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

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? electrons as example: ψ = ψ ( r,s ;r,s ), including spin of both electrons 1 1 2 2 But labels can' t affect any measurable quantity. E.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 ;r,s ) 12 1 1 2 2 with P = permutation operator r,s ;r,s 12 1 1 2 2 and eigenvalues of ± 1 Finally, all particles in two classes : FERMIONS : ( incl. e ' s ) : ψ antisymmetric 1 3 5 s =,,... P12ψ = 1ψ 2 2 2 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

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 0 1 2 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

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) + photoelectron @ E kin = 0 Atom Q N electrons

What does the hole do?

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

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!

Atomic orbitals:

z x y

Filling the Atomic Orbitals: 1s ± ± Maximum Occupation Filling = Degeneracy degeneracy 2 Total No e - 2 2s 2p x2 2 6 8 3s 2 2 3p x2 6 18 3d x2 x2 10 10 + 14 for nf

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

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 ]

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

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

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 9 9 13 13 45 17 17 Interpolated, extrapolated Missing valence B.E.s Valence levels

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

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

H a H b ε positive (unoccupied) ε a.u. = +7.21 ev Anti-Bonding ϕ anti MO ϕ 1sa - ϕ 1sa ε negative (occupied) Bonding ϕ bonding MO ϕ 1sa + ϕ 1sa ε a.u. = -16.16 ev (Compare 13.61 for H atom 1s)

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)

Basic Concepts of XPS Chapter 3

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

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

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

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 0 2 2 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 = 13.605 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

Electronic bands and density of states for free-electron metals- Rydberg = 13.605 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

Vacuum level The electronic structure of a transition metal fcc Cu φ Cu = 4.4 ev = work function V 0,Cu =13.0eV - 8.6 ev Experimental points from angle-resolved photoelectron spectroscopy (more later)

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

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

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 -1.0-1.5 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

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

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

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)

Fe: ANGLE AND SPIN-RESOLVED SPECTRA AT Γ POINT

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)

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.

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)

Basic Concepts of XPS Figure 1

NO. ATOMS QUANTITATIVE SURFACE ANALYSIS

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

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

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

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.

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)

Variation of Near-Edge X-Ray Absorption Fine Structure (NEXAFS) with Atomic No. for Some 3d Transition Metals White lines = 2p 3/2 = 2p 1/2 0 0.5 2 1.8 3 2.4 4 :ATOM 3.5 :SOLID J. Stohr, NEXAFS Spectroscopy Number of d-holes

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

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

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

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) 1 3 2 1 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

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

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)

Au N 6,7 O 4,5 O 4,5 X-Ray Data Booklet Fig. 1.4 65 70 75 80 85 Kinetic Energy (ev) 2p 3/2 2p 1/2 Ag MNN 2s 1/2 1253.6 - Auger Energy (ev) 1s 1/2 Ni LMM 1253.6 - 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 9 543.1-17 - 13 513 ev E kin = 508.3 O KLL 1253.6 - Auger Energy (ev)

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

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

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

Kβ 3p 1/2,3/2 3s 1/2 E b (Mg 1s) - E b (Mg 2p 1/2,3/2 ) = 1303.0-49.7 = 1253.3 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

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

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

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)

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

Electron binding energies Diff. = 11.2 Diff. = 11.4

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