Spectroscopy at nanometer scale 1. Physics of the spectroscopies 2. Spectroscopies for the bulk materials 3. Experimental setups for the spectroscopies 4. Physics and Chemistry of nanomaterials
Various spectroscopic methods Electrons EELS AES IPS APS Neutrals He Scattering n 0 Scattering Sample Ions ISS RBS SIMS PIX Photons PL FTIR Raman XPS UPS
Born-Oppenheimer Approximation
Electron Spectroscopy 1. Photons in, photons out PL 2. Photons in, electrons out UPS, XPS 3. Electrons in, electrons out EELS
Binding energy and effective radius for the exciton E e = (m*/m e )(ε/ε 0 ) -2 (13.6 ev) a eff = (ε/ε 0 )(m*/m e ) -1 (0.0529 nm) For GaAs, ε/ε 0 ~ 13.2 and m*~ 0.067m e then E e ~ 5 mev and a eff ~ 10 nm
Concentric Hemispherical Analyzer (CHA)
Prism S Grating α β = mλ s = d (sinα sinβ) d
Vibrational Spectroscopy 1. Photons in, photons out IR, Raman 2. Electrons in, electrons out EELS
The Theory of Raman Spectroscopy
TIGP Introduction technology (I) November 17, 2006 Properties of individual nanoparticles Clusters
Particle nature of photons Einstein s proposal: E = hν P = h/λ m e v ϑ λ φ Compton Scattering λ
Wave nature of electrons de Broglie s proposal: λ = h/p ν = h/e For electrons: λ (nm) = 1.22/E 1/2 (ev) Grids e-gun 20 200 ev Crystal LEED
Fundamentals of quantum mechanics 1. Quantization 2. Tunneling ρ kt 3. Statistics 1 ε
Critical Length scale C. Joachim et al., Nature 408, 541 (2000).
One dimensional size effect Ψ(x) V(x) 5 4 3 -a/2 0 a/2 x 2 n = 1 -a/2 0 a/2 sin(nπx/a), n even Ψ(x) = { cos(nπx/a), n odd E = n 2 π 2 h 2 /2ma 2, n = 1,2,3 x Atomic Levels
NanoSci Nano Lab Size effect Size
Ratio of surface atoms ratio (%) 100 80 60 40 20 0 1/d 0 10 20 30 40 50 Diameter of particle d (nm)
Enhanced catalytic effect
Au nanoparticle as an example E F = (ħ 2 /2m) (3π 2 n) 2/3 g(e F ) = (3/2) (n/e F ) δ = 2/[g(E F )V] = (4/3) (E F /N) 10 nm Number of valence electrons (N) contained in the particles is roughly 40,000. Assume the Fermi energy (E F ) is about 7 ev for Au, then δ ~ 0.22 mev ~ 2.5 K
Electronic Structure of Single-wall Nanotubes Nature 391, 59 (1998).
Optical properties of nanoparticles (in the infrared range) (1) Broad-band absorption: Due mainly to the increased normal modes at the surface. (2) Blue shift: Due mainly to the bond shortening resulted from surface tension.
Optical properties of nanoparticles (in the visible light range) (1) Blue shift: Due mainly to the energy-gap widening because of the size effect. + (2) Red shift: Bond shortening resulted from surface tension causes more overlap between neighboring electron wavefunctions. Valence bands will be broadened and the gap becomes narrower. Excitons + (3) Enhanced exciton absorption: Due mainly to the increased probability of exciton formation because of the confining effect.
Optical properties
Semiconductor quantum dots (Reproduced from Quantum Dot Co.)
Mass Analyzer B r qv = ½ mv 2 F = qvb = mv 2 /r m/q = ½ B 2 r 2 /V
Reactivity of nanoclusters
Magic clusters
Mackay icosahedra P = 1 20 fcc(111) faces P = 2 P = 3 Shell model N = 1 + Σ (10p 2 + 2)
Nanopucks of same size and shapes (a) (b) Deposited at 110 K and annealed to 175 K Flux = 0.1 ML/min
Atomically resolved Ag nanopucks 12 34 37 127
Size distribution of Ag nanopucks Counting rate (%) 35 30 25 20 15 10 5 0 6 7 10 8 12 19 24 22 37 34 40 61 58 0 20 40 60 80 100 120 Ag atom number N 91 127
di/dv curves of Ag 34 nanopucks Ag 34 di / dv -2.0-1.5-1.0-0.5 0.0 0.5 1.0 1.5 2.0 Sample Bias (V)
Energy levels of some magic clusters (a) Ag 24 (b) Ag 24 2.0 1.5 1.0 0.5 di / dv 0.0-0.5 E (ev) -1.0-1.5 (c) Ag 34 (d) Ag 34-2.0 2.0 1.5 1.0 di / dv 0.5 0.0-0.5 E (ev) -1.0-1.5-2.0 (e) Ag 40 (f) Ag 40 2.0 1.5 1.0 0.5 di / dv 0.0-0.5 E (ev) -1.0-1.5-2.0-1.5-1.0-0.5 0.0 0.5 1.0 1.5 2.0 Sample Bias (V) Experiment Theory -2.0
Binding energy per atom Binding energy per atom (ev) 2.4 2.3 2.2 2.1 2.0 1.9 1.8 1.7 1.6 1.5 1.4 Ag atom number N 6 12 25 100 6 7 8 10 12 22 24 19 58 40 34 127 91 61 37 0.4 0.3 0.2 0.1 0.0 (Ag atom number N) -1/2 2-D magic nanopucks 2-D hexagonal magic nanopucks 1-layer Ag thin film Guided line of geometrical effect
E = (E n+1 +E n-1 )-2E n 0.35 0.30 0.25 0.20 0.15 0.10 0.05 0.00-0.05-0.10-0.15 30 Stability of Ag nanopucks 6 8 10 12 Counting rate 35 25 20 15 10 5 19 24 22 6 7 10 8 12 37 34 40 0 0 20 40 60 80 100 120 Ag atom number N 22 24 5 10 15 20 25 30 Ag atom number 61 58 91 Nan o 127 Sci La La b
Size-,, site- & shape-controlled self-organized growth 10 nm Ratio (%) 70 60 50 40 30 20 10 0 2224262830323436384042 Ag atom number N
STS of Si(111)-(7x7) Science 234, 304 (1986). UPS IUPS
STS of Si(111)-(7x7) topograph 1. Science 234, 304-309 (1986). 2. Phys. Rev. Lett. 56, 1972-1975 (1986).
Density of states of various dimensions 3D 2D D(ε) D(ε) ~ ε 1/2 D(ε) D(ε) = m * /πh 2 1D ε F ε 0D ε F ε D(ε) D(ε) ~ (ε E n ) 1/2 D(ε) E 1 E 2 E 3 ε F ε δε ε F ε
Quantum size effect λ = de Broglie wavelength of electron a = thickness of metal film a >> λ a λ M a M Substrate Substrate a k z Fermi surface k z n=5 n=4 k n=3 F n=2 n=1 k y k y k x k x
Spectroscopic images 4 4 V = -0.36V V = -0.56V Topography 5 7 7 6 6 7 di/dv ( arb. unit) 11 ε 11 n =10 F 1 13 4 16 17 14 1 7 /e 12 1 5 18-2 -1 0 1 2 Sample bias (Volt) (N) (4) (6) (8) (9) (5) (7) V = 1.28V V = 0.56V di/dv mapping
Inelastic Tunneling
Single Molecule Vibrational Spectroscopy and Microscopy B.C. Stipe, M.A. Rezaei, and W. Ho, Science 280, 1732-1735 (1998).
Atomic Scale Coupling of Photons to Single-Molecule Junctions S.W. Wu and N. Ogawa and W. Ho, Science 312, 1362-1365 (2006)
NanoSci Nano Lab Quantum corral 5 nm D.M. Eigler, IBM, Amaden
Artificial atom