Outline. Surface, interface, and nanoscience short introduction. Some surface/interface concepts and techniques

Size: px

Start display at page:

Download "Outline. Surface, interface, and nanoscience short introduction. Some surface/interface concepts and techniques"

Jordan Wilson
5 years ago
Views:

1 Outline Surface, interface, and nanoscience short introduction Some surface/interface concepts and techniques Experimental aspects: intro. to laboratory-based and SR-based Electronic structure a brief review The basic synchrotron radiation techniques: more experimental and theoretical details Core-level photoemission Valence-level photoemission

What properties do wave functions of overlapping (thus indistinguishable) particles have?

g. probability density : ψ(r,s ;r,s ) = ψ(r,s ;r,s ) 2 2 1 1 2 2 2 2 1 1 Therefore ψ(r 1,s 1;r 2,s 2 ) =± 1 ψ(r 2,s 2;r 1,s1 ) P ψ (r,s

FERMIONS : ( incl. e ' s ) : ψ antisymmetric 1 3 5 s =,,... P12ψ = 1ψ 2 2 2 BOSONS : ( incl. photons ) : ψ symmetric s = 0,1,2,.

2 What properties do wave functions of overlapping (thus indistinguishable) particles have? electrons as example: ψ = ψ ( r,s ;r,s ), including spin of both electrons But labels can' t affect any measurable quantity. E.g. probability density : ψ(r,s ;r,s ) = ψ(r,s ;r,s ) Therefore ψ(r 1,s 1;r 2,s 2 ) =± 1 ψ(r 2,s 2;r 1,s1 ) P ψ (r,s ;r,s ) with P = permutation operator r,s ;r,s and eigenvalues of ± 1 Finally, all particles in two classes : FERMIONS : ( incl. e ' s ) : ψ antisymmetric s =,,... P12ψ = 1ψ BOSONS : ( incl. photons ) : ψ symmetric s = 0,1,2,... P ψ =+ 1ψ 12 Probability of finding two electrons at the same point in space with the same spin is zero: the Fermi Hole e 2- e 1- e 3- the Exchange Interaction Hund s 1 st rule & magnetism

3 A first try at many-electron wave functions: The Hartree-Fock Method Assume N-electron, P nucleus wave function to be: Ψ Φ= Slater deter minant space: like 1s, 2s, spin: α( ) or β( ) φ1( r1) χ1( σ1) φn( r1) χn( σ1) 1 (35a) = N! φ1( rn) χ1( σn) φn( rn) χn( σn) and also require orthonormality of one-electron orbitals φ * ( r) φ ( r) dv = δ i j ij Minimize total energy Hartree-Fock equations: ˆ Hr ( 1 ) φi ( r1 ) = εiφi ( r1 ); i= 1,2,... N (42) N with: 0 εi = εi + Jij δms, m K One-electron energies s ij (47) i j j = 1 or eigenvalues or One-electron integral: binding energy P Z εi = φi( r1) 1 Koopmans Theorem φi( r1) (48) 2 = 1 r1 Note--K ij often Two-electron coulomb integral: J ij in solid-state ˆ * * 1 Jij φi ( r1) J j φi ( r1) φ ( r1) φ ( 2) ( 1) ( 2) i j r φi r φj r dv1dv (45) = 2 r12 Two-electron exchange integral: ˆ * * 1 Kij φi ( r1) K j φi ( r1) = φ ( r1) φ ( 2) ( 1) ( 2) i j r φj r φi r dv1dv2 (46) r12 Lowers energy attractive Paper [1]--Basic Concepts of XPS

4 Basic energetics Many e - picture hν = E + E = E + φ + Vacuum Fermi binding kinetic binding spectrometer E kinetic E (Qn j,k) = E (N 1,Qn j hole,k) E (N) Vacuum binding final initial Ion Q + K th state n j hole N-1 Relaxation/screening Vacuum E binding (Qn j,k) + E kin = 0 Atom Q N electrons

5 What does the hole do?

6 Paper [1]-- Basic Concepts of XPS Figure 18

7 α(σ) β(σ) PLUS SPIN: α(σ)= m si = +½ = β(σ)= m si = -½ = α(σ) β(σ) Δm s = m sf -m si = 0!

9 Atomic orbitals:

10 z x y

11 Filling the Atomic Orbitals: 1s ± ± Maximum Occupation Filling = Degeneracy degeneracy 2 Total No e - 2 2s 2p x s 2 2 3p x d x2 x for nf

12 And the same thing for the d orbitals: e g Ligand (e.g. O) 3z 2 -r 2 x 2 -y 2 t 2g z y x Transition Metal (e.g. Mn) e g and t 2g not equivalent in octahedral (cubic) environment yz zx xy

feels nuclear charge more than p, more than d, more than

13 Intraatomic electron screening in many-electron atoms--a simple model In many-electron atoms: For a given n, s feels nuclear charge more than p, more than d, more than f k C 1/(4πε 0 ) Lifts degeneracy on in hydrogenic atom [Z eff ]

14 Intraatomic electron screening in many-electron atoms--a selfconsistent Q.M. calculation Plus radial oneelectron functions: P n (r) rr n (r)

17 WITH C1 AND C2 TABULATED CLEBSCH-GORDAN OR WIGNER 3j SYMBOLS

19 X-Ray Data Booklet--Section 1.1 ELECTRON BINDING ENERGIES The energies are given in ev relative to the vacuum level for the rare gases and for H 2, N 2, O 2, F 2, and Cl 2 ; relative to the Fermi level for the metals; and relative to the top of the valence bands for semiconductors (and insulators). Electronic configuration Valence levels Interpolated, extrapolated Missing valence B.E.s Valence levels

20 X-Ray Data Booklet--Section 1.1 ELECTRON BINDING ENERGIES Valence levels Valence levels

21 The quantum mechanics of covalent bonding in molecules: H 2+ with one electron ϕ - = ϕ antibonding ϕ 1sa - ϕ 1sb ϕ + = ϕ bonding ϕ 1sa + ϕ 1sb Total Energy ϕ antibonding =R

22 H a H b ε positive (unoccupied) ε a.u. = ev Anti-Bonding ϕ anti MO ϕ 1sa - ϕ 1sa ε negative (occupied) Bonding ϕ bonding MO ϕ 1sa + ϕ 1sa ε a.u. = ev (Compare for H atom 1s)

23 36

24 Theoretical Calculations of charge density for CO bound to Ni(001)- ontop : O C Ni CO 5σ + + Ni 3d z σ bond 2 Ni Density gain CO 2π = π* Ni 3d xy π back bond Zangwill, p. 307, plus PRL 55, 2618 ( 85)

25 Basic Concepts of XPS Chapter 3

26 For all states in crystalline (ordered) solids: Ψ ( r ) = u ( r )e, where u ( r ) = u( r + A) a Bloch function ik r K K K A typical Bloch function ik r Re or Im part of e A u (r) has periodicity of lattice, same in each unit cell K

27 Different directions in k-space: The first (reduced) Brillouin zone: k z fcc crystal k z bcc crystal k y Δ k y k y k x

28 L

29 DIRECT TRANSITIONS FOR NEARLY-FREE ELECTRONS IN A WEAK PERIODIC POTENTIAL 1 DIMENSION

30 Fig. 13 Valence-band photoemission: Angle-Resolved Photoemission (ARPES) E(K k f, = K f f ) = f, 2 2 E(k K f f ) V0 K f /2me f hν Surface k f, K Barrier f, k =V f E(k f f ) hν E(k i i ) k f /2me g bulk (and /or g surf ) k i kf = k i + g bulk ( + gsurf ) + khν + kphonon Brillouin High energy a/o Zone High temp. E(k i i ) I( E,k ) ˆε φ (E = hν + E, k = k + g ) r φ(e,k ) e exp( L / 2 Λ ) f f photoe f i f i i i Direct or k-conserving transitions 2

Electronic bands and density of states for free-electron metals- Rydberg = 13.

32 Electronic bands and density of states for free-electron metals- Rydberg = ev Lithium bcc, a = 3.49 Å 1s 2 2s 1 a 0 k x (k ) E(k x ) 2m 2 2 x 2π/a =1.8Å -1

33 Electronic bands and density of states for free-electron metals- Rydberg = ev Aluminum fcc, a = 4.05 Å 1s 2 2s 2 2p 6 3s 2 3p 1 a Lithium bcc, a = 3.49 Å 1s 2 2s 1 a 0 k x 2π/a =1.8Å -1 (k ) E(k x ) 2m 2 2 x 0 2π/a =1.55Å -1 (k ) E(k x ) 2m 2 2 x

34 Vacuum level The electronic structure of a transition metal fcc Cu φ Cu = 4.4 ev = work function V 0,Cu =13.0eV ev Experimental points from angle-resolved photoelectron spectroscopy (more later)

35 And the d orbitals are not equivalent in different bonding environments: Ligand (e.g. O) e g Transition Metal (e.g. Mn) 3z 2 -r 2 x 2 -y 2 t 2g z y x e g and t 2g not equivalent in octahedral (cubic) environment zx z xy y yz zx xy x yz Face-centered cubic 12 nearest neighbors

36 Copper densities of states-total and by orbital type: zx z xy yz x y

37 3s 2 3p 6 filled + 3d,4s CB 3d 2 4s 2 3d 3 4s 2 3d 5 4s 1 3d 6 4s 2 The electronic structures of the 3d transition metals rigid-band model + Exchange! + Exchange! + Flat corelike Ar 3s, 3p bands at Rydbergs 3d 7 4s 2 3d 8 4s 2 3d 10 4s 1 3d 10 4s 2 + Exchange! + Exchange! + Flat corelike Zn 3d bands at -0.8 Rydberg

38 (e) Spin-down Spin-up Ferromagnetic Conductor (The exchange interaction)

39 The electronic bands and densities of states of ferromagnetic iron μ S = 2.2 Bohr magnetons (Atomic iron: 2.0 Bohr magnetons) Exchange splitting Spin-down (Minority) Spin-up (Majority) 4 x ½ = 2 k = 0 k = 0

40 Vacuum level φ Fe = 4.3 ev V 0,Fe =12.4 ev ΔE exch -8.1 ev Hathaway et al., Phys. Rev. B 31, 7603 ( 85)

41 Fe: ANGLE AND SPIN-RESOLVED SPECTRA AT Γ POINT

42 Electronic bands and density of states for a semiconductor-germanium 1s 2 2s 2 2p 6 3s 2 3p 6 3d 10 4s 2 4p 2 Anti- Bonding (empty at T = 0) Bonding (filled at T = 0)

43 The Soft X-Ray Spectroscopies Valence PE hν CB E F VB hν e - Core PE e - Core PE = photoemission = photoelectron spectroscopy XAS = x-ray absorption spectroscopy AES = Auger electron spectroscopy XES = x-ray emission spectroscopy RIXS = resonant inelastic x-ray scattering / x-ray Raman scatt.

44 MATRIX ELEMENTS IN THE SOFT X-RAY SPECTROSCOPIES: DIPOLE LIMIT Photoelectron spectroscopy/photoemission: hv I eˆ ϕ (1) r ϕ (1) f i 2 ϕ f (free) Vacuum ϕ i (bound)

46 Basic Concepts of XPS Figure 1

48 NO. ATOMS QUANTITATIVE SURFACE ANALYSIS

49 36

50 Vibrational fine structure Kimura et al., Handbook of HeI Photoelectron Spectra

51 SAME SUBSHELL COUPLING + TOTAL L,S MONOPOLE (N-1)e - SHAKE-UP/ SHAKE-OFF 1e- DIPOLE dσ/dω Basic Concepts of XPS MONOPOLE Chapter 3

52 36

53 Valence-level Photoelectron spectra of CO adsorbed on various transition metal surfaces

54 Theoretical Calculations of charge density for CO bound to Ni(001)- ontop : O C Ni CO 5σ + + Ni 3d z σ bond 2 Ni Density gain CO 2π = π* Ni 3d xy π back bond Zangwill, p. 307, plus PRL 55, 2618 ( 85)

55 The Soft X-Ray Spectroscopies Valence PE hν CB e - Core PE e - E F VB hν XAS Core PE = photoemission = photoelectron spectroscopy XAS = x-ray absorption spectroscopy AES = Auger electron spectroscopy XES = x-ray emission spectroscopy RIXS = resonant inelastic x-ray scattering / x-ray Raman scatt.

56 MATRIX ELEMENTS IN THE SOFT X-RAY SPECTROSCOPIES: DIPOLE LIMIT Photoelectron spectroscopy/photoemission: hv I eˆ ϕ (1) r ϕ (1) Near-edge x-ray absorption: f i 2 ϕ f (free) Vacuum ϕ i (bound) I eˆ ϕ (1) r ϕ (1) f i Vacuum ϕ f (bound) hv 2 ϕ i (bound)

57 Variation of Near-Edge X-Ray Absorption Fine Structure (NEXAFS) with Atomic No. for Some 3d Transition Metals White lines = 2p 3/2 = 2p 1/ :ATOM 3.5 :SOLID J. Stohr, NEXAFS Spectroscopy Number of d-holes

58 Magnetic Circular Dichroism in X-Ray Absorption (XMCD) Ferromagnetic cobalt with magnetization along incident light direction RCP LCP

59 Variation of Near-Edge X-Ray Absorption Fine Structure (NEXAFS) for Different Polymers H. Ade, X-ray Microscopy 99, AIP Conf. Proc. 507, p.197

60 Electron-out: surface sensitive hν CB The Soft X-Ray Spectroscopies Valence PE e - Core PE e - 1 e - 3 e - AES E F VB hν XAS hν Core PE = photoemission = photoelectron spectroscopy XAS = x-ray absorption spectroscopy AES = Auger electron spectroscopy XES = x-ray emission spectroscopy REXS/RIXS = resonant elastic/inelastic x-ray scattering e - 2

61 MATRIX ELEMENTS IN THE SOFT X-RAY SPECTROSCOPIES: DIPOLE LIMIT Photoelectron spectroscopy/photoemission: hv Auger electron emission: 2 Direct I I eˆ ϕ (1) r ϕ (1) Near-edge x-ray absorption: f i 2 ϕ f (free) Vacuum I eˆ ϕ (1) r ϕ (1) 2 e e ϕ (1) ϕ (2) ϕ (1) ϕ (2) ϕ (1) ϕ (2) ϕ (1) ϕ (2) f ϕ i (bound) f 3 2 r12 r12 f Exchange i 2 Vacuum ϕ f (bound) hv 2 ϕ i (bound) Vacuum ϕ 3 ϕ f ϕ 2 ϕ 1

62 Auger kinetic energies do not change with photon energy Photoelectron kinetic energies shift linearly with photon energy Basic Concepts of XPS Figure 1

63 ε positive The equivalent core or Z+1 approximation ε negative + + Or more accurately: K.E. B.E. 5Z -B.E. 3 Z+1 -B.E. 1 Z B.E. 5Z -B.E. 3Z -B.E. 1 Z+1 (average of two above)

64 Au N 6,7 O 4,5 O 4,5 X-Ray Data Booklet Fig Kinetic Energy (ev) 2p 3/2 2p 1/2 Ag MNN 2s 1/ Auger Energy (ev) 1s 1/2 Ni LMM Auger Energy (ev) K.E. B.E. 1s Z=8 -B.E. 2p9 -B.E. 2p 8 B.E. 1s8 + B.E. 2p8 -B.E. 2p ev E kin = O KLL Auger Energy (ev)

65 X-Ray Data Booklet--Section 1.1 ELECTRON BINDING ENERGIES The energies are given in ev relative to the vacuum level for the rare gases and for H 2, N 2, O 2, F 2, and Cl 2 ; relative to the Fermi level for the metals; and relative to the top of the valence bands for semiconductors (and insulators). Electronic configuration Valence levels Interpolated, extrapolated Missing valence B.E.s Valence levels

66 Electron-out: surface sensitive hν CB E F VB hν Core The Soft X-Ray Spectroscopies Valence PE XAS e - Core PE e - hν e - 1 e - 3 XES Photon-out: bulk, deeper interfaces PE = photoemission = photoelectron spectroscopy XAS = x-ray absorption spectroscopy AES = Auger electron spectroscopy XES = x-ray emission spectroscopy REXS/RIXS = resonant elastic/inelastic x-ray scattering e - 2 AES hν

67 ε positive + ε negative Or more accurately: hν = B.E. 5 -B.E. 3 or core +

68 MATRIX ELEMENTS IN THE SOFT X-RAY SPECTROSCOPIES: DIPOLE LIMIT Photoelectron spectroscopy/photoemission: hv Auger electron emission: 2 Direct I I eˆ ϕ (1) r ϕ (1) Near-edge x-ray absorption: f i 2 ϕ f (free) Vacuum I eˆ ϕ (1) r ϕ (1) 2 e e ϕ (1) ϕ (2) ϕ (1) ϕ (2) ϕ (1) ϕ (2) ϕ (1) ϕ (2) f ϕ i (bound) f 3 2 r12 r12 f Exchange i 2 Vacuum ϕ f (bound) hv 2 ϕ i (bound) Vacuum ϕ 3 ϕ f ϕ 2 ϕ 1

69 If fluorescence yield FY FY = probability of radiative decay x-ray emission) 1 - FY = probability of non-radiative decay Auger electron emission X-Ray Data Booklet Section 1.3

70 Kβ 3p 1/2,3/2 3s 1/2 E b (Mg 1s) - E b (Mg 2p 1/2,3/2 ) = = ev 1s 1 (2s2p) 6 1s 1 (2s2p) 5 1s 1 (2s2p) 4 1s 1 (2s2p) 3 1s 1 (2s2p) 6 2p 3/2 2p 1/2 Kα 2s 1/2 1s 1/2 Mg K series of x-rays: atomic no. = 12 Fluorescence Yield 0.03 Basic Concepts of XPS Figure 2

71 Electron-out: surface sensitive hν CB The Soft X-Ray Spectroscopies Valence PE e - Core PE e - e - 1 e - 3 AES hν Photon-out: bulk, deeper interfaces REXS hν hν E F VB hν XAS hν hν XES RIXS Core PE = photoemission = photoelectron spectroscopy XAS = x-ray absorption spectroscopy AES = Auger electron spectroscopy XES = x-ray emission spectroscopy REXS/RIXS = resonant elastic/inelastic x-ray scattering e - 2

72 MATRIX ELEMENTS IN THE SOFT X-RAY SPECTROSCOPIES: RESONANT EFFECTS Resonant inelastic x-ray scattering: I Ψ ( N) eˆ r Ψ ( N) Ψ ( N) eˆ r Ψ ( N) f emi m m inc i hν + E ( N) E ( N) iγ f m i m m δ ( hν ( E ( N) E ( N))) m i Vacuum 2 hv ê inc Ψ i (N) Ψ m (N) ΔE ê emi Ψ f (N) hv = hv- ΔE 2Γ t m N (t) = N (0)e = N (0)e m m m τ t lifetime

73 X-ray fluorescence spectroscopy =X-ray emission spectroscopy (XES) Resonant inelastic x-ray scattering (RIXS) and Resonant elastic x-ray scattering (REXS) 10.0 ev NON-RESONANT Mn 2p 3/2 2p 1/2 X-ray absorption spectroscopy (XAS) XES REXS RIXS Vac. 3d 3p 3s 2p 3/2 2p 1/2 Butorin et al., Phys. Rev. B 54, 4405 ( 96)

74 X-Ray Nomenclature (from X-Ray Data Booklet ) In general: N 6 N 4 N 2 M 4 M 2 =4f =4d 7/2 5/2 =4p =4s 3/2 1/2 =3d 5/2 =3p 3/2 =3s 1/2 Δj=0,±1 nl Spin-norbit nl j=l+1/2 j=l-1/2 =2p 3/2 =2p 1/2 =2s 1/2 =1s See Section 1.2 in X-Ray Data Booklet

75 Electron binding energies Diff. = 11.2 Diff. = 11.4

76 The five ways in which x-rays Interact with Matter: X-Ray Data Booklet Section 3.1

Photon Interaction. Spectroscopy

Photon Interaction. Spectroscopy Photon Interaction Incident photon interacts with electrons Core and Valence Cross Sections Photon is Adsorbed Elastic Scattered Inelastic Scattered Electron is Emitted Excitated Dexcitated Stöhr, NEXAPS