From micro to nano - fundamentals and recent developments of Raman spectroscopy

Transcription

1 From micro to nano - fundamentals and recent developments of Raman spectroscopy Dr. Matthias Krause, Nanocomposite materials group, Helmholtz-Zentrum Dresden-Rossendorf, Germany

2 Introduction into Raman spectroscopy Dr. Matthias Krause, Nanocomposite materials group, Helmholtz-Zentrum Dresden-Rossendorf, Germany

3 Outline 1. Introduction into light scattering 2. Vibrational frequency diatomic molecule, diatomic linear chain, characteristic frequencies 3. Raman activity and intensity conservation laws, factor group analysis, scattering tensor, double resonance scattering 4. Experimental aspects 5. Instrumentation 6. Literature 7. Summary Page 3

4 1. Introduction into light scattering Page 4

5 Introduction into light scattering Rayleigh scattering I Rayleigh 1 λ 4, ν 4 [1] I 450 nm I 650 nm 1 (450 nm) 4 1 (650 nm) 4 4.4[2] [1] John William Strutt, 3. Baron Rayleigh, nobel prize in physics 1904 [2] Page 5

6 Introduction into light scattering "A New Type of Secondary Radiation", Nature 501, 121 (1928) Nobel prize in Physics 1930 Page 6

7 Introduction into light scattering G. Landsberg, L. Mandelstam, "Eine neue Erscheinung bei der Lichtzerstreung in Krystallen", Naturwissenschaften 28, 557 (1928) Page 7

8 Introduction into light scattering Page 8

9 Introduction into light scattering Rayleigh and Raman scattering vs. infrared absorption Page 9

10 A typical Raman line Introduction into light scattering I ν = Lorentz-Line: 1 + I max ν ν vib Γ 2 I max FWHM, 2 ν vib Page 10

11 Raman parameter Introduction into light scattering I max : I ν : ν vib : amplitude integrated area, transition probability of a Raman excitation Raman shift, ~ transition energy of a Raman excitation 2 : full width at half maximum, life time of the excited quantum state Page 11

12 2. Vibrational frequency diatomic molecule, diatomic linear chain, characteristic frequencies E = hν vib = h c 0 λ = h c 0 ν vib J = Js s 1 = Js ms 1 m E ν vib (wave number, cm 1 ) Page 12

13 Vibrational frequency diatomic molecule, diatomic linear chain, characteristic frequencies Diatomic molecule (classical treatment) ν vib = 1 2π f 12 1 m m 2 ν vib = 1 2π f 12 μ s 1 = Nm 1 kg = kg m s 2 m 1 kg Page 13

14 Vibrational frequency diatomic molecule, diatomic linear chain, characteristic frequencies Diatomic linear chain ν 2 = f 12 4π 2 1 m m 2 ± f 12 4π 2 1 m m m 1 m 2 1 cos qa ν = f q, π a q π a Page 14

15 Vibrational frequency diatomic molecule, diatomic linear chain, characteristic frequencies Diatomic linear chain Optical phonon branch Acoustic phonon branch H. Ibach, H. Lüth, Festkörperphysik - Einführung in die Grundlagen, 6th ed., Springer Berlin - Heidelberg - New York, 2002 Page 15

16 Vibrational frequency diatomic molecule, diatomic linear chain, characteristic frequencies Characteristic frequencies and wave numbers ν vib = 1 2π f 12 1 m m 2 s 1 ; ν vib = 1303 f 12 1 m m 2 (cm 1 ) molecular hydrogen, H 2 : 4167 cm -1 molecular nitrogen, N 2 : 2330 cm -1 molecular oxygen, O 2 : 1556 cm -1 bonded hydrogen, Si-H, C-H, N-H, O-H: cm -1 C C, C C, C C stretching frequencies: 2100, 1650, 1100 cm -1 Page 16

17 Vibrational frequency diatomic molecule, diatomic linear chain, characteristic frequencies f Dia f Si = m Dia m Si 2 ν Dia 2 = 2.8 ν Si f Si f Ge = m Si m Ge 2 ν Si 2 = 1.2 ν Ge Page 17

18 3. Raman activity and intensity in crystals Raman scattering in crystals a three step description 1. Absorption of an incoming photon (ν 0, k 0 ), generation of an electron-hole (e/h) pair 2. Scattering of the electron by excitation or de-excitation of a crystal vibration with (ν vib, k vib ) 3. Recombination of the e/h-pair, emission of a scattered photon (ν 1, k 1 ) ) S. Reich, C. Thomsen, J. Maultzsch, Carbon Nanotubes - Basic Concepts and Physical Properties, Wiley-VCH, Weinheim, 2004 Page 18

19 Raman activity and intensity conservation laws, factor group analysis, scattering tensor, double resonance scattering Energy conservation: hν 0 = hν 1 ± hν vib Page 19

20 Raman activity and intensity conservation laws, factor group analysis, scattering tensor, double resonance scattering Momentum conservation for Raman scattering in crystals: Page 20

21 Raman activity and intensity conservation laws, factor group analysis, scattering tensor, double resonance scattering Momentum conservation for Raman scattering in crystals: hk 0 = hk 1 ± hk vib, hk vib, max = hk 0 hk 1 2 hk 0 2 hk 0 λ 0 = 500 nm = 4 x 10 4 cm 1 ; 0 hk vib π a = π 2.46 x 10 8 cm = 1.3 x 108 cm 1 Page 21

22 Raman activity and intensity conservation laws, factor group analysis, scattering tensor, double resonance scattering Momentum conservation for second order Raman scattering in crystals: hk 0 = hk 1 ± hk vib, hk max = hk 0 hk 1 2 hk 0 = hk vib Page 22

23 Raman activity and intensity conservation laws, factor group analysis, scattering tensor, double resonance scattering 2 TO 2 TA W.H. Weber, R. M. E. Raman Scattering in Materials Science; Springer: Berlin - Heidelberg - New York, 2000 Page 23

24 Raman activity and intensity conservation laws, factor group analysis, scattering tensor, double resonance scattering Raman activity first order crystal phonons with k vib = 0: point phonons, can be treated by factor group analysis for unit cell atoms second order crystal phonons, resemble phonon density of states Page 24

25 Raman activity and intensity conservation laws, factor group analysis, scattering tensor, double resonance scattering Factor group analysis of -Al 2 O 3, space group 167 (D 6 3d, R3c) Number of atoms and vibrations in the primitive cell: 10 (30-3=27) Site symmetries of Al and O: 4c, C 3 ; 6e, C 2 (R.W.G. Wyckoff, Crystal structures, Vol. 1, Interscience Publishers, A Division of J. Wiley& Sons, New York, 2 nd edition, 1963) Irreduzible presentations of corresponding translation vectors (character tables): C 3 : A (T z ), E (T x, T y ) C 2 : A (T z ), B (T x, T y ) Correlation with irreproducible presentations of the factor group (crystal class) Page 25

26 Raman activity and intensity conservation laws, factor group analysis, scattering tensor, double resonance scattering Page 26

27 Raman activity and intensity conservation laws, factor group analysis, scattering tensor, double resonance scattering Intensity of Raman excitations I Ra = C ν 0 ν 1 4 I 0 q i 2 N i=1 xyz ρσ α ρσ 2 I Ra has unit W s dω q i : i th Raman active crystal vibration I 0 = 1 2 ε 0 c E 0 2 Wm 2, excitation light power density Page 27

28 Raman activity and intensity conservation laws, factor group analysis, scattering tensor, double resonance scattering Raman scattering tensor I Ra = C ν 0 ν 1 4 I 0 N i=1 α xx α xy α xz α yx α yy α yz α zx α zy α zz 2 q i At least one tensor element must be non-zero Page 28

29 Raman activity and intensity conservation laws, factor group analysis, scattering tensor, double resonance scattering Our example: -Al 2 O 3, factor group D 3d α ρσ (D 3d ) = α A 1g + α E g, 1 + α E g, 2 α ρσ (D 3d ) = a a b + c c d 0 d c d c 0 0 d Raman-active irreproducible representations: A 1g, E g 4 Raman-active tensor elements: a, b; c, d Γ Raman, α Al2 O 3 = 2A 1g + 5 E g Page 29

30 Raman activity and intensity conservation laws, factor group analysis, scattering tensor, double resonance scattering How can the tensor elements of -Al 2 O 3 be measured? Alignment of crystal and light E-vector coordinates Porto notation: [a(bc)d] a: propagation direction of exciting light b: polarization direction of exciting light relative to crystal coordination system c: polarization direction of scattered light relative to crystal coordination system d: propagation direction of scattered light Page 30

31 Raman activity and intensity conservation laws, factor group analysis, scattering tensor, double resonance scattering How do the Raman spectra of -Al 2 O 3 look like? Page 31

32 Raman activity and intensity conservation laws, factor group analysis, scattering tensor, double resonance scattering Factor group analysis may work fine, but... Second order scattering can hide first order modes Vibrations of polar crystals split in TO- and LOcomponents Raman modes show dispersion, i.e. change their frequency in dependence of exciting light wavelength Page 32

33 How are these effects manifested in the Raman spectra? Page 33

34 How are these effects manifested in the Raman spectra? Page 34

35 How are these effects manifested in the Raman spectra? Page 35

36 Raman activity and intensity conservation laws, factor group analysis, scattering tensor, double resonance scattering Resonance Raman scattering I Ra K 2f,10 2 I Ra const 2 e E 0 E 2 e ai E 0 hν vib E 2 const2 bi E 0 E ai e 4 S. Reich, C. Thomsen, J. Maultzsch, Carbon Nanotubes - Basic Concepts and Physical Properties, Wiley-VCH, Weinheim, 2004 Page 36

37 Raman activity and intensity conservation laws, factor group analysis, scattering tensor, double resonance scattering Resonance Raman scattering Page 37

38 Raman activity and intensity conservation laws, factor group analysis, scattering tensor, double resonance scattering Double Resonance Raman scattering S. Reich, C. Thomsen, J. Maultzsch, Carbon Nanotubes - Basic Concepts and Physical Properties, Wiley-VCH, Weinheim, 2004 Page 38

39 Raman intensity (arb. un.) Raman activity and intensity conservation laws, factor group analysis, scattering tensor, double resonance scattering Double Resonance Raman scattering in graphite Dispersion of D * -Line: 46 cm -1 / ev = cm nm 785 nm 514 nm 501 nm 488 nm 476 nm 457 nm 1.17 ev 1.58 ev 2.41 ev 2.47 ev 2.54 ev 2.60 ev 2.71 ev Raman shift (cm -1 ) Page 39

40 Raman activity and intensity conservation laws, factor group analysis, scattering tensor, double resonance scattering Beyond crystalline solids Page 40

41 Raman activity and intensity conservation laws, factor group analysis, scattering tensor, double resonance scattering in situ Raman study of a-si/ Ag at 500 C 30 nm Ag 60 nm a-si R. Wenisch, PhD thesis, in preparation Page 41

42 Raman activity and intensity conservation laws, factor group analysis, scattering tensor, double resonance scattering in situ Raman study of a-si/ Ag at 500 C 30 nm Ag 60 nm a-si R. Wenisch, PhD thesis, in preparation Page 42

43 Raman activity and intensity conservation laws, factor group analysis, scattering tensor, double resonance scattering in situ Raman study of a-si/ Ag at 500 C 30 nm Ag 60 nm a-si R. Wenisch, PhD thesis, in preparation Page 43

44 Raman activity and intensity conservation laws, factor group analysis, scattering tensor, double resonance scattering in situ Raman study of a-si/ Ag at 500 C 30 nm Ag 60 nm a-si R. Wenisch, PhD thesis, in preparation Page 44

45 Raman activity and intensity conservation laws, factor group analysis, scattering tensor, double resonance scattering Particle-size and stoichiometry effects ν ref A 1g = 612 cm 1 V. Swamy et al., APL 89, (2006), Size-dependent modifications of the Raman spectrum of rutile TiO 2, J.C. Parker, R.W. Siegel, APL 57, 943 (1990), Correlation of the Raman spectrum to the oxygen stoichiometry of nanophase TiO 2, Page 45

46 4. Experimental aspects Method Light source Beam optics Sample stage Analyzer Detector Raman Laser Plasma line and Rayleigh filter FTIR Interferometer UV-Vis- NIR Microscope Blackbody Blackbody BMS, UV-Vis- NIR optics T+R stages T+R stages Grating IR optics, Aumirrors Grating XRD X-Ray X-Ray optics CCD CCD (256x1024) DTGS, Photodiode Photodiode, Ion beams 2 MeV Magneto optics Si diodes He + Page 46

47 Illumination and scattering beam optics Experimental aspects Page 47

48 Diffraction and detection Experimental aspects Page 48

49 Measured quantity: wavelength of scattered light Experimental aspects Page 49

50 Experimental aspects Measured quantity: wavelength of scattered light Determined quantity: Raman shift Page 50

51 5. Instrumentation Page 51

52 Instrumentation Labram HR Raman spectrometer, 2 gratings, microscope stage Lateral resolution: ~ 0.5 µm Lateral reproducibility: 1 µm Spectral resolution, 532 nm: ~ 1.5 cm-1 (3 Pixels, 1800/ mm grating) Laser wavelength 532 nm and nm Polarization measurement equipment LN2 cooled front-illuminated CCD, QE 50% Page 52

53 in situ Raman spectrometer ihr 550 at cluster tool, 3 gratings Instrumentation Lateral resolution: ~ 5 µm Lateral reproducibility: ~ 1 µm Spectral resolution, 532 nm: ~ 2 cm-1 (3 Pixels, 1800/ mm grating) Laser wavelength 473 nm and 532 nm no polarization measurement equipment LN2 cooled deep-depleted CCD, QE 90% Page 53

54 in situ Raman spectrometer ihr 550 at cluster tool Instrumentation Lateral resolution: ~ 60 µm Lateral reproducibility: ~ 1 µm Depth resolution: ~ 250 µm Page 54

55 6. Literature 1. J. Weidlein, U. Müller, K. Dehnicke, Schwingungsspektroskopie - Eine Einführung, Georg Thieme Verlag Stuttgart, 2. Aufl., S. Reich, C. Thomsen, J. Maultzsch, Carbon Nanotubes - Basic Concepts and Physical Properties, Wiley-VCH, Weinheim, H. Kuzmany, Solid State Spectroscopy - An Introduction, Springer-Verlag, Berlin, R.W.G. Wyckoff, Crystal structures, Vol. 1, Interscience Publishers, A Division of J. Wiley& Sons, New York, 2nd edition, Hellwege, K.-H. Einführung in die Festkörperphysik, Springer Berlin, Heidelberg, New York, Harald Ibach, H. L. Festkörperphysik - Einführung in die Grundlagen, 6th ed., Springer Berlin - Heidelberg - New York, Misra, P. K. Physics of condensed matter, Academic Press Amsterdam, W.H. Weber, R. M. E. Raman Scattering in Materials Science, Springer Berlin - Heidelberg - New York, 2000 Page 55

56 7. Summary - Raman spectroscopy 1. Non-destructive, fast, easy-to-operate method for the analysis of gases, liquids, surfaces, amorphous and crystalline solids 2. High energy-resolution, ~1µm lateral resolution, ~ 3µm depth resolution 3. Chemical composition, bond strength, molecular and phase structure, degree of long-range ordering, defects, molecular and crystal orientation 4. Low and high temperatures, high pressures, high electric or magnetic fields, sealed air-sensitive samples 5. Coupling techniques with AFM and electrochemistry available Page 56