the structure Quantization of electron (hole) energy levels in solids: Schroedinger equation ψ ψ E H = ˆ ψ ψ ψ E U m = + h z y x + + = Cartesian coordinates: = L z n L y n L x n L z y x z y x n π π π ψ sin sin sin ),, ( 3 ( ) 8 z y x n n n n ml h E + + = L - size of the solid Eigenfunctions: Eigenenergies: U

3 Confinement to 0D ( n + n n ) h E n = x y + 8mL z Δ E = En+ 1 En+ 1 1 ml ρ As the length scale decreases the energy level separation increases! D 1D 0D m ( E = πh ( E ) D ) Θ E i i const ρ 1D ( m ) = π h 1 iθ( E Ei ) 1 ( E E ) E i i n ρ 0 ( E ) = δ ( E ) D E i i

4 Quantum Dots as Artificial Atoms atom 3D solid hybridization Pauli principle confinement D QD 1D confinement confinement QD behave like atoms, but energies and length scales can be controlled

5 Quantum Dot as an Artificial Atom physics is determined by the symmetry atoms are spherical -> if we want to mimic atoms we need spherical (or at least cylindrical) potential well! = x + y + z = 1 r r 1 1 sinθ + r + r sinθ θ θ sin θ ϕ U kze = r Coulomb potential Bohr model of an atom: R Y n, l m l ψ ( r, θ, ϕ) = R( r) Y ( θ, ϕ) l r na r 0 ( r) = e Ln, l ( r a0) a 0 ( θ, ϕ) l + 1 ( l m)! e 4π ( l + m)! L n, l a ( cosθ ) ( r ) 0 Laguerre polynomial imϕ m = Pl s selection rules : l = 0... n 1 m = l, l + 1,...0,..., l 1, l quantum numbers : n, l, m, m = ± 1 n m s Bohr radius: a 0 = h m e e (0.05nm for FE) Z E n 0 Z E n = = 13.6eV n Pauli principle : n electrons on n - th shell

6 Quantum Dot as an Artificial Atom Realization of artificial atom in vertical QD structure: Electrical current through the dot as a function of gate voltage The effective size of the dots (and number of electrons) can be changed by the gate voltage (negative V squeezes the dot) Energy necessary to add an e - E add = e C + ΔE Coulomb Energy level differences

7 Quantum Dot as an Artificial Atom Spacing between energy levels is not equal: it is more difficult to inject e - #, #6, #1 Orbit 1 (n=0) has no angular momentum, s= ±1/ => e - Orbit (n=1) has l= ± 1, s= ±1/ => 4e - Orbit 3 (n=) special if radial confinement is parabolic. Possible states: l= ±, s= ±1/ => 4el= 1, s= ±1/ => e- Max spin (half filling) Full shells Leo Kouwenhoven and Charles Marcus, Physics World, June 1998

8 Fabrication of GaAs Vertical Quantum Dots physical structure band structure confining barriers SEM image of QD

9 Growth of GaAs Vertical Quantum Dots Using Molecular Beam Epitaxy Precise control of monolayer growth

10 Simulation of Band Structure in Heterostructures Self-consistent calculation of the energy diagram of the unpatterned double-barrier heterostructure from which the pillars are fabricated

11 QD Pillars Growth + Lithography + Etch Axel Scherer (Caltech)

12 Self-Assembled Quantum Dots: Stranski-Krastanov Growth

13 Self-Assembled Quantum Dots: Stranski-Krastanov Growth

14 Self-Assembled Quantum Dots: Stranski-Krastanov Growth SEM/ AFM Imaging

15 Self-Assembled Quantum Dots - Photoluminescence Photoluminescence Defect-free overgrowth: good electrical properties good optical properties excitation of electron-hole pairs through light absorption recombination through photon emission

16 Size Estimates Excitons in GaAs Energy of exciton Effective exc mass E m exciton eff = = e m eff m ev ( ε ε ) n memh m + m 0 h Parameters for excitons in GaAs: Effective e-h mass Dielectric constant m m e eff m h = 0. = 0.059m ε e Bohr radius a = h m e 0 = 0 o 0.5A Energy and radius of exciton E a exc exc = 4.6 mev 11.8 nm Exciton radius a eff = m eff ε m 0 a 0 With decreasing nanoparticle size the energy level separation of the exciton increases -> this leads to recombination at higher energy -> blue shift of QD

17 Photoluminescence of InAs dots on (110) GaAs

18 QD Photoluminescence Dot Size Uniformity

19 QD Photoluminescence Size Effects Increase of deposition time = increase of QD size

20 Application of Semiconductor QD Improving semiconductor diode lasers Change wavelength with dot size Lower threshold currents (improve efficiency) Trap carriers to avoid defects (blue lasers and light-emitting diodes) Mid-infrared detectors (thermal IR imagers)

21 Chemical Synthesis of Quantum Dots Synthesis of CdSe Nanodots in solution - Narrow size distribution (~5%) is obtained by the fast injection of the chemical reagents into the flask at high temperature (~ 350 C) -The precursors are prepared in the glove box to avoid oxygen and water - Careful temperature regime provides narrow size distribution of desired size nanoparticles QD prepared: semiconductor: CdSe, PbSe, CdTe, (optical properties) metal (elemental, core-shell): Pt, Pt 3 Co, Pt 3 Fe (catalysis)

22 Chemical Synthesis of QD TEM images of PbSe quantum cubes after size selection (reaction temperature 15 o C), size 1nm Orgaanometallic synthesis of TiO Chris Murray, Wolfgang Gaschler, Franz Redl Jing Tang, et al., "A Low-Temperature Synthesis of TiO Nanoparticles", Nano Letters 5, (005).

23 TEM Image of CoPt 3 Nanoparticle

24 Size-Dependent Light Absorption in QD Method of Estimating QD Size Fluorescence induced by exposure to ultraviolet light in vials containing various sized CdSe quantum dots Main application bio markers

25 Application of QD in Medicine: Imaging of Mouse Intestine Different size QD functionalized with different molecules A mouse intestinal section visualized using fluorescent Qdot nanocrystal conjugates. Actin was labeled with a mouse anti-actin monoclonal antibody and visualized using redfluorescent Qdot 655 goat F(ab') anti mouse IgG (Q110MP, Q111MP). Laminin was labeled with a rabbit anti-laminin polyclonal antibody and visualized using green-fluorescent Qdot 55 goat F(ab') anti rabbit IgG (Q11441MP). Thomas Deerinck and Mark Ellisman, The National Center for Microscopy and Imaging Research

26 Lateral Quantum Dots Sample requirements: Growth of heterostructures to obtain the DEG (good quality, large mean free-paths) Metallic electrodes electrostatically deplete charge: confinement Sets of electrodes to apply bias etc. LOW TEMPERATURE! (~100 mk)

27 Electrical Transport in Lateral QD Role of the gate electrode:

28 Electrical Transport in QD Quantum dots contain an integer number of electrons Adding an electron to the QD changes its energy => electrostatic charging energy In order for a current to pass an electron must tunnel onto the dot, and an electron must tunnel off the dot For conduction at zero bias this requires the energy of the dot with N electrons must equal the energy with N+1 electrons. i.e. charging energy balanced by gate potential

29 Electrical Transport in Lateral QD Coulomb Blockade Current blocked at low T Current flowing at low T

30 Electrical Transport in Lateral QD Coulomb Blockade Conductance modulated by gate voltage (on a single electron level) Single Electron Transistor - SET

31 Potential Applications of QD Single photon emitters ( single photon on demand ) for quantum cryptography Spin Qubits for quantum computer (also in cryptography) Single-electron memories