Photoemission Spectroscopy: Fundamental Aspects

Transcription

1 Photoemission Spectroscopy: Fundamental Aspects G. Stefani Dipartimento di Scienze,Universita Roma Tre CNISM Unita di Ricerca di Roma 3 XIV SILS School G. Stefani 1

2 hn Basic Concepts - E e E, e K e ˆ E MAX e hn E e hn energy XIV SILS School G. Stefani 2

3 Outline 1.Photoelectron energy and bound state energy 2.Satellite structures and multiplet splitting 3.Chemical shift 4.Molecular photoelectron spectra 5.Photoelectron angular distributions 6.Hole state relaxation 7.Photoemission in solids 8.EDC and core ionization 9.Angular resolved PES 10.High energy photoemission HAXPES XIV SILS School G. Stefani 3

4 Photoemission Schematics: He Ia=21.23eV He IIa=40.82eV Mg Ka1,2 = 1253,6 ev Al Ka1,2=1486,6eV Synchrotron Radiation hn W E e Amp. Counter Je(hn,Ee,q,f,s XIV SILS School G. Stefani 4

5 ENERGY CONSERVATION, BINDING ENERGY AND PHOTOELECTRON ENERGY E kin f E b E kin 2 p 2m p 2mE kin XIV SILS School G. Stefani 5

6 The photoemission process 2 p E e h n BE 1 (24.6 ev s h hn n 1s 1 a S 2 0 1s 1 a S 2 0 XIV SILS School G. Stefani 6

7 Interaction radiation matter and transition probability ds 2 4 ahn ˆ B r i dhn B i A 2 ( E B E A hn Bertoni s lectures at this school Initial state A = Neutral ground(excited state Final state B = Residual ion + free electron(s ds dhn E W ds dwde dwde XIV SILS School G. Stefani 7

8 X-section vs. Photoemission current J e ds ( hn,, f J h l n ( Fan( E, W det dwde EW ( E dwde Photoemission peak lineshape 1. Photon monochromaticity Gaussian 2. Electron analyzer resolution Gaussian 3. Final state lifetime (uncertainty principle Lorentian Lineshape =Convolution (1,2,3 XIV SILS School G. Stefani 8

9 Energy balance for 2e atom ˆ E B E A hn Af f A Af 1 2 B 1 2 ˆ E 1s E E E e 1s 1 s hn E e h n BE (24.6eV 1 s One single photoemission peak is expected Energy and momentum are conserved XIV SILS School G. Stefani 9

10 Complexity of the photoemission spectrum Satellite structures Main peak (x ,6 XIV SILS School G. Stefani 10

11 How complex can it be? [Ar] 3d 10 4s 2 4p 6 4d 10 5s 2 5p 6 RELATIVE BINDING ENERGY (ev PHYSICAL RE V IEW A VOLUME 9, NUMBER 4 APRIL XIV SILS School G. Stefani 11

12 Primary photoionization processes XIV SILS School G. Stefani 12

13 Photon = single particle operator 2 or more particles involved in final state = e-e correlation Relaxation & e-e correlation in photoemission = satellite hn e ph [ ] hn - (E i E f* J ( hn - (E i E f [, Binding Energy ] XIV SILS School G. Stefani 13

14 The He satellite structure Ekin=hv-BE XIII SILS School G. Stefani 14

15 XIV SILS School G. Stefani 15 A many electron atom ( ( ( 0 N A N A N A E H i N i j N j i ij N i N i s l r r e r Ze m p o s H e e H n e H kin H H ( 2 ( ( ( ( ;, ( ( 1 ( ( N R i i j N A r A s f ( ( ( ' 0 N B N B N B E H Single particle orbital

16 XIV SILS School G. Stefani 16 sudden approximation ; ( ˆ 1 ( ( N B l N B A W B A A N B e N R N B j j j j l e h E E E r r h de d d, 1 ( 2 1 ( 1 ( (, ( ˆ 1 n s f n s frozen core approvimation 0 ' 0 H H W B A j e j j j j l e h E r r h de d d, 2 (, ( ˆ 1 n s f n s Neglect nucleus motion

17 Total photoemission cross section 4d Cooper minimum He Xe 1s 3d 1s Threshold 3d Threshold XIV SILS School G. Stefani 17

18 XIV SILS School G. Stefani 18 Photoelectron current vs. photoelectron energy ' ',... (4, (3, (2 (1,... (4, (3, (2 (1 (1 ( n n n He p He p He p He s He h He s He s He s He s He h s He s He h n=1 95 Monopole and dipole selection rules

19 Koopmans energy vs. photoemission peaks J ( k [ ] k E i relax i I i I i i adiab k shake-off shake-up adiabatic XIV SILS School G. Stefani 19

20 Spin orbit splitting E i s i hn =227 ev Au 4f 227 mev 232 mev XIV SILS School G. Stefani 20

21 Molecular multiplet splitting O 2 XIV SILS School G. Stefani 21

22 CuCl 2 multiplet & satellite XIV SILS School G. Stefani 22

23 Chemical shift C 1s ev O 1s ev C 1s CO ev C 1s CH ev XIV SILS School G. Stefani 23

24 Chemical shift vs.electronegativity XIV SILS School G. Stefani 24

25 Sensitivity to the local environment in free clusters J. Chem. Phys., Vol. 120, No. 1, 1 January 2004 Tchaplyguine et al. XIV SILS School G. Stefani 25

26 PES spectrum of N 2 XIV SILS School G. Stefani 26

27 Experimental PE spectrum of N 2, and MOs LUMO HOMO XIV SILS School G. Stefani 27

28 XIV SILS School G. Stefani 28 Molecular PE x-section M j i ij j i i N i j N j i ij N i N i r Z Z e s l r r e r Ze m p n n H o s H e e H n e H kin H H ( 2 ( ( ( ( ( Born Oppenheimer W B A N R N B A A A j l e C r h de d d, 2 1 ( 1 ( ˆ 1 f n s ( 1 ( 2 hn E E E A N B e vib A vib B vib B A N B A N B A, (, (,

29 Frank Condon Factors XIV SILS School G. Stefani 29

30 PES O 2 vibrational and multiplet splitting XIV SILS School G. Stefani 30

31 XIV SILS School G. Stefani 31 PE angular distribution W B A N R N B j j j j l r r h d d, 2 1 ( 1 (, ( ˆ 1 s f n s ˆ ˆ dw, ( f q - e e K E, hn

32 Angular distributions ˆ ds dw s 4 1 P2 cos( XIV SILS School G. Stefani 32

33 dw J e direct i i scattered 2 hn ˆ ( q, f E, K - e e Je( q, f d 0 S 2 S ˆ J e ( q, f O 0 C XIV SILS School G. Stefani 33

34 Fixed in space molecules CO C 1s F. Heiser et al. XIV SILS School G. Stefani 34

35 Application to surfaces XIV SILS School G. Stefani 35

36 Core hole relaxation Global energy, angular Momentum and parity Energy, angular momentum, Dipole selections at each step XIV SILS School G. Stefani 36

37 Auger decay Ne Ne + Ne ++ E p E A L 3 (2p 3/2 L 2 (2p 1/2 L 1 (2s K (1s Auger Transition Double ion valence configuration Multiplet Terms KL 1 L 1 2s 0 2p 6 1 S 0 KL 1 L 2,3 2s 1 2p 5 1 P 1, 3 P 0, 3 P 2, 3 P 1 KL 2,3 L 2,3 2s 2 2p 4 1 S 0, 3 P 0, 3 P 2, 1 D 2 EA(KL 1 L 2 = E(K E(L 1 E(L 2, L 1 XIV SILS School G. Stefani 37

38 Kr Auger spectrum K. Siegbahn et al ESCA Applied to free molecules 0 Kr I i Kr II L 2, L 3 f Kr III M M i j XIV SILS School G. Stefani 38

39 Zn Auger multiplet splitting L 3 M 45 M 45 Aksela et al. PRL 33,999 (1974 XIV SILS School G. Stefani 39

40 Auger chemical shift XIV SILS School G. Stefani 40

41 From central to periodic potential E K XIV SILS School G. Stefani 41

42 Photoemission Spectroscopy In Solids How real spectra look like: Primary and Secondary Electrons XIV SILS School G. Stefani 42

43 Spectral Function in Interacting Solids Nf = A N-1 f kf Je S if M 2 if S m m im 2 (E N i+hn- E N-1 m-e kin A(k, = S m (< N-1 mc k N i> 2 ( + E N-1 m - E N i Je(k, S if M if 2 A(k, E kin - hn f(e kin - hn For non interacting particles A(, k=( - E k where E k =E i N-1 -E i N A(, k = 1/ S''(k, / [ - E k - S'(k, 2 + S''(k, 2 ] XIV SILS School G. Stefani 43

44 The Three-Step model 1 XIV SILS School G. Stefani 44

45 1. Dipole transition The three-step model 2 Je= S if f(e i [1-f(E f ] M 2 if [E kin -(E f -] (E f -E i -hn (k i +G-k f 2. Elastic transport d(e f, k = a/(1+a 3. Exit to vacuum 0 if E f < E F + T(E f, k ext = 1/2 [1-(E F + /Ef] if E f > E F + Total current Je S if f(e i [1-f(E f ] M 2 if T(E f, k ext d(e f, k [E kin -(E f -] (E f -E i - hn (k i +G-k f (k // i+g // -k // ext XIV SILS School G. Stefani 45

46 How to reconstruct the initial state in 3 step model XIV SILS School G. Stefani 46

47 Surface vs. Bulk Sensitivity in Photoemission electron mean free path 3 Copper Lattice XIV SILS School G. Stefani 47

48 Photoemission spectrum at Fermi Edge METAL INSULATOR Intensity (arb. units Intensity (arb. units Binding energy (ev Binding energy (ev XI SILS School G. Stefani 48

49 Valence band Energy Distribution Curves and Cooper minimum Valence Band EDCs of the clean Pt(997 surface (thin lines and of Co-nanowires grown on Pt(997 (dots and thick lines, taken at different photon energies XIV SILS School G. Stefani 49

50 Autoionizing decay Ne Ne * Ne + E A M 2,3 L(3p 3 (2p 3/2 L 2 (2p 1/2 L 1 (2s K (1s XIV SILS School G. Stefani 50

51 Resonant photoemission EDC Valence Band EDCs of a CuPc thin-film taken at different photon energies (left panel and X-ray Absorption Spectroscopy (XAS from the same CuPc across the N K-edge (right panel. XIV SILS School G. Stefani 51

52 2D electron gas spatially confined Cs/InAs(110 XIV SILS School G. Stefani 52

53 Photoemission Core Level Spectroscopy Wide XPS spectrum of graphite (C XIV SILS School G. Stefani 53

54 Photoemission Spectroscopy Core level XPS spectrum of graphite (C The singlet C 1s line is characterized by: 1 A specific binding energy which reflects the specific atomic species (C in a specific chemical environment 2 A finite width reflecting the instrumental resolution, lifetime broadening and other many-body effects XIV SILS School G. Stefani 54

55 Core Levels, chemical shift The Si 2p line is characterized by the occurrence of 5 chemically distinct components which reflect different chemical states of the Si atoms at the interface XIV SILS School G. Stefani 55

56 Surface core level shift vs. mean free path In 4d Highresolution In- 4d core-levels at freshly cleaved InAs(110, taken with He IIa and He IIb radiation; Voigt-profiled fit with surface (S, blu lines and bulk (B, red lines doublet components (left panel XIV SILS School G. Stefani 56

57 Valence PE vibrational spectrum 7.4 Å 16.6 Å pentacene: C 22 H 14 benzene-thiol: C 6 H 5 -SH Betti, Kanjilal and Mariani, J. Phys. Chem. A 111, (2007 XIV SILS School G. Stefani 57

58 Cooper Minimum Photoemission It is possible when one of the valence band orbital shows a Cooper minimum in the photoionization cross section Cooper minimum in the Pt 5d cross section A Cooper minimum exists when the radial part of the orbital wave function exhibits a node The Pt 5d and Si 3p cross sections are comparable XIV SILS School G. Stefani 58

59 Cooper Minimum Photoemission Pt 5d anti-bonding Pt 5d non-bonding Pt 5d bonding A joint analysis of VB photoemission spectra taken at and off the Cooper minimum enables one to disentangle the differing site- and orbital-specific contributions XIV SILS School G. Stefani 59

60 Angular resolved photoemission Ke + Ke Ke // XIV SILS School G. Stefani 60

61 angular resolved photoemission How to photo-excite electrons from a crystal in a periodic potential, by photoemission graphs from Ph. Hoffmann XIV SILS School G. Stefani 61

62 electronic surface states at Cu(111 S.D. Kevan, Phys. Rev. Lett. 50,526 (1983. quasi-free electron surface state on Cu(111, Schockley state, s-like XIV SILS School G. Stefani 62

63 Dangling bonds Si(111-(2x1 Dangling-bond surface state dispersion at the Si(111-(2x1 reconstructed surface along the GJ direction of the Surface Brillouin Zone (SBZ. One of the first experimental ARPES danglingbond dispersion (left panel; recent high-resolution ARPES dangling-bond dispersion. XIV SILS School G. Stefani 63

64 Physisorbed Xe c(2x2/cu(110 Experimental band structure of the 5p levels of Xe physisorbed in an ordered c(22 structure onto the Cu(110 surface. ARPES bands XIV SILS School G. Stefani 64

65 Pentacene HOMO on Cu(119 2-nm thick pentacene film grown on Cu(119. ARPES selection of spectra taken at normal emission and varying the photon energy (left; highest-occupied molecular-orbital (HOMO band dispersion along k (right. XIV SILS School G. Stefani 65

66 ARPES graphite (HOPG Valence band of graphite (HOPG, stacking of the ARPES spectra as a function of polar angle (left and experimental band structure (right. XIV SILS School G. Stefani 66

67 Graphene band structure Graphene band structure along GKM and zoom of the Dirac cone around the K point of the SBZ. ARPES data taken with high-resolution ARPES and a He discharge source XIV SILS School G. Stefani 67

68 Band formation in graphene multilayers Formation of an electronic band, stepwise: from 1-layer (extreme left to 4-layer (extreme right graphene band structure along across the Dirac point. XIV SILS School G. Stefani 68

69 K shell dispersion in graphene Spectral function of the C 1s core-level in graphene as a function of the emission polar angle Silvano Lizzit, et al.: Nature Physics 6, (2010 XIV SILS School G. Stefani 69

70 Why Hard X-ray PES (HAXPES? From C.S. Fadley In: J.C. Woicik ed., «Hard X-ray photoelectron spectroscopy (HAXPES, Springer series in Surface Science PES is extremely surface sensitive: typically information is retrieved from the topmost Å. XIV SILS School G. Stefani 70

71 (Å PES typical energy range Hard x-ray photoemission spectroscopy HAXPES 10 ~ 5-20 Å Low energy photoemission spectroscopy LEPES Courtesy of F. Offi Electron energy (ev IMFP enhanced at both low (< 10 ev and high energy (> 5 kev XIV SILS School G. Stefani 71

72 Main difficulty with HAXPES Photoionization cross section: Au 4f Cross section (Barns Yeah and Lindau 10 6 Scofield times more than TWO ORDERS OF MAGNITUDE! Energy (ev J. J. Yeh and I. Lindau, At. Data Nucl. Data Tables 32, 1 (1985 J. H. Scofield, LLNL Report, UCRL (1973 Courtesy of F. Offi XIV SILS School G. Stefani 72

73 Early attempts Au 4f core level Courtesy of F. Offi 25 counts/s ~8 kev Kinetic Energy Total Energy Res. 420 mev NOT POSSIBILE TO MEASURE VALENCE BAND I. Lindau, P.Pianetta, S. Doniach, W.E. Spicer Nature 250, 214 (1974 XIV SILS School G. Stefani 73

74 RECENT RESULTS ON VALENCE BAND Au polycrystalline hn = 5934 ev T = 220 K 3 hn = 5934 ev T = 18 K Energy resolution E 70 mev Resolving power R Intensity (counts* Intensity (counts* slit 0.8 mm E p =40 ev slit 0.4 mm E p =20 ev Binding energy (ev Binding energy (ev G. Paolicelli et al., Journal of Electron Spectroscopy and Related Phenomena , 963 (2005 Courtesy of F. Offi XIV SILS School G. Stefani 74

75 Estimation of the bulk sensitivity Bulk sensitivity in PES is typically estimated via measurements of electron effective attenuation lenght (, the thickness of the overlayer that reduces to 1/e the intensity I S of a core level emission from the substrate. The overlayer experiment: I 0 = intensity from the bare substrate I S ( x I 0 e x I ( x I T (1 e x Overlayer: Co, Cu, Ge, and Gd 2 O 3 IT = intensity for an infinite overlayer M. Sacchi et al., Phys. Rev. B 71, (2005 Courtesy of F. Offi XIV SILS School G. Stefani 75

76 Contribution of the surface layer Information depth layer thickness from which 95% of the total signal is produced E (ev EAL (Å Inf. Depth (Å 20 5 Å 15 Å Courtesy of F. Offi I( x e x Å 75 Å Å 195 Å XIV SILS School G. Stefani 76

77 EAL in different materials Courtesy of F. Offi For most materials the experimental values of EAL are quite higher than what obtained at lower photon energies and quite in agreement with theoretical models M. Sacchi et al., Phys. Rev. B 71, (2005 XIV SILS School G. Stefani 77

78 The non negligible recoiling nucleus - hn XIV SILS School G. Stefani 78

79 XIV SILS School G. Stefani 79

80 References C.S. Fadley Basic Concepts of X-ray, in Electron Spectroscopy, theory, techniques and applications, Brundle and Baker Eds. (Pergamon Press, 1978 Vol. 11, ch.1 available at: S. Hufner, principle and applications (Berlin Springer rd Edition V. Schmidt Photoionization of atoms using synchrotron radiation Report on Progress in Physics 55( C.M. Bertoni in Synchrotron Radiation Basics, Methods and Applications (Springer Verlag Berlin Heidelberg 2015, pg. 145 C. Mariani and G. Stefani in Synchrotron Radiation Basics, Methods and Applications (Springer Verlag Berlin Heidelberg 2015, pg. 275 J.C. Woicik ed., «Hard X-ray photoelectron spectroscopy (HAXPES, Springer series in Surface Science XIV SILS School G. Stefani 80