Spectroscopy at nanometer scale

Transcription

1 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

2 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

3 Born-Oppenheimer Approximation

4 Electronic Spectroscopy 1. Photons in, photons out PL 2. Photons in, electrons out UPS, XPS 3. Electrons in, electrons out EELS

5 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 ( nm) For GaAs, ε/ε 0 ~ 13.2 and m*~ 0.067m e then E e ~ 5 mev and a eff ~ 10 nm

6 Concentric Hemispherical Analyzer (CHA)

7 Prism S Grating α β = mλ Δs = d (sinα sinβ) d

8 Vibrational Spectroscopy 1. Photons in, photons out IR, Raman 2. Electrons in, electrons out EELS

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10 The Theory of Raman Spectroscopy

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12 One dimensional size effect Ψ(x) V(x) 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

13 NanoSci Nano Lab Size effect Size

14 Ratio of surface atoms ratio (%) /d Diameter of particle d (nm)

15 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

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17 Electronic Structure of Single-wall Nanotubes Nature 391, 59 (1998).

18 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.

19 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.

20 Optical properties

21 Semiconductor quantum dots (Reproduced from Quantum Dot Co.)

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23 Mass Analyzer B r qv = ½ mv 2 F = qvb = mv 2 /r V m/q = ½ B 2 r 2 /V

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27 Reactivity of nanoclusters

28 Magic clusters

29 Mackay icosahedra P = 1 20 fcc(111) faces P = 2 P = 3 Shell model N = 1 + Σ (10p 2 + 2)

30 Scanning Tunneling Spectroscopy 1. Barrier Height Imaging Up to now homogeneous surfaces were considered. If there is an inhomogeneous compound in the surface the work function will be inhomogeneous as well. This alters the local barrier height. Differentiation of tunneling current yields Thus the work function can directly be measured by varying the tip-sample distance, which can be done by modulating the current with the feedback turned on.

31 STM Images of Si(111)-(7 7) Empty-state image Filled-state image

32 Electronic Structures at Not Tunneling Surfaces Empty-State Imaging Tunneling Filled-State Imaging

33 2. di/dv imaging If the matrix element and the density of states of the tip is nearly constant, the tunneling current can be estimated to Differentiation yields the density of states di/dv Density of state (DOS)

34 The mapping of surface density of states can be deduced by Modulation of the bias voltage (di/dv imaging): The tip is scanned in the constant current mode to give a constant distance to the sample. A dither voltage of ~1k Hz is added to the bias voltage while the feedback loop remains active. A lock-in technique is employed to obtain the current change at the dither frequency. Current-Imaging Tunneling Spectroscopy (CITS): The tip is scanned in the constant current mode to give a constant distance to the sample. At each point the feedback loop is disabled and a current-voltage curve (I-V curve) is recorded.

35 STS of Si(111)-(7x7) Science 234, 304 (1986). UPS IUPS

36 STS of Si(111)-(7x7) topograph 1. Science 234, (1986). 2. Phys. Rev. Lett. 56, (1986).

37 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

38 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

39 NanoSci Nano Lab Pb islands on the IC Pb/Si(111) T~200K + Pb IC (1) IC (1)

40 NanoSci Nano Lab ε F Spectra for Pb Films 3 5 (di/dv) / (I/V) n = ε F Sample bias (Volt) 8 10 k F C.M. Wei and M.Y. Chou d 0 = 2.85 Å λ F = 3.94 Å 2d 0 3(λ F /2)

41 NanoSci Nano Lab Scanning Tunneling Spectroscopy (STS) (feedback off) I-V spectrum (feedback on) Z-V spectrum I Z V V I 0 evρ s (E F -ev+ε) ρ T (E F +ε)d ε ρ T is constant di/dv ρ s (E F -ev) scanning sample

42 NanoSci Nano Lab Gundlach Oscillation in STS E F of tip < E vac of sample E vac Standing-wave states in tunneling gap E F E F sample tip normal tunneling E F of tip > E vac of sample E vac E F tip E F sample field emission sample Superposition of image potential and applied potential

43 NanoSci Nano Lab Transmission Resonance in Ag Films on Si(111) Ag film on Si(111) at RT 0.8 (111) dz/dv crystal 9-layer Sample bias (V) Work function of Ag/Si(111) = 4.41 ev

44 Quantum Size Effect above Vacuum Level NanoSci Nano Lab Intensity (Arb. Unit) (a) thickness Exp. Cal unit: ev (11) (10) (9) Sample bias (V) E reflection t 1 1 V =1+4 2 sin T E(E+V) 2 (kt); R=1-T; ħ 2 k 2 2m = E+V kt=nπ T=1 transmission resonance Transmission Probability V (b) 9-layer 10-layer 11-layer Electron energy (ev) transmission

45 NanoSci Nano Lab Finger print of film thickness Low temperature deposition followed annealing to room temperature dz/dv Sample bias (V) dz/dv Sample bias (V)

46 NanoSci Nano Lab Summary Quantum well states are measured with STS in the Pb films of varied thickness on the Si(111) surface. Quantum phenomenon of the transmission resonance can be observed with STS in Ag films on the Si(111) surface. Positions of the transmission resonance measured with STS can serve as finger prints for the Ag films of varied thickness.

47 NanoSci Nano Lab Work function measurements for thin films work function measurement for thin film using photo-emission spectroscopy Broad beam technique require layer by layer growth Average work function of various thickness J. J. Paggel et al. 66, Phys. Rev. B (2002) Local probe technique, e.g. STM

48 NanoSci Nano dz/dv (Å/V) dz/dv (Å/V) Lab (a) (c) 1-layer Ag Au(111) (d) Au(111) Ag 0 (b) Ag layer Ag Cu(111) Sample bias (V) Cu(111) Lin et al., Phys. Rev. Lett. 99, (2007) Constant Energy Shift Energy shift (ev) Energy shift (ev) (e) Ag/Au Ag/Cu Order (a) order 1 order ΔE 3/2 (ev 3/2 ) Energy E v1 E v2 E F (b) φ 1 φ 2 z z ev -0.3 ev

49 NanoSci Nano Lab Comparison with PES measurement Photoemission (-0.33 ev) Gundlach oscillation (-0.3 ev) dz/dv (Å/V) Energy shift (ev) layer Ag Cu(111) Sample bias (V) Order Bulk Materials Ф(eV) Wallauer et al., Surf. Sci 331, 731 (1995) Au(111) 5.31 Ag(111) 4.74 Cu(111) 4.98

50 Detection of Subtle Variation of Work Function NanoSci Nano Lab (a) A Co/Cu(111) B Cu(111) dz/dv (Å/V) Energy shift (ev) (b) Island A Island B Cu(111) (c) Sample bias (V) 0.1 ev Island A-Cu Island B-Cu Order Vázquez de Parga et al.,phys. Rev. Lett. 85, 4365

51 NanoSci Nano Lab Summary A general phenomenon of the constant energy shift is observed in high order Gundlach oscillation. The work function of a thin metal film can be measured with the constant energy shift. The precision of the measurement can be better than 0.02 ev, comparable to the photoemission results.

52 Inelastic Tunneling

53 Single Molecule Vibrational Spectroscopy and Microscopy B.C. Stipe, M.A. Rezaei, and W. Ho, Science 280, (1998).

54 Atomic Scale Coupling of Photons to Single-Molecule Junctions S.W. Wu and N. Ogawa and W. Ho, Science 312, (2006)

55 NanoSci Nano Lab Quantum corral 5 nm D.M. Eigler, IBM, Amaden

56 Artificial atom