2004 Debye Lecture 3 C. B. Murray. Semiconductor Nanocrystals Quantum Dots Part 1

Transcription

1 2004 Debye Lecture 3 C. B. Murray Semiconductor Nanocrystals Quantum Dots Part 1

2 Basic Physics of Semiconductor Quantum Dots C. R. Kagan, IBM T. J. Watson Research Center, Yorktown Heights, NY Conduction Band Valence Band Energy Gap Lowest Unoccupied Molecular Orbital Highest Occupied Molecular Orbital Bulk Semiconductor Quantum Dot Like a Molecule

3 Quantum Confinement Low Dimensional Structures ρ c ( E) ( E E C ) ρ c ( E) = cons tant ρ c ( E) ρc ( E) δ ( E E ) ( E E ) n 1 n

4 Particle-in-a-Sphere a Φ ( r, θ, φ ) m Y l ( θ,φ ) = C j l m ( k r ) Y ( θ, φ ) n, l is a spherical harmonic r l Potential V 0 r 2s 1s j k ( k r ) l n, l n, l α = a n, l is the l th order spherical Bessel function solutions give hydrogen-like orbitals with quantum numbers n (1, 2, 3 ) l (s, p, d ) m E n, l = 2 2 η kn, l η α = 2m 2m a o 2 2 n, l 2 o Discrete energy levels size-dependence

5 The Quantum Dot is a Semiconductor The Effective Mass Approximation parabolic conduction and valence bands E E g Direct Bandgap Semiconductor n=conduction band k 2 2 c η k E k = + E 2 m E v k c eff n=valence band 2 η k = 2m 2 v eff g Ψ nk Bloch s Theorem ρ ρ ρ ρ ( r ) = u ( r ) exp( ik r ) nk with periodicity of crystal lattice Free particles treated by effective mass: describing graphically the curvature of the bands representing the potential presented by the lattice

6 Combining the Effective Mass Approximation with a Spherical Boundary Condition E (1) Ψ sp Single Particle (sp) Wavefunction ρ ρ ρ ρ ( r ) = C u ( r ) exp( ik r ) k nk nk linear combination of Bloch functions E g E hν (2) Ψ sp ρ ρ ( r ) = u ( r ) C ( ik r ) u ( r ) f ( r ) ρ ρ n0 nk exp = k n0 ρ sp ρ k assume u nk has weak k-dependence (3) u n0 ρ ( r ) = C ϕ ( r r ) i ni Envelope Function Approximation valid for r QD > lattice constant which for QDs is given by the Particle-in-a-Sphere n ρ ρ i linear combination of atomic orbitals with atomic wavefunctions ϕ n (n= CB or VB) i=lattice sites

7 e - h e - h Coulomb Attraction Bulk semiconductors, Coulomb attraction creates bound excitons Confinement Energy 1/a 2 Coulomb Attraction 1/a For small a: Confinement Energy>Coulomb Attraction electron and hole are treated independently Coulomb interaction added as a correction E ehp 2 η 2a 2 ϕ m nh, Lh ne, Le ( nhlhnele ) = Eg + + Ecoulomb 2 v eff 2 ϕ m c eff For 1S e pairs of states E coulomb =1.8e 2 /εa Brus, J. Phys. Chem. 90, 2555 (1986).

8 Size Dependence of Electronic Structure E E E g E hν E g E hν k k Decreasing Dot Diameter

9 Development of Electronic Structure Similar to Length Dependence in 1D polyenes p-orbitals form π-bonds with associated energy levels with an energy separation in the visible Example of alternating double/single bond π-bond extends over many C atoms Lowest Unoccupied Molecular Orbital Highest Occupied Molecular Orbital LUMO HOMO π * π Ground Polyene s with increasing chain length

10 Size Dependent Absorption Example: CdSe 150Å 150 Å Absorbance (arbitrary units) 90 Å 72 Å 55 Å 45 Å 33 Å Absorbance (arbitrary units) 29 Å 21 Å 17Å Energy (ev) 17 Å Energy (ev)

11 Semiconductor Materials Range from 30 nm QDs to bulk crystal Graph from H. Weller, Pure Appl. Chem. 72, 295 (2000).

12 Absorption Spectra of Semiconductor Nanocrystals Changing the Core InAs Core HgS A. P. Alivisatos, UC Berkeley PbSe PbS PbTe InP NRL group 12 nm IR Absorption (Arb. Unit) 8.0 nm 7.0 nm 6.0 nm 5.0 nm 4.0 nm IR Absorption (Arb. Unit) 3.0 nm 4.0 nm 5.2 nm 7.4 nm IR Absorption (Arb. Unit) 8 nm 8.5 nm 3.5 nm 3.0 nm Wavelength (nm) Wavelength (nm) Wavelength (nm) O. Micic, A. Nozik, NREL C. B. Murray, IBM

13 Real Band Structure Example: CdSe Cd 5s orbitals 2-fold degenerate at k=0 E J=1/2 E g cf crystal field splitting Se 4p orbitals 6-fold degenerate at k=0 Introduces splitting of bands so k hh lh heavy hole light hole J=3/2 so spin-orbit splitoff J=1/2 J = L + S where L=orbital angular momentum S=spin angular momentum J good quantum number due to strong spin-orbit coupling

14 Size Evolution of Electronic States CdSe InAs 2S 3/2 1S e 1P 3/2 1P e Low Band gap InAs modeling must also account for valenceconduction band coupling 1P 3/2 1P e 2S 3/2 1S e 1S 3/2 1S e 1S 3/2 1S e D. J. Norris, M. G. Bawendi, Phys. Rev. B 53, (1996). U. Banin et al., J. Chem. Phys. 109, 2306 (1998). F=J+L where L=envelope angular momentum J=Bloch-band edge angular momentum Hole states labeled by n h L F [L F =L + (L+2)] Electron states labeled n e L e

15 Selection Rules 2 ˆ h e p e P Ψ Ψ = ρ polarization vector of light momentum operator acts only on unit cell portion of wavefunction 2 2 ˆ h e v c f f p u e u P = ρ h e h e L L n n c u v p e u P,, 2 ˆ δ δ = ρ Overlap of the electron and hole wavefunctions within the QDs

16 Towards the Homogeneous Distribution: Photoluminescence and Photoluminescence Excitation Absorbance (arbitrary units) K Luminescence (arbitrary units) K Wavelength (nm) Wavelength (nm) Absorption Luminescence Wavelength Wavelength Photoluminescence Excitation smallest QDS Photoluminescence largest QDS Distribution in ensemble from size, structure, and environmental inhomogeneities

17 Fluorescence Line Narrowing and Photoluminescence Excitation Band Edge Exciton Structure Splitting due to crystal field, non-spherical shape, and exchange interactions of quantum dots D. J. Norris, Al. L. Efros, M. Rosen, M. G. Bawendi, Phys. Rev. B 53, (1996)

18 Diffraction Limited Spot Single Molecule Spectroscopy

19 Fluorescence Intermittancy in CdSe QDs On-period decreases with increasing illumination intensity Off-period intensity independent Excitation every 10-5 sec Relaxation every 10-8 sec But occasionally Two electron-hole pairs may exist in a single QD QDs blink like molecules Auger ionization Probability of photoionization/excitation 10-6 Neutralization time ~0.5 sec M. Nirmal, L. E. Brus, Acc. Chem. Res. 32, 407 (1999).

20 Auger Ionization Consistent with single molecule spectroscopy and photodarkening observed in QD doped glasses Al. L. Efros, M. Rosen, Phys. Rev. Lett., 78, 1110 (1997).

21 S. A. Empedocles, M. G. Bawendi, Acc. Chem. Res. 32, 389 (1999). Single Dot Spectroscopy Individual quantum dots Histogram of Å QDs Including all phonon lines Single Quantum Dot Emission Spectral diffusion driven by environment

22 Metal Nanoparticles Metal - - Particle Surface Plasmon Resonance dipolar, collective excitation between negatively charge free electrons and positively charged core Au nanoparticle absorption energy depends on free electron density and dielectric surroundings resonance sharpens with increasing particle size as scattering distance to surface increases

23 Electronic Properties of Semiconductor and Metal Nanoparticles a ε Charge not completely solvated as in infinite solid Nanoparticle capacitance C = 4πε oεa Charging Energy E c = 2 e 2C( a) 10 nm Al NC Courtesy of C. T. Black, Thesis, Harvard U. Coulomb blockade at k B T<E c Structure from discrete electronic states of metal NC

24 STM Measurements on Single QDs InAs QDs U. Banin et al. Nature 400, 542 (1999).

25 Synthesis of monodisperse CdSe nanocrystals HDA TOPO TOP, 300 C Cd(CH3 ) 2 + (oct) 3PSe CdSe +... absorbance, PL intensity [a.u.] add. inj. add. inj. 200 min 120 min 60 min 12 min TEM and HRTEM images of as-prepared CdSe nanocrystals. 0.5 min wavelength [nm] UV-Vis and PL spectra of CdSe nanocrystals in growth at 300 C D. V. Talapin, A. L. Rogach, A. Kornowski, M. Haase, H. Weller. Nano Lett. 2001, 1, 207.

26 Wet Chemical Synthesis of PbSe Nanocrystals and Superlattices Synthesis Pb(OAc) 2 + R 3 PSe oleic acid, R 3 P, T=150 C R= octyl PbSe Size Selective Processing Size selective precipitation in solvent/ non solvent pairs like hexane-methanol Self Assembly Evaporation of the solvent

27 T. J. Watson Research Center PbSe Nanocrystals and Nanowires Nanocrystals: nm diameters atoms Conduction band Valence band LUMO HOMO bulk nanocrystals molecular clusters PbSe Nanocrystal Small Bandgap (0.28 ev, cf CdSe : 1.70 ev) IR detector, IR diode Laser Material Larger Bohr Radius (PbSe 46 nm, CdSe 12nm) Strong Confinement of Electron-Hole Pair Larger Optical Nonlinearity, Thermoelectric Cooling (ZT = 1 : PbTe) Semiconducting, Solar Cells, Thermoelectric, Biological Application PbSe Nanowire Solution Phase Synthesis using the Nanoparticles as a Building Block Formation of the Nanowires from the Self Assembling the Particles Controlling the wire Properties by Changing the Size and Shape of the Particles Semiconducting device, Interconnect, Building Blocks for the Nanodevice

28 Nucleation Threshold Staturation Seconds Concentration of Precursors (arbitrary units) Injection Nucleation Growth From Solution A Monodisperse Colloid Growth (La Mer) Ostwald Ripening

29 Growth Solution Size selective processing: 100 A 37Å Major Dia. σ = 12% Major Diameter <002> Size Selected B 39Å Major Dia. σ =4.5% Major Diameter <002> C MeOH Hexane BuOH Normalized Counts 0=P 0=P 0=P 0=P 0=P 0=P 0=P 0=P 0=P 0=P R P=0 P=0 Se=P 0=P 0=P P=O P=0 P=O P=0 P=0 P=Se P=0 0=P P=0 P=Se P=0 0=P Se=P 0=P 0=P r r 0=P 0=P P=0 0=P 0=P P=0 20 P=0 P=0 P=0 P=0 Se=P P=0 0 P=0 P=0 P=0 P=0 Se=P P=0 Steric Repulsion (R -12 ) 100 a Normalized Counts b c d 20 Energy (arbitrary units) van der Waals (R -6 ) Attraction 0 Center to Center Distance R (arbitrary units)

30 Results of size selected Percipitation A B Absorbance (arbitrary units) (a) 37Å+12% (b) 39Å+8% (c) 40Å+5% (e) 39Å+11% (f) 41Å+6% Absorbance (arbitrary units) (d) 42Å+<4% Wavlength (nm) (g) 45Å+<4% Wavelength (nm)

31 Absorption and Photoluminescence of PbSe Nanocrystals 12 nm 77K IR Absorption (Arb. Unit) Absorbance (arbitrary units) 8.0 nm(g ) 7.0 nm (f) 6.0 nm (e ) (d ) 5.0 nm 4.0 nm (c ) 298K Relative intensity PbSe Nanocrystals 3.5 nm 3.0 nm (b ) (a ) size: 4.0 nm W a v e le n g th (n m ) Wavelength (nm) Wavelength (nm) PbSe nanowires

32 Confinement Energy (ev) Based on IR & TEM Calculated using Scherrer Formula (XRD) PbSe in Phosphate Glass (1) Effective Mass Approx Equivalent Radius (A)

33 T. J. Watson Research Center Shape Change from Sphere to Cubic and SAXS in Polymer Matrix 50 nm 5 nm Reflected Intensity (Arb. Uint) Experiment Sphere Particle 10 7 D = 9.8 nm, Rg = 3.8 nm (σ = 8 %) θ (Degree) 50 nm 10 nm Reflected Intensity (Arb. Unit) 10 7 Experiment Cubic Particle L = 10.5 nm, Rg = 5.25 nm (σ = 10 %) θ (Degree) K.-S. Cho, W. Gaschler

34 PbSe Quantum Cubes

35 Reflected Intensity (Arb. Unit) (200) < 3 nm 4.3 nm 5.1 nm 7.6 nm 8.3 nm 9.5 nm 13.2 nm (111) (200) (220) > 16 nm (311)(222) θ (Degree) Reflected Intensity (Arb. Unit) θ (Degree) Sphere Cube intensity / a.u. intensity / a.u. (200) Θ (200) (220) (220) Θ WAXS of 10 nm PbSe quantum cubes slowly deposited from toluene (top) and rapidly precipitated from methanol (bottom)

36 Shape evolution of PbSe Nanocrystals Highly symmetric rock salt structure

37 Modeling of x-ray diffraction: The Debye equation which is valid in the kinematical approximation is shown in equation 4.6 (8). Iq ( ) = I0 Fm F m n n sin( qr ) (4.6) Where I(q) is the scattered intensity, Io is the incident intensity, q is the scattering parameter [q = 4πsin(θ)/l] for X-rays of wavelength l diffracted through angle θ. The distance between atoms m and n is r mn. A discrete form of the Debye is shown in eguation (4.7) (9). (4.7) f ( q) Iq ( ) = I o q 2 ρ k qr ( r ) r k k where is the incident intensity, f(q) is the angle dependent scattering factor q is the scattering parameter[4πsin(θ)/λ] for X-rays of wavelength λ diffracted through angle θ. The sum is over all inter atomic distances, and ρ(r k ) is the number of times a given interatomic distance r k occurs. Since the number of discrete interatomic distances in an ordered structure grows much more slowly than the total number of distances, using the discrete form of the equation is significantly more efficient in the simulation of large crystallites (9). mn, mn, sin ( qr)

38 Modeling NP Shape Modeling Stacking faults Equivalent Diameter ~63Å Scattered Intensity (arbitrary units) (b) (a) Spherical 1:1 Prolate θ

39 Small angle X-ray Scattering SAXS (4.8) sin( qr) qr cos( qr) 2 Iq ( ) = IN o [( ρ ρ o) πr[ 3 ]] 3 3 ( qr) Where ρ and ρ o are the electron density of the particle and the dispersing medium respectively. I o is the incident intensity and N is the number of particles. F(q) is the material form factor (the fourier transform of the shape of the scattering object) and is the origin of the oscillations observed. Thus for a spherical particle of radius R (4.9) (4.10) Iq ( ) = IN( ρ ρ ) 2 F 2 ( q) o o 4 3 sin( qr) qr cos( qr) Fq ( ) = πr [ 3 ] 3 3 ( qr)

40 Combined SAXS and WAXS Modeling.

41 Qunatum cubes: Cubic 12 nm PbSe nanocrystals Assembling into a superlattice. (100) (112) (111) (101)

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43 Self-assembled CdSe nanorod solids without polarizers with crossed polarizers 20 µm 20 µm Optical micrograph of self-assembled CdSe nanorods (between crossed polarizers).

44 III-V semiconductor nanocrystals : InP TOPO TOP, C InCl3 (oct) 3P + [(CH) 3Si] 3P InP +... InP etching agent hν absorbance, a.u. ~8nm InP (as - prepared, weak HF, TOPO, hν PL) InP ( strong PL) <2nm wavelength, nm Size-dependent evolution of absorption spectra of InP colloidal quantum dots PL quantum efficiency ~25-40% J. Phys. Chem. B, 2002, 106,

45 CdSe/CdS quantum dot - quantum rods CdSe/CdS CdSe cores CdSe/CdS 40 nm Cd:S=1:1 Cd:S=1:3 CdSe CdS

46 Luminescent II-VI nanocrystals Room temperature PL quantum efficiencies 50-70% Colloidal solutions of CdSe/ZnS coreshell nanocrystals. CdSe/CdS core-shell nanocrystals in a polymer matrix Single particle luminescence of CdSe/ZnS nanocrystals

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