Energy Spectroscopy Excitation by means of a probe Energy spectral analysis of the in coming particles -> XAS or Energy spectral analysis of the out coming particles Different probes are possible: Auger -> electrons (2 10 kev) XPS (or ESCA) -> X rays (0.2 2 kev) (x-rays photoelectron spectroscopy) UPS -> Ultraviolet photons (10 50 ev) (UV photoelectron spectroscopy) Out coming particles: electrons Electromagnetic spectrum E = hν = hc/λ c = 3 10 8 m/s h = 6.6 10-34 Js
The Auger process Auger spectroscopy is based upon a single electron in - electron out process. Ejected electron Vacuum level Ejected electron E kin KL 1 L 3 excitation radioactive Auger relaxation E kin E(L 3 ) = E(L 1 ) E(K) E(L i ) and E(K) depend on the atomic structure -> E kin does not depend on E i chemical sensitivity N.B.: the sample must be a conductor and must be connected to ground to avoid charging
Auger experimental setup CMA = Cylindrical Mirror Analyzer electrons sample electron gun Electron energy: in out grids channeltron 1-10 kev 10 2000 ev Auger spectrum: number of emitted electrons as a function of their kinetics energy
Counting mode MgO Auger spectrum Derivative mode The monotone background is due to multi-scattered electrons Auger transitions for the different chemical elements
Thickness sensibility The thickness of the investigated surface depends: 1) Electron energy 2) Probability of the Auger transition 3) Atomic scattering cross section 4) Abortion of the Auger electrons Electron beam intensity at depth z: J(z) = I(0) r -z/d r = layer attenuation factor; d = atomic layer thickness Auger electrons (detected at surface) coming from depth z: I(z) = I(0) r -z/d s -z/d = I(0) exp(-z/d ln(rs)) = I(0) exp(-z/λ) s = attenuation factor for the Auger electrons; λ = d/ln(rs) electron mean free path Total Auger electron current measured at surface: I = 0 z I(z) dz = I(0) λ (1-exp(-z/λ)) λ = electron mean free path 1/λ = 1/λ ι + 1/λ Auger 1/λ Auger λ ι >> λ Auger surface sensibility is given by the reduced mean free path of the out coming electrons Depth sensibility (D): 95% of the signal coming from a film with infinite thickness -> I(D) = 0.95 I(0) λ (1-exp(-D/λ)) -> D = - λ ln(0.05) 3 λ
Continuous film of thickness h B A h h < 4 5 ML E B = Energy of the Auger electron generated in B E A = Energy of the Auger electron generated in A I B = I(0) λ B (1-exp(-h/ λ B (E B ))) J(h) = I(0) (λ ι > 10 ML) electrons impinging on A I(h) = I(0) λ A Auger electrons from A moving through B => I A = I(0) λ A exp(-h/ λ B (E A )) n < h < n+1 layers -> I A and I B proportional to h Discontinuous film of thickness h B A h θ > fraction of the surface covered by the film I B = I(0) λ B θ (1-exp(-h/ λ B (E B ))) I A = I(0) λ A [(1-θ) + θ exp(-h/ λ B (E A ))]
Growth of Ni films on 1ML Co/Pt(111) 848
Alloying during annealing of 2 ML Ni/1 ML Co/Pt(111) Co 53 Co 656 Ni 102 Ni 848 -> λ = 3.9 Å -> λ = 11.4 Å -> λ = 4.6 Å -> λ = 13.2 Å Co 53 increases and Ni 102 decreases -> Ni-Co alloying on top of Pt(111) Co 53 and Ni 102 decrease while Pt 237 increases -> Ni-Co alloying with the Pt surface Co 656 and Ni 848 decrease while Pt 237 increases -> Ni-Co alloying with Pt bulk C. S. Shern et al. Phys. Rev. B 70, 214438 (2004)
XPS and UPS Exciting particle -> photons Emitted particle -> electrons X ray photons (0.2 2 kev) -> to investigate core levels UV photons (10-45 ev) -> to investigate valence levels Photoelectron spectroscopy is based upon a single photon in/electron out process. The energy of a photon is given by the Einstein relation : E = h ν h - Planck constant ( 6.62 x 10-34 J s ) ν frequency (Hz) of the radiation Free atom Atom in a solid E kin E kin E vacuum E bond E bond W s = work function E kin = hν -E bond E kin = hν W s -E bond
Experimental Details 1) source of fixed-energy radiation (an x-ray source for XPS or, typically, a He discharge lamp for UPS) 2) electron energy analyzer (which can disperse the emitted electrons according to their kinetic energy, and thereby measure the flux of emitted electrons of a particular energy) 3) high vacuum environment (to enable the emitted photoelectrons to be analyzed without interference from gas phase collisions) Detectors: CMA or hemispherical analyzer V out V in r out Only the electrons satisfying the relation: V out V in = E e (r out /r in -r in / r out ) move through the analyzer e - r in
Laboratory photon sources X-rays: electron beam impinging at energies of 10-50 kev on an anode excites the core electron of the anode -> during the relaxation photons are emitted Mg K α E = 1253.6 ev ΔE = 0.7 ev Al K α E = 1486.6 ev ΔE = 0.9 ev UV-rays: discharge in a lamp containing rare gas at low pressure (0.1 mbar) -> during the relaxation photons are emitted He I E = 21.2 ev ΔE = 0.01 ev He II E = 40.8 ev ΔE = 0.01 ev Ne I E = 16.9 ev ΔE = 0.01 ev Photon penetration depth > 1-10 μm -> the surface sensibility is given by the reduced mean free path of the out coming electrons
XPS Spectrum 2 ML MgO/Fe Energy (ev) Sensibility to Auger transition To distinguish between photo-electrons and Auger-electrons is sufficient to take two spectra at different energies: XPS -> the energy of the out coming electron depends on hν Auger -> the energy of the out coming electron depends on the core transition
UPS Spectrum MgO is an insulator with a gap of 8 ev Fe electronic structure -> 3d 6 4s 2 d - band Intensity (arb. un.) He 2 40.8 ev Fe 3d Bonding energy (ev) Shift of the 3d Fe peak following MgO deposition -> Fe oxidation O 2 dose He I UP spectra of the pure Fe film and after its exposure to various oxygen doses at 300 K. Sicot et al. Phys. Rev. B 68, 184406 (2003) K. Ruhrnschopf et al. Surf. Sci. 374, 269 (1997)
ARUPS: Angle Resolved UPS Measure of the dispersion relation (energy vs wave vector) of surface states i.e. the band structure of a surface. Three-step model: 1) The electron is excited from an initial to a final state within the crystal; 2) The electron travels through the solid towards the surface; 3) The electron crosses the surface and is emitted into the vacuum with a certain kinetic energy. Measurement of the dispersion curve requires a determination of the wave vector of the emitted photoelectrons. The wave vector has a component both parallel and perpendicular to the surface, so that the kinetic energy of the photoelectron should be written: Measuring the photoelectron intensity as a function of E and θ one gets the dispersion relation
Relationship between the k outside (value of the photoelectron in vacuum outside the crystal) and the value of k inside (of the electron in the solid) Elastic scattering -> E kin = hν -W s -E bond Momentum conservation: the photon momentum is negligible and thus the electron s final momentum must equal its initial momentum in the solid. p e = (2mE) 1/2 -> ~ 4 10-25 for 1 ev electron p hv = E/c -> ~ 3 10-28 for 1 ev photon However, the photoelectron must, after traveling through the solid, traverse the surface into the vacuum. The surface represents a scattering potential with only 2D translational symmetry. As for LEED, the electron will be scattered by a reciprocal lattice vector of the surface. Thus, the relationship between the photoelectron s wave vector in the solid and in vacuum is: k outside = k inside + G s where G s is a reciprocal lattice vector of the surface. Note that, the component of wave vector perpendicular to the surface is not conserved. Thus, from a measurement of the energy and emission angle of the photoelectron the value of k within the solid can be determined.
UPS Spectrum UV photons (10-45 ev) -> to investigate valence levels Note: You can measure the wave vector k and the energy at the same time (band structure) With STM only access to the DOS (density of state as a function of energy, but no information on k)
Surface State The surface states are localized at surface -> k ~ 0 E s = E F E 0 + 1/2m* (ħk) 2 m* -> effective mass of the surface state electron Conduction electrons behave likes a 2D gas of free electrons
Surface states on Au(788) // to the steps to the steps L = terrace size = 3.8 nm One dimensional quantum well of size L perpendicularly to the steps Ψ k (r) exp(ik // y) cos(k x) k = nπ/l E n = E F E 0 + n 2 /2m* (ħπ/l) 2 A. Mugarza et al., Phys. Rev. Lett. 87, 107601 (2001)
Carbon based material Electronic structure: 1s2 2s2 2p2 Diamond: sp3 bonding Graphite: sp2 bonding
Graphene Graphene is an atomic-scale honeycomb lattice made of carbon atoms. Nature Materials 6, 183 191 (2007) graphene: E k Free electron gas: E k 2