2 What affects Lineshapes? Intrinsic lineshape:spin-orbit couplinglifetimeFinal state effects:Satellites,VibrationsInstrumental broadening:Analyser,SourceDifferent chemical states.
3 Lifetime BroadeninghνPhotoemissionSecondary processThe core hole is filled by a ‘secondary process’ (Auger or X-ray emission). Finite lifetime of core hole τ (10-16 – s)The outgoing electron ‘knows’ about the lifetime of the core hole.Heisenberg’s relation: τ · ΔE ≈ h/π (ΔE = 1.3 eV for τ = s)
4 Lifetime - Lineshapeτ = 1x10-15sDecay of core hole is exponential: |Ψ(t)|2 exp (-t / τ)This causes a Lorentzian energy distribution of photoelectrons: L(E) [(E-E0)2 + Γ2]-1 (FWHM = 2Γ)FWHMΓ = 1eV
5 Lifetime Lifetime decreases with increasing BE FWHM increases with increasing BEExample C1s and O1s of COAdditional lifetime broadening through Coster-Kronig processes:C.K.: vacancy is filled by an electron from a higher sub-shell of the same shell.Super-C.K.: emitted Auger electron is also from the same shell (e.g. L1L2L3).Not possible for lowest sub-shell with lowest BE (always narrowest).L3L2Same ShellL1C.K. Auger process
7 Lifetime Lifetime decreases with increasing BE FWHM increases with increasing BEExample C1s and O1s of COAdditional lifetime broadening through Coster-Kronig processes:C.K.: vacancy is filled by an electron from a higher sub-shell of the same shell.Super-C.K.: emitted Auger electron is also from the same shell (e.g. L1L2L3).Not possible for lowest sub-shell with lowest BE (always narrowest).L3L2Same ShellL1C.K. Auger process
8 Lifetime Example: Pt4f, Pt4d Pt4f: lowest BE in N shell; FWHM ≈ 1eV Pt4d: Super C.K. (through 4f); FWHM≈4eVPt4d5/2Pt4f
9 Spin-orbit (LS) Coupling The spin of the excited (missing) electron combines with the angular momentum of the orbital to a total angular momentum J = L - ½ or L + ½.Two peaks observedonly L > 0p orbital (L = 1): J = 1/2 or 3/2; p1/2 and p3/2d orbital (L = 2): J = 3/2 or 5/2; d3/2 and d5/2f orbital (L = 3): J = 5/2 or 7/2; f5/2 and f7/2Energy difference (splitting) increases with increasing BE.decreases with increasing LBE(L+½) < BE(L-½)L-½L+½
10 Spin-orbit (LS) Coupling Multiplicity 2J+1: J, J-1, … , -J+1, -J Number of quantum states with same J. (e.g. J = 3/2: 3/2, 1/2, -1/2, -3/2).Intensity ratio between (L+½) and (L-½) is (2L + 2) / 2L = (L+1) / L.(L+½) state is more intense and narrower (see later)L-½L+½BE
11 Pt 4d, 4f and 5p levels Pt4d Pt4f Pt5p3/2 Pt4f Pt4d Pt5p3/2 Med L, high BE: large LS splitting (17eV)Super C.K: large FWHM (4eV)High L, Low BE: small LS splitting (3.3eV)C.K for 4f5/2: larger FWHM (1.3 vs 1.1eV)Low L, Low BE: large LS splitting (24eV)Super C.K: large FWHM (4eV)
12 Final State Effects Secondary electron energy losses: electronic transitions with well-defined energy (satellites)PlasmonsIntra-band transitions (continuous energy)Vibrational (‘vibronic’) excitations.
13 Secondary electron energy losses ‘Shake up’‘Naïve Picture’:Photoelectron interacts with other electrons on its way out and loses energy.Lower kinetic energy: additional intensity at BE higher than the actual peak.Possible excitations:Excitons (electron hole pair): between bands: narrow satellite peak (shake up). within the same band (metals): asymmetric broadening of main lineElectron emission (shake off): broad satellite peak.Plasmons (collective excitation of all electrons): series of narrow satellite peaks with the same energy separation.Photoelectron‘Shake off’Photoelectron
14 Secondary electron energy losses CO on AlShake offPlasmonShake off
15 Secondary electron energy losses Examples Ni 6 eV satellite disappears when Ni is diluted in CuMetallic Cr: asymmetric peakOrgano-metallic compound: symmetric peak
17 Vibronic excitationsExcitation of molecular vibration in connection with photo-ionisation.Sometimes resolved as shoulders (isotopic difference!).Mostly just seen as additional asymmetric broadening.ΔBE for vibronic excitation of C6H6 is √2 x that of C6D6
18 What affects Lineshapes? Intrinsic lineshape:spin-orbit couplinglifetimeFinal state effects:Satellites,VibrationsInstrumental broadening:Analyser,SourceDifferent chemical states.
19 Instrumental Broadening Instrumental broadening is caused by:Finite analyser resolution,Band width of X-ray sourceUsually modelled by Gaussian line shape (normal distribution)The observed spectrum is a convolution ofintrinsic line (Lorentzian shape),final state effects (e.g. asymmetry, satellites)instrumental broadening (Gaussian shape)Additional broadening can be caused by inhomogeneous distribution of chemical states.
21 Voigt Function Convolution of Gaussian and Lorentzian. Often Approximated by Sums or products of Gaussian and Lorentzian functions.GL mix defines how ‘Gaussian’ or ‘Lorentzian’ the function is.Asymmetry can be added through exponential decay function (exp(-α·E) ) at the high BE side of the peak.
22 Background Step-like background shape at peak position. Each photoemission line contributes to secondary electrons at lower kinetic energies.In general proportional to peak intensity.Long-range structure of background due to inelastic losses.Very noticeable at low kin. energies.Usually not important for short (high res.) spectra.
23 Background Simple background functions Shirley (step-like) Linear Quadratic B(E) = Eoff + a·E + b·E2Shirley (step-like)Background is proportional to integral over peak up to the point where background id determined S(E) = Eoff + a·∫0 to E I(E’)dE’Strictly, S(E) is found by iterative approachCan be approximated by analytical function.
24 Background Tougard background Use experimental (parametrised) electron energy loss spectrum.Only important for accurate quantification of element concentration.Very similar to Shirley background near peaks
25 Peak Fitting Spectra consist of Peaks Background Position Height Width (FWHM)(GL mix, Asymmetry)BackgroundOffsetLinear, quadratic coefficientsShirley parameter
26 Peak Fitting – General Rules Determine number of peaks needed fromchemical formula,literature,common sense.R-factor / Chi square = quality of fit (should be small).Optimisation uses search algorithmCan be trapped in local minimum.Use different sets of start parameters.As many fit parameters as necessary as few as possible.Use constraintsDetermine peak parameters from related data
27 IGOR Practice session - 1 Create a wave E_axis representing 201energy data points ranging from 90 – 110 eV. (Use the make command of IGOR)Create waves Gaus_1 and Lor_1 (201 data points) containing Gaussian and Lorentzian peaks with peak positions at 100 eV and FWHM = 4eV and height Use E_axis for the energy values.Add linear backgrounds to both curves (and save in Gaus_2 and Lor_2)
28 IGOR Practice session - 1 make \n=201 E_axis E_axis =duplicate E_axis Gaus_1 Gaus_1 = 100 * exp( -(E_axis – 100)^2 *4*ln(2)/ 4^2 ) duplicate E_axis Lor_1
29 LiteratureS. Hüfner, ‘Photoelectron Spectroscopy’, Springer. Good general Text book (more UPS than XPS)CASA XPS manual (from Internet). Contains a good selection of actual formulaeBriggs and Seah, ‘Surface Analysis’ General text book, more emphasis on quantitative element analysis.