manual of igor pro - sorbonne-universite.fr · 2021. 4. 9. · manual of igor pro paris...

Manual ofIgor Pro Paris Photoemission Package

Remi Lazzari

Institut des NanoSciences de ParisCNRS UMR 7588 / Sorbonne Universite4 Place Jussieu, F-75005 Paris, France

[email protected]

April 8, 2021

The IGOR Pro Paris Photoemisssion Package (I4P) has been developed by R. Lazzari (CNRS,[email protected]) to load, display, analyse and fit photoemission data, mainly from lab-oratory sources (Al-Kα, Mg-Kα, He I/II). The core of the package is based on a strongly revisedXPSmania procedure by F. Bruno [1]. It is intended for fitting with various line shapes the followingtypes of experimental data:

• X-ray Photoemission Spectroscopy (XPS; core levels);

• Ultraviolet Photoemission Spectroscopy (UPS; Fermi or work function edges);

• Ion Scattering Spectroscopy (ISS)/Low Energy Ion Spectroscopy (LEIS) (energy loss to massscale);

• Electron Energy Loss Spectroscopy (EELS).

Number of peaks, line shapes, fitting constraints are handled in a smart way via a peak booklet. Agraph windows is used to visualize fit quality and a full report is accessible as text file. Batch fit aswell record of fit templates are also possible.Treatments such as peak overlap, transmission function correction, background subtraction, sourcesatellite deconvolution are also available. The package is associated with a database of (i) corelevels and Auger lines for peak identification and (ii) of photo-ionization cross sections. Inelastic andtransport mean free paths as well as effective attenuation lengths can be calculated from predictiveformula and a material database. Film thickness and concentration can be evaluated from peak areas.Command lines for some common tasks are available.

CONTENTS

1 Forewords 1

2 The I4P Load/Plot menu 22.1 Load Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22.2 Plot spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22.3 Overlap peaks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22.4 Binding to kinetic energy / Kinetic to binding energy . . . . . . . . . . . . . . . . . . 32.5 I4P graph style . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

3 The I4P Analysis menu 43.1 Peak characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43.2 Get BE-KE-AP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43.3 Shift binding energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43.4 Correct from transmission function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43.5 Get transmission function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43.6 Subtract background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53.7 Subtract satellites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53.8 Deconvolute satellites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53.9 Remove ghost lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63.10 Ion Scattering Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

4 The I4P Database menu 74.1 Periodic table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74.2 Find peaks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84.3 Mean free paths and EALs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84.4 Quantification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94.5 Clean I4P Database . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

5 The I4P Fit menu 125.1 Starting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125.2 Loading spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125.3 Data fit graph . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145.4 Peak manager panel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

5.4.1 Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155.4.2 Background and resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165.4.3 Peak parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185.4.4 Peak parameters for step functions . . . . . . . . . . . . . . . . . . . . . . . . . 205.4.5 Columns in the table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

5.5 Fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

CONTENTS

5.6 List of peak profiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225.7 Manage fit from an existing I4PFit folder . . . . . . . . . . . . . . . . . . . . . . . . . 26

6 The I4P Help menu 276.1 Clean all . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276.2 Help Command . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

6.2.1 Background corrected area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276.2.2 Correction from analyzer transmission function . . . . . . . . . . . . . . . . . . 286.2.3 Photo-ionization cross section . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286.2.4 List of closest core levels and Auger transitions . . . . . . . . . . . . . . . . . . 296.2.5 Inelastic mean free path from ”universal” equation . . . . . . . . . . . . . . . . 296.2.6 Transport mean free path from Jablonski’s databases . . . . . . . . . . . . . . . 296.2.7 Effective attenuation lengths or emission depth distribution function . . . . . . 306.2.8 Surface excitation parameter . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

6.3 Help Plot Command . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 306.3.1 I4P Fit command . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 306.3.2 Load a Vamas file from command line . . . . . . . . . . . . . . . . . . . . . . . 316.3.3 Resize a spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 316.3.4 Convert a spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 316.3.5 Shift the binding energy scale of a spectrum . . . . . . . . . . . . . . . . . . . . 326.3.6 Convert a spectrum from usual binding energy scale to kinetic energy scale . . 326.3.7 Parameters of all background corrected spectra in the top graph . . . . . . . . 336.3.8 Plot of the inelastic electron scattering cross section . . . . . . . . . . . . . . . 33

6.4 Help I4P . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 336.5 About I4P . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

7 Annex 357.1 List of wave extension used in I4P . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 357.2 Spin-orbit splitting of atomic levels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 367.3 Spectroscopic notations of atomic levels . . . . . . . . . . . . . . . . . . . . . . . . . . 367.4 Quantification in photoemission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 377.5 Tougaard background parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 387.6 X-ray satellite and ghost-lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 387.7 Portfolio of fits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

CHAPTER 1FOREWORDS

Users unexperienced with Igor Pro software should first take the ”Guided Tour” at the beginning ofIgor Pro manual.

I4P should work for version 6.3.7 of Igor Pro or above. The whole set of I4P procedures shouldbe placed in the Igor Pro user procedures folder:

C:\Users\UserName\Documents\WaveMetrics\Igor Pro 6 User Files\User Procedures.

I4P will be loaded with the command #include ”I4P” in a procedure windows followed by compi-lation. Alternatively, the file ”I4P.ipf” can be put in the folder:

C:\Users\UserName\Documents\WaveMetrics\Igor Pro 6 User Files\Igor Procedures,

so that the package is automatically loaded at Igor Pro start up.Several menus will be created: I4P Load/Plot, I4P Analysis, I4P Database, I4P Fit and I4PHelp. The present package creates an internal Igor Pro subfolder root:I4P: that should not bemodified to avoid any potential crash.

The Igor Pro wave scaling is exploited for spectra. Data are systematically stored by evenlyspaced increasing binding energy or energy loss (units eV). All available informations contained inthe input file (such as excitation energy, step, instrument, pass energy, etc. . . ) are included as wavenotes. Treated spectra are labelled with specific wave extensions as given in Annex 7.1. Integrationand convolution are performed numerically and therefore may depend on energy step and range;oversampling and wide energy range are advised for meaningful calculations.

Hereafter, EB and EK will stand for the binding and kinetic energy, respectively.

1

CHAPTER 2THE I4P LOAD/PLOT MENU

2.1 Load Data

The menu Load File is used to load ASCII photoemission data, in either the (*.vms) Vamas [6],the (*.xy) SpecLabProdigy or the (*.txt) EIS Omicron format. Other kinds of file format couldbe handled upon request to the author. Multiple files can be selected. For each file, an Igor Prointernal folder that contains all spectra is created. If required, binding energy waves (wave BE),transmission function waves (wave TF) and transmission function corrected data (wave TFC) canbe created. Data are systematically normalized to number of sweeps and counting time (units cps);they are stored by increasing binding energy or energy loss (units eV).A pair of energy and counts waves supplied by the user can be converted to a formatted spectrum(wave CON) suitable for treatment by the present package through the submenu Convert to spec-trum. Data do not need to be evenly spaced or sorted in energy; they are interpolated with aconstant energy step.

2.2 Plot spectra

The menu Plot spectra will plot as function of binding energy the selected spectrum or all spectracontaining a given string (i.e. ”*C1s*”) in the current folder.

2.3 Overlap peaks

The menu Overlap peaks is useful for comparison of spectra line shapes. On the top graph, it willoffset all the plotted traces on a given master trace selected through cursors A and B. Three overlapoptions are possible: (i) on the background (on the low binding energy side of the peak) and on thepeak position/maximum in between cursors A and B, (ii) on the background through subtraction or(iii) on the background through a multiplication. If selected, all traces can be offset on the mastertrace or to a target binding energy; this option is useful to get rid of charge effect. Backgroundoffset is defined by averaging over a given windows around background cursor binding energy; thecharacteristics of the peak (position and intensity) in between cursors are obtained through a parabolicfit over a given windows around peak maximum. Data are not modified; only traces are shifted. Ifselected by the user, wave differences are calculated over the common binding energy windows betweenthe master trace and the shifted ones. Corresponding waves ( SUB) are stored in the folder of thetrace and eventually plotted. At last, following their initial order in the graph, all traces can be shiftedvertically for clarity by a given fraction of the master peak background-to-maximum amplitude.

2

CHAPTER 2. The I4P Load/Plot menu

2.4 Binding to kinetic energy / Kinetic to binding energy

The menu Binding to kinetic energy / Kinetic to binding energy changes the bottom axisof the top graph from binding (kinetic) energy to kinetic (binding) energy scale. Only offsets areapplied to all traces of the graph. Wave scalings are left untouched.

2.5 I4P graph style

The macro XPS graph style, ISS graph style and Auger graph style modify the layout ofa graph for XPS/UPS, ISS and Auger data, in particular with a reverse binding energy scale inphotoemission or a mass scale.

CHAPTER 3THE I4P ANALYSIS MENU

3.1 Peak characteristics

From the top graph, the menu Peak characteristics gives information in the command windowson the peak bounded by the two cursors A and B. Accuracy is limited by the energy step.

3.2 Get BE-KE-AP

From the top graph, the menu Get BE-KE-AP gives in the command line the positions in bindingand kinetic energy as well as the Auger parameter of the two cursors A and B. Accuracy is limitedby the energy step.

3.3 Shift binding energy

The menu Shift binding energy applies a shift of the binding energy scale to the selected waves inthe current data folder. This option is useful for correcting analyzer work function calibration, forpolarized sample measurements in UPS or EELS measurements. Wave scalings of the data as wellas * BE waves and optionally the excitation energy are modified.

3.4 Correct from transmission function

The menu Correct from transmission function creates, either from the wave pointed by cursorA on the top graph or from the current data folder, spectra corrected from the transmission functionTf of the analyzer. In FAT (Fixed Analyzer Transmission) or CAE (Constant Analyzer Energy),Tf = (hν/2EK)n where the exponent n is user given. In FRR (Fixed Retardation Ratio) or CRR(Constant Retardation Ratio), Tf = 2EK/hν.

3.5 Get transmission function

The menu Get transmission function estimates the exponent n of the transmission functionTf = (hν/2EK)n by seeking at the minimum between a transmission function corrected spectrumand its Tougaard background (Eq. 5.5 and Tab. 7.2; see below for choices). The analysis is applied tothe trace of the top graph between cursors A and B. The analysis should be applied preferentially ona FAT wide spectrum on the largest energy range to increase accuracy. A spectrum of a bulk materialwith a few transitions and clearly isolated background ranges is preferred (i.e. pure element).

4

CHAPTER 3. The I4P Analysis menu

3.6 Subtract background

The menu Subtract background removes a background from a spectrum of the top graph as pointedby cursors A or B. One of the two cursors can be free. Background wave (wave BG) and backgroundcorrected data (wave BGS) between cursors are created in the spectrum folder and plotted in the topgraph. Informations are given in the command history, in particular the peak area.Several choices are available with background pinned on cursors (i.e. background=data on cursors)or with user fixed parameters:

• Shirley: Shirley integral background [39] (Eq. 5.3);

• Generalized Shirley: Generalized Shirley background following the slope background ofRef. [11] (Eq. 5.4);

• Tougaard : Tougaard integral background [43,44] (Eq. 5.5); parameters are fixed at tabulatedvalues from Refs. [36, 37,43] or user given;

• Distorted Shirley: Distorted Shirley background [46,47] (Eq. 5.6); parameters are user given;

• Blend : a blend of Generalized Shirley, Tougaard and linear backgrounds (Eqs. 5.3, 5.4, 5.5)with Generalized Shirley (Sh, Sl, Sb), Tougaard (B,C,D,G) and linear slope (Ls) parametersas given by the user;

• Linear: linear background between cursors (Eq. 5.2);

• None: no background, but useful to extract a subwave between cursors;

For Tougaard background, a dropdown menu allows to select the universal value of the two-parametersloss function [36,37,43,44] (B = 3006 eV2; C = 1643 eV2) 1, the B−C that are element specific [36,37]or the three-parameters loss function B,C,D for some peculiar materials [43, 44]. Used values aregiven in Tab. 7.2. Gap (G; Eq. 5.5) is user given. A list semi-column separated values should beentered for user given parameters. The adaptation of the prefactor (Sh, B,Bs) of integral backgroundspinned on cursors requires a higher intensity at higher than lower binding energy. It is performediteratively until preset convergence thresholds.

3.7 Subtract satellites

The menu Remove satellites operates in a similar way as the Remove background menu but forthe satellite of the source (Mg-Kα, Al-Kα or He I/II). The contribution of the satellites are actuallysubtracted assuming the same Full-Width at Half-Maximum (FWHM) for all source lines. Valuesof the relative intensities and positions of the Kα3,4,5,6 −Kβ lines relative to the sum and centroidof Kα1,2 are extracted from Ref. [25, 26, 48] (Tab. 7.4-7.3). Approximate (depends on gas pressure)He line satellites He Iβ, He Iγ, He IIα, IIβ, IIγ can also be subtracted for a given ratio He II/He I.Satellite wave (wave SA) and satellite subtracted data (wave SAS) are automatically created in thedata folder.

3.8 Deconvolute satellites

The menu Deconvolute satellites removes satellites of the source (Mg-Kα, Al-Kα or He I for a givenratio He II/I) through actual deconvolution and not through subtraction as in the previous menu. Itcan also improve the apparent resolution. Resolution function is defined as a sum of lorentzian peakscorresponding to Kα1,2,3,4,5,6 −Kβ lines (which values of relative intensities, positions and FWHMsare extracted from from Refs. [25, 26, 48]; see Tab. 7.4-7.3) convoluted by an apparatus Gaussianfunction of given FWHM. The division of the Fourier transformed spectrum by that of the resolutionfunction is performed with or without Wiener filtering to prevent noise amplification. Spectrum is

1The B = 3006 eV2 value determined given by Seah [36] instead of that of Tougaard [43] (B = 2866 eV2) is takenfor the universal B-parameter.

CHAPTER 3. The I4P Analysis menu

reconvoluted either by a Dirac peak, by the Kα1 line only or by the Kα1+Kα2 line sum. The firstcase enhances resolution but requires Wiener filtering and in general an oversampling of the data;for this latter, noise is estimated through fitting over a moving windows. Removal/deconvolution ofsatellites is not valid for Auger lines. Deconvoluted data (wave SAD) and the difference spectrum(wave SA) are automatically created in the data folder.

3.9 Remove ghost lines

The menu Remove ghost lines is similar to the menu Remove satellites but for the ghost-linesof the X-ray source. The intensity ratio between the ghost lines (Al/Mg-Kα, O-Kα, Cu-Lα) to themain line should be given by the user (Tab. 7.6). Ghost line wave (wave GL) and subtracted data(wave GLS) are automatically created in the data folder.

3.10 Ion Scattering Spectroscopy

The menu Ion Scattering Spectroscopy is used in case of ISS/LEIS. Knowing the scattering angle,the incident ion mass and its kinetic energy, it converts the energy loss scale of selected waves to themass scale of atoms from which ions have been scattered off [30]. A new scaled wave (wave ISS) iscreated by regularly interpolated data on mass scale and optionally the full mass scale (wave MA).

CHAPTER 4THE I4P DATABASE MENU

4.1 Periodic table

The menu Periodic table launches an interactive periodic table (Fig. 4.1). When clicking on agiven element, its core levels and Auger transitions for the selected X-ray source are displayed aslabelled bars in the top graph. Their intensities are proportional to the relative sensitivity factor(RSF), the normalization being done on C 1s at Al-Kα excitation and magic angle of the X-ray source(ψm = 54.74◦). RSF is the product (i) of the photoionization cross section corrected from asymme-try at the selected (unpolarized) source/analyzer angle [Angle (deg)] and (ii) of the transmissionfunction of the analyzer given by 1/EnK where n is the selected exponent [Trans. func. exp.]. Theinformation regarding each chemical element can be displayed in the command line windows of IgorPro with option Print info. The option Auger allows plotting the Auger lines for a given elements;no relative intensity is evaluated for such lines. Satellites and ghost lines lines of core levels for anunmonochromated source can be shown with the options Ghost lines, Satellites (Tabs. 7.3-7.6;values are plotted in the table order). The button [Plot] displays a self-standing plot of the spec-troscopic fingerpints of the selected elements. The button [None] cleans the top graph. The useddatabase are from Ref. [28] for binding/kinetic energies, satellites, ghost lines and from Ref. [49] forthe cross-sections and asymmetry parameters.

1.2

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Al L23M1M23

Fe 2s

Fe 2p1/2

Fe 2p3/2

Fe 3sFe 3p

Fe LM23M23

Fe L3M23M45(1P)

Fe L3M45M45

''Wide scan''

Figure 4.1: Periodic table menu: (top) panel with options of X-ray source, source/analyzer angle andinformation printing (bottom) an example of graph display.

7

CHAPTER 4. The I4P Database menu

4.2 Find peaks

When clicking on the Find peaks menu or the corresponding button of the Periodic table manager,a list of the closest core levels and Auger transitions (within ±1.5 eV) to the cursor A of the top graphis displayed in the command line windows and on the top graph. Otherwise the closest transitionsare given. The tool takes into account the offsets of the trace on which the cursor is placed.

4.3 Mean free paths and EALs

The menu Mean free paths and EALs launches an interactive calculator (Fig. 4.2) for:

• the inelastic mean free path λi (IMFP in A) from TTP2M [38,40,41] or Gries [10] ”universal”equations;

• the transport (or elastic) mean free path (TRMFP in A) λtr from the transport theory (calcu-lations of Jablonski : Ref. [15]: database 1; Ref. [21]: database 2 recommended for compounds;Ref. [17]: database 3 recommended for pure elements);

• the albedo factor ω = λi/(λi + λtr) used in the kinetic Boltzmann equation in the transportapproximation [19];

• the mean escape depth (MED in A) [20];

• the effective attenuation lengths (EAL in A) of a bulk, a film and a marker as defined anddetailled in Ref. [19];

• the surface excitation parameter (SEP) S [32, 33].

Figure 4.2: Mean free paths, effective attenuation lengths and emission depth distribution func-tion panel manager.

Calculations are performed from a material database [42] at the kinetic (or binding energy) given bythe user. As a side product, the molar density (mol.cm−3) of the material is displayed. The anglesα,ψ, θx (deg) between the directions given by sample normal/analyzer, analyzer/X-rays, samplenormal/X-rays respectively, as well as the asymmetry factor β [49] of the considered core level, arerequired in the calculations of EALs [19]. These latter are obtained for a bulk, a film of user giventhickness or a marker at user given depth; these practical EALs are those used in quantification(see Sect. 4.4). Calculations can be performed with different approximations for the Chandrasekharfunction required in the kinetic Boltzmann equation in the transport approximation: (i) Refs. [16,19]:integral (more accurate but time consuming), (ii) Ref. [5]: approximate 1(accurate up to a few %),


35Å

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Material : Ag IMFP TRMFP MED EAL(bulk) EAL(film) EAL(marker)

ID(95.000%) = 36.02 ÅEAL(ave) = 12.39 ± 0.29 Å

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Material : Ag CF

Figure 4.3: Examples of plots of EALs as function of (i) kinetic energy or (ii) of thickness and (iii) EDDF or(iv) CF versus depth.

(ii) Ref. [5]: approximate 2(accurate up to a few %), (iii) Ref. [5]: approximate 3(accurate up to a∼ 0.1 %), (iv) Ref. [23, 24]: approximate 4 (polynomial approximation accurate up ∼ 10−6). Whiledisplayed values are calculated at a given kinetic energy or thickness/depth, all quantities can beplotted as function of these variables but a the expense of CPU time (Fig. 4.3). In particular, inthe case of a film, the plot of EAL as function of thickness gives access to the average value andthe information depth (ID) defined up to a threshold given by the user [19]. The emission depthdistribution function (EDDF) [19] and the ratio of EDDF with to without elastic scattering (CFfunction) [22] can also be visualized (Fig. 4.3).

4.4 Quantification

The menus Quantification (see Annex 7.4) are used to determine [8]:

• a film thickness (i) from a ratio of core level areas of the substrate and of the film (QuantificationFilm|Substrate) or (ii) from the relative damping of two substrate lines in the film (QuantificationSubstrate|Substrate);

• the composition of a perfect semi-infinite alloy (Quantification Alloy).


Three film geometries are available: (i) a continuous layer geometry, (ii) pancakes of constant thick-ness or (iii) hemispheres of same radius covering a fraction of the surface (Fig. 4.4). On calling, aninteractive panel with parameters to fill (Fig. 4.5) is opened. Since only ratios are considered, theunits (as soon as they are the same) are of poor importance, except for lengths. Once the tableis modified, results of dichotomy search (up to the selected accuracy) or of direct calculation aredisplayed in the panel in red. Parameters and results of quantification can be saved to or loaded froman Igor Pro formatted (*.itx) text file through the corresponding buttons.

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α

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Figure 4.4: Morphology used in theQuantification menu: a) continu-ous thin film; b) film of pancakes;c) film of hemispheres; d) homo-geneous alloy. The substrate maybe covered by a continuous layer ofthickness tl

For substrate and film core levels (Quantification Film|Substrate and Quantification Substrate|Substrate),the required parameters are (Fig. 4.5):

• user informations about used core levels for substrate and film;

• peak areas;

• transmission functions of the analyzer at the considered kinetic energies; a good estimate is1/EK [34]; one can encompass the detector efficiency in this value;

• photoionization cross sections; values can be found in Ref. [49] and calculated from Periodictable menu or the command line (Sect. 6.3.1);

• effective attenuation lengths [19] (in A) of the substrate photoelectron in the bulk of the sub-strate (bulk EAL) and in the film (practical EAL(film)) and (ii) that of the film photoelectronin the corresponding bulk (bulk EAL) and in the film (practical EAL(film)) (see Ref. [18]);values can be obtained from Mean free paths and EALs menu using universal formulaand the kinetic Boltzmann equation in the transport approximation (Fig. 4.2); when used in-stead of IMFP in the exponential damping of signal used in the quantifiquation equations (seeAnnex 7.4), EALs allow accounting for elastic scattering; if one wants to account only frominelastic damping, one should enter the same values for bulk and film EAL;

• surface excitation parameters of substrate or film photoelectron at each crossed interfaces;values for material/vacuum interface can be estimated from the calculator (Fig. 4.2);

• atomic concentration; can be given as the ratio of bulk density to molar mass (mol.cm−3, seeFig. 4.2);

• coverage (0 < Θ < 1); fraction of the surface covered by pancakes or hemispheres; the equationsare valid only in normal emission geometry;

• sample normal/analyzer angle (in deg);

• overlayer thickness; in case of a substrate already covered by a first film (see Fig. 4.4);

• effective attenuation length (practical EAL(film)) of the substrate photoelectron in the overlayermaterial.


Figure 4.5: Quantification panel managers: a) Film thickness from a ratio of film and substrate core levelareas; b) Film thickness from the damping of two core levels of the substrate through a film; c) Compositionof an homogeneous alloy.

As a side product, the stoichiometry for an alloy made of ”substrate” and ”film” materials is alsogiven (Fig. 4.4-d).

For a perfect semi-infinite alloy with an arbitrary number of elements (Fig. 4.4-d), similar pa-rameters for each element are required in the form of a list in panel (Quantification Alloy). Thecorresponding composition element per element (in %) is given as an output.

4.5 Clean I4P Database

The menu Clean I4P Database kills the periodic table, quantification and IMFP-TPP2M panelsas well as the corresponding folders.

CHAPTER 5THE I4P FIT MENU

The I4P Fit procedure is based on a strongly revised initial version developed in 2006 by F. Bruno.When fitting experimental data requires a large set of parameters and special line shapes such asin photoemission, the Igor Pro built-in peak fitting routine becomes rather unpractical. I4P Fitprovides a user friendly and efficient interface where the fitting function can be initialized from adatabase of peaks in order to create a convenient starting curve for the data interpretation. Duringthe actual fitting process, the user is then given the possibility to control in detail all the parametervalues, limits and mutual constraints in a meaningful way. Background is fitted actively [12]. Alist of examples of fits of core levels and their corresponding templates is provided in the I4P Helpsubfolder of the I4P installation (see App. 7.7).

5.1 Starting

From the menu I4P Fit, Start I4P Fit will create two windows (I4P Fit/PEAK MANAGERand I4P Fit/DATA FIT) and initialize the fitting program by creating a folder :root:I4P:I4PFit.In a reverse way, the menu Clean I4P Fit will kill the windows and erase the folder and its contents.

5.2 Loading spectrum

To load experimental data from scratch, click on Load Spectrum button of I4P Fit/PEAKMANAGER and select the type of required error bars and remap step value (see below for defini-tion). To load from an existing graph, put two cursors on the trace to define the binding energy rangeand select Load from graph option from Load Spectrum windows. Error bars can be definedas constant, the square-root of intensity or from polynomial interpolation over a moving windows.The more accurate the error bars, the more meaningful the resulting χ2 reliance factor. To increaseaccuracy in integral calculations (integral background and convolution), data can be oversampledalong an user selected energy step. Data are then automatically loaded in I4P Fit.

Alternatively to load experimental data that need to be evenly spaced, use the command line

data load(wave be,wave counts,wave err,remap,folder,comment).

where:

• wave be is the experimental binding energy. It needs to be evenly spaced, but the minimumstep should not be zero or ridiculously small. Otherwise you will get an error message later. Ifthe binding energy scale is so uneven that you have ”zero” steps, use the remap option.

• wave counts is the signal;

12

CHAPTER 5. The I4P Fit menu

Figure 5.1: I4P Fit/PEAK MANAGER : (top) resolution and background windows and (bottom) anexample of peak parameters.

• wave err is the error bars of the signal. A non-zero wave is required;

• remap=0 leaves data untouched while with remap=positive, data will be loaded using anew (evenly spaced) binding energy scale with energy step=remap;

• folder is the data folder;

• comment is a data comment.

The data load function or Load Spectrum button put data into the following waves, whichare used for the fit:

• data be: binding energy, sorted from low to high binding energy;

• data counts: the count rate;

• data err: the error bars

• peak# : peaks (same lenght as data);

• bkr# : background per peak (same lenght as data);

• data fit: the fit curve;

• data res: the residual of fit;

• background tot: the total background.


5.3 Data fit graph

The windows I4P Fit/DATA FIT displays data and fit results:

• data counts: the user data;

• data fit: the global fit function i.e. the sum of peaks and of all backgrounds;

• background tot: the sum of polynomial and integral global backgrounds;

• peak#: background-free peak number #;

• bkr#: background of peak number #;

• data res : fit residuals normalized by error bars.

Figure 5.2: I4P Fit DATA FIT windows: data (circles), fit (red line), total background (grey line), peaks(shaded peaks), peak background (dotted line) and fit residuals normalized by error bars (top). Each peakis labelled on bottom scale.

5.4 Peak manager panel

The I4P Fit/PEAK MANAGER panel let you build up your fitting function in an user friendlyway.The buttons Load database and Save database can be used to load and save a specific peakdatabase configuration from an Igor Pro formatted (*.itx) text file on computer disk. Everythingis saved/loaded (peak types, parameters values, active peaks . . . ) but not the data/fit waves. Con-versely, the buttons Load data+fit and Save data+fit can be used to load and save data, peaksand fits but not the content of peak manager. To help user, some templates of fits are provided inthe I4P Help subfolder of I4P installation on the disk.Alternatively, both data, fit and peak manager content can be reloaded from an already saved I4Pfolder in the current Igor Pro experiment using the corresponding menu of I4P Fit (see Sect. 5.7).

The I4P Fit/PEAK MANAGER panel consists of a ”booklet” of peaks, which are indexedfrom n = 1, . . . , N . On the panel, a table and some other indications describe the details of one peakat a time, like a particular page of a booklet. Browsing between peaks is done through the backward[�] and forward [�] buttons. The maximum number of peaks in the browser is user selectable from


Number of peaks in database. The index n = 0 corresponds to intrinsic background and resolu-tion parameters. The RESET button reinitialize all parameters.

The ACTIVE checkbox is used to include/exclude the current peak from the calculation. Allthe parameters are left untouched when a peak is deactivated, so that it can be reincluded later onin a glimpse. The idea is to create a ”database” of peaks, and activate the ones that are needed atat a given moment. The n = 0 ”peak” (background and resolution) is always active. The numberof active peaks is also shown in the yellow area. You don’t need to change the Number of peaksin database value at all time. Just make it large enough so that you have a comfortable number ofpeaks to activate/deactivate. The maximum number is 15, but can be changed in the procedure itself.

For index n > 0, the peak line shape can be chosen through the Peak type variable among thefollowings:

1. Lorentzian/Voigt (Eq. 5.7,5.9)

2. Gaussian (Eq. 5.8)

3. Pseudo-Voigt (Eq. 5.10)

4. Lorentz X Gaussian (Eq. 5.11)

5. Oscillator (Eq. 5.12)

6. Doniach-Sunijch (Eq. 5.13)

7. Generalized Doniach-Sunijch (Eq. 5.14)

8. Mahan (Eq. 5.15)

9. Post-collision interaction (Eq. 5.16)

10. Asymmetric Voigt (Eq. 5.17)

11. Asymmetric Pseudo-Voigt (Eq. 5.19)

12. Fermi step (Eq. 5.19)

13. Work function step (Eq. 5.19)

14. Fano (Eq. 5.20)

15. Plasmon (Eq. 5.21)

16. Band bending Lorentz (Eq. 5.22)

17. Gadzuk-Sunjic (Eq. 5.23)

Their description also appears in the text box in the yellow panel. Their definitions are given inSect. 5.6 with the corresponding references to literature. Note that a given shape can be obtainedas a limit for several Peak type (e.g. Lorentzian). Peak label is an user editable tag to pinpointpeak position in the graph I4P Fit/DATA FIT windows.

5.4.1 Operations

The CALCULATE button performs the function calculation accordingly to the current sets of pa-rameters for active peaks. The FIT button performs the data fitting, using the value column asstarting point, and returns the optimized parameters and their variance in the fit value and sigmacolumns. After each fit run, the original starting point parameters are left untouched in the valuecolumn so that the fit will restart from there. Otherwise, the Update values button updates thefit value fitted values in the value column used for calculations. Note that useful informations are


shown in the command line of Igor Pro at each calculation/fit.

Calculation and fit are performed over the full range by default (only cursor A present) or betweencursors [A,B] of the graph. Convolution, if needed, is performed numerically by Fourier transformbased on the convolve operation of Igor Pro. Integration for background is based on trapezoidalintegration (integrate in Igor Pro); the accuracy depends on data spacing.

5.4.2 Background and resolution

The n = 0 Background and Resolution panel set the options and values used to define thebackground and the apparatus resolution.

• [0] Transmision func.: type of transmission function Tf applied to the whole spectrum andbackground, but not to individual peaks.

– 0 = None;

– 1 = FAT (Fixed Analyzer Transmission) or CAE (Constant Analyzer Energy) with Tf =(hν/2EK)n;

– 2 = FRR (Fixed Retardation Ratio) or CRR (Constant Retardation Ratio) with Tf =2EK/hν;

– 3,4 = same as option 1,2 but with Tf normalized by its average value over the scan range.

• [1] Photon energy: photon energy hν to define kinetic energy EK = hν − EB ;

• [2] Expo. trans. func.: exponent n of the FAT/CAE transmission function;

• [3] Broadening: choice of the instrumental broadening obtained by convolution. The broad-ening is applied to the whole spectrum and to the total background but not to the individualpeaks.

– 0 = None;

– 1 = Gaussian function;

– 2 = Gate (or slit) function;

– 3 = Gaussian broadening of a spectrum acquired in FRR/CRR mode;

– 4 = Triangle function.

• [4] Broad. FWHM: FWHM of the broadening function.

• [5] FRR/CRR slope: slope s of Gaussian FWHM broadening on kinetic energy FWHM =FWHM0+sEK ; typical for a spectrum acquired in FRR/CRR mode for which the pass energyscales with EK ;

• [6] Satellites: emission satellites of the excitation source (Kα1,2,3,4,5,6 and Kβ). The tabulatedpositions, intensities and FWHM values stored internally in wave satellites can be modifiedby the user but not fitted. Plus sign (+) option corresponds to a sum over satellites for eachpeak while minus (−) sign stands for an actual convolution (see Fig. 7.1 for explanations). Theintroduced peak area always includes all the satellites.

– 0 = None

– ±1 = Mg Kα: values relative to the average of Kα1+Kα2 lines with same FWHMs for allsatellites [48] (Tab. 7.3; Fig. 5.3-a);

– ±2 = Al Kα : values relative to the average of Kα1+Kα2 lines with same FWHMs for allsatellites [48] (Tab. 7.3; Fig. 5.3-b);

– ±3 = He I: values relative to He Iα (He II=0.02 %; can be changed internally) [2];

– ±4 = Mg Kα: values relative to Kα1 line only with actual FWHMs of all satellites [25](Tab. 7.4; Fig. 5.3-c);


1.2

1.0

0.8

0.6

0.4

0.2

0.0

Inte

nsity

-15-10-50510

Binding energy (eV)

0.6

0.5

0.4

0.3

0.2

0.1

0.0

Inte

nsity

-15-10-50510

Binding energy (eV)

0.6

0.5

0.4

0.3

0.2

0.1

0.0

Inte

nsity

-15-10-50510

Binding energy (eV)

1.0

0.8

0.6

0.4

0.2

0.0

Inte

nsity

151050-5-10

Photon energy (eV)

Leading X-ray line 1

FWHM s1

X-ray line 2

FWHM s2

FWHM

FWHM

0.6

0.5

0.4

0.3

0.2

0.1

0.0

Inte

nsity

-15-10-50510

Binding energy (eV)

FWHM

FWHM + FWHM s2 - FWHM s1

(a)

(b) X-ray source

Lorentzians

Main peak

(intrinsic +

leading X-ray line 1 )

Main peak

(intrinsic)

Final peak with satellites

Figure 5.3: Satellites management in I4P fit: (a) option> 0: sum of the main peak and of its satellites;the satellites are shifted in energy with the right tabulated relative area as compared to the main peak;their FWHMs are given by the sum of the main peak FWHM and the difference between tabulated satelitteFWHMs and that of the leading line (Kα1 or Kα1+Kα2); so the peak FWHM introduced in I4P correspondsto all broadenings plus that of X-ray source (Kα1 or Kα1+Kα2). (b) option< 0: convolution of the peak bythe sum of lorentzian X-ray source lines; the introduced peak FWHM corresponds to all broadenings exceptthat of the X-ray source. The most accurate and general option is the convolution; it theoretically doesnot depend on the selected peak line shape but it requires sufficient sampling in energy for accuracy at theexpense of calculation time, in particular for fits. In fact, the option> 0 is strictly valid only for lorentzianor Voigt peaks; it is an approximation for other line shapes.

– ±5 = Al Kα: values relative to Kα1 line only with actual FWHMs of all satellites [25](Tab. 7.4; Fig. 5.3-d);

– ±6 = Mg Kα: only Kα2 satellite (relative to Kα1 line) [25] (Tab. 7.4; Fig. 5.3-c);

– ±7 = Al Kα: only Kα2 satellite (relative to Kα1 line) [25] (Tab. 7.4; Fig. 5.3-d).

• [7-10] Cnt. bkgr, Lin bkgr., Sqr. bkgr, Cub. bkgr.: coefficients of the polynom back-ground always added to the total signal (Eq. 5.2);

• [11] Integral bkgr. type: type of selected integral background applied to the sum of all peaks;

– −1 = blend of generalized Shirley, Tougaard and distorted Shirley;

– 0 = no integral background;

– 1 = generalized Shirley background (Eq. 5.4);

– 2 = Tougaard background with a two-parameters loss-function (Eq. 5.5);

– 3 = same as option 2 but with B such that the loss function is normalized to one;

– 4 = Tougaard background with a three-parameters loss-function (Eq. 5.5);

– 5 = same as option 4 but with B such that the loss function is normalized to one

– 6 = distorted Shirley cross section (Eq. 5.6);

– 7 = same as option 6 but with Bs such that the loss function is (nearly) normalized toone.


• [12-14] Generalized Shirley: Sh, Sl, Sc: generalized Shirley background parameters (Eq. 5.4)(constant Sh ∼ 0.01 eV−1; slope Sl ∼ 0.001 eV−2; curvature Sc ∼ 0.0001 eV−2 );

• [15-17] Tougaard B,C,D: Tougaard background coefficients with B,C,D ≥ 0 (Eq. 5.5) (B '3006 eV2, C ' 1643 eV2, D = 0 for an universal background);

• [18-20] Distorted Shirley: Bs, Cs, Ds: distorted Shirley background parameters withBs, Cs, Ds ≥0 (Eq. 5.6) (Bs ∼ 17.5 eV; Cs ∼ 750 eV2; Ds ∼ 0.1 eV−1 );

• [21] Gap : gap of the material used in the Tougaard background (G in Eq. 5.5);

• [22] Energy offset : binding energy offset applied to all peaks; used to define peak positionsas relative values.

• [23] Area/height multiplier : multiplicative coefficient applied to the area/height of all peaks;used to define peak areas/heights as relative values.

5.4.3 Peak parameters

The definition of all peaks and the parameter meanings are given is Sect. 5.6.

• Common parameters for peak type #1,2,3,4,5,6,7,8,9,11,14,15,16.

– [0] Area: area A of the peak;

– [1] Binding Energy: position of the peak E0; for a peak pair, the position of the lessbound component;

– [2] FWHM: FWHM of the Lorentzian component or of the Lorentzian limit for mostasymmetric shapes;

– [4] Branching ratio: the ratio Br of the area of spin-orbit split peak to the area of theprincipal one Br ≥ 0 (Eq. 5.24); for peak doublet, the theoretical branching ration Br is1/2; 2/3; 3/4 for p; d; f levels, respectively (Annex 7.2);

– [5] Spin-orbit splitting: the spin-orbit splitting Eso > 0 (Eq. 5.24);

– [6-8] Shirley Sh, Sl, Sc: generalized Shirley parameters with Sh ≥ 0, Sl, Sc (Eq. 5.4);

– [9-11] Tougaard B, C, D: if D = 0, two-parameters Tougaard background with coeffi-cients B,C ≥ 0; if D > 0, three-parameters Tougaard background with B,C ≥ 0, D > 0(Eq. 5.5);

– [12-14] Shirley Bs, Cs, Ds: distorted Shirley parameters with Bs, Cs, Ds ≥ 0 (Eq. 5.6);

– [15] Gap: gap of the material G ≥ 0 (Eqs. 5.5,5.6).

The values Area, Binding Energy, FWHM do not necessarily correspond to actual peakarea, maximum position and FWHM. An example is the Doniach-Sunjic lineshape which isnon-integrable. Actual peak characteristics obtained by numerical analysis are given in thefit report for each peak. A blend of backgrounds is calculated for each peak to account fordifferent behaviours of different core levels [12]. But it is added to the total background definedon the sum of all peaks; so be careful not include twice the background ! The correspondingbackground is stored in wave bkr#.

• For peak type #1,5,6,7,8,9,10,14,15,16 an individual Gaussian broadening can be includedthrough convolution.

– [3] Gauss broad FWHM: FWHM of the Gaussian broadening by convolution (Eq. 5.25).

• For peak type #2, Gaussian (Eq. 5.8).

– [3] FWHM slope: slope s of the FWHM for the asymmetric gaussian (FWHM =FWHM0 + s(E − E0));

– [4] FWHM Gauss: Gaussian FWHM.


• For peak type #3 Pseudo-Voigt (Eq. 5.10).

– [5] Mixing ratio: the pseudo-Voigt mixing 0 ≤ η < 1 (η = 0 is a Lorentzian and η = 1 isa Gaussian).

• For peak type #4, Lorentz X Gaussian (Eq. 5.11).

– [3] FWHM Gauss: Gaussian FWHM.

• For peak type #6, Doniach-Sunjiic (Eq. 5.13).

– [16] Asymmetry: the Doniach-Sunjic asymmetry factor 0 ≤ α < 1.

• For peak type #7, Generalized Doniach-Sunjic (Eq. 5.14).

– [16] Gamma: Lorentzian asymmetry parameter γ > 0;

– [17] Mu: Artan asymmetry parameter µ > 0; (γ = 1;µ = 0 corresponds to a lorentzian).

• For peak type #8, Mahan (Eq. 5.15).

– [16] Beta: the asymmetry parameter β > 0;

– [17] Ksi: width of the occupied band ξ > 0.

• For peak type #9, Post-collision interaction (Eq. 5.16).

– [16] Asymmetry: the asymmetry parameter δ ≥ 0.

• For peak type #10, Asymmetric Voigt (Eq. 5.17).

– [2] FWHM high-BE: lorentzian FWHM on the high binding energy side;

– [16] FWHM low-BE: lorentzian FWHM on the low binding energy side.

• For peak type #11 Asymmetric pseudo-Voigt (Eq. 5.19).

– [3] Mixing ratio: the pseudo-Voigt mixing (0 ≤ ηle1; η = 0 is a Lorentzian and η = 1 isa Gaussian);

– [16] Asymmetry: the asymmetry parameter ε > 0;

– [17] Sigmoidal shift: the sigmoidal shift Esf .

• For peak type #14, Fano (Eq. 5.20).

– [16] Asymmetry: asymmetry parameter (−1 < ν < 1).

• For peak type #15, Plasmon (Eq. 5.21).

– [16] Plasmon energy: plasmon energy shift from central position;

– [17] Plasmon FWHM: lorentzian plasmon FWHM;

– [18] Extrinsic damping a: extrinsic plasmon damping a (0 < a < 1);

– [19] Intrinsic damping b: intrinsic plasmon damping b (0 < b < 1).

• For peak type #16, Band-bending Lorentz (Eq. 5.22).

– [16] Band bending: the amplitude of the band bending Vbb (signed);

– [17] Width SCL: the width of the space charge layer W > 0;

– [18] Attenuation length: the attenuation length of the photoelectron λbb > 0.

• For peak type #17, Gadzuk-Sunjic (Eq. 5.23).

– [16] Asymmetry: the Gadzuk-Sunjic asymmetry factor 0 ≤ α < 1;

– [17] Cut-off energy: the cut-off energy of the order of the Fermi energy 0 ≤ ωc;– [18] Damping: the damping of core-hole potential 0 ≤ η.


5.4.4 Peak parameters for step functions

For Fermi step (peak #12; Eq. 5.19, the function tends to zero on the low binding energy side; thisis the opposite for the work function step (peak #13).

• [0] Step height: the height Hs > 0 of the step;

• [1] Binding Energy: the position E0 of the step edge;

• [2] Erf FWHM: Erf FWHM ≥ 0;

• [3] Atan FWHM: Atan FWHM ≥ 0;

• [4] Fermi width (Kelvin): Fermi function width in Kelvin ≥ 0;

• [5] Exp. decay lambda: exponential decay length (no decay for λd ≤ 0);

• [6] Lin. Poly decay: linear polynomial coefficient Bs;

• [7] Sqr. Poly decay: quadratic polynomial coefficient Cs;

• [8] Cub. Poly decay: quadratic polynomial coefficient Ds.

Note that there are three basic shapes for the step function (Eq. 5.19):

• Erf: error function i.e. a convolution of a abrupt step with a gaussian. The Erf step FWHMparameter is that of the Gaussian; it can be measured at the 12%-88% of the step height.

• Atan : arctangent shape. The Atan step FWHM parameter is defined so that the slope ofthe Atan step at the edge position E0 is the same as in the case of an Erf step with the sameFWHM. It can be measured at the 19%-81% of the step height.

• Fermi: exact Fermi edge using the Fermi function.

The three shapes can be used in ”pure” or ”blended” way. If only one of the three width parametersis non-zero, the corresponding ”pure” shape is obtained. If two or three of the width parametersis non-zero, an (arithmetic) average is computed which can be used to describe more exotic shapes.The decay parameters are used to shape the non-zero (high or low binding) side of the step. Theshaping function does not impact the step height. The difference between Fermi and work functionsteps is only the direction of the step.

5.4.5 Columns in the table

• what: description of the parameters;

• value: input values used for the function calculation (button CALCULATE) and start valuesfor the data fit (button FIT);

• fit value: output values from the data fit;

• sigma: output standard deviations of the fit value;

• epsilon: ε values for the fit routine; ε tells Igor Pro which is the significant variation of eachparameter to define the derivatives; should not be zero to start the fit process; ε is somehowrelated to the accuracy of the fitted values;

• fix it, low, high : are used to impose limits to the parameter variations.

– [fix it = 0]: parameter fixed;

– [fix it = 1]: free in the range [low, high] defined as ”absolute limits”;

– [fix it = 2]: free in the range [value-low, value+high] defined as ”relative limits”;

– [fix it = 3]: equal to the same parameter of the peak of index low within a range ± high;high can be zero for equality;


– [fix it = 4]: equal to the same parameter of the peak of index low plus an additiveconstant high; high can be negative; high can be zero for equality;

– [fix it = −4]: equal to the same parameter of the peak of index low plus the value of thesame parameter of the peak of index high;

– [fix it = 5]: equal to the same parameter of the peak of index low multiplied by a constanthigh; high can be negative;

– [fix it = −5]: equal to the same parameter of the peak of index low multiplied by thevalue of the same parameter of the peak of index high.

Warning: Do not modify the empty cells (filled with Not a Number: NaN) of the parametertable. Otherwise, values could lead to errors.

Warning: Parameters are set positive or bounded internally if necessary (for instance FWHM¿0).But these constraints do not appear in the report.

5.5 Fit

When the FIT button is pressed, data are fitted according to the table of parameters using non-linear least-squares Levenberg-Marquardt algorithm with preset constraints as implemented in IgorPro. Fit is performed over the full range by default (only cursor A present) or between cursors [A,B]of the graph.

Beyond fit graph, fit quality can judged from reduced χ2 that should be close to one, RB close tothe ReB and Ab close to one (Abbe Ab values close to 2/0 means anti-correlated/correlated residuals)defined as:

χ2 =1

N − n

N∑i=1

[(yti − yeiσi

]2;

Rb =

∑Ni=1 |yti − yei |∑Ni=1 |yei |

;

Reb =

√N − n∑N

i=1(yei /σi)2

;

Ab =1

2

∑Ni=1[yti+1 − yei+1 − (yti − yei )]∑N

i=1(yti − yei )2. (5.1)

yei , yti , σi with i = 1, . . . , N are the experimental data, the calculated points and the input error bars.

n is the number of free parameters of the fit. χ2, RB , ReB and the matrix of correlation coefficients

between parameters as obtained from the curvature of χ2 at minimum are given in the fit report.

The fit does not start (i) if the starting points of some parameters are outside limits, or (ii) if theepsilon values are not set properly (zero for example) or (iii) if the user attempts to fit useless pa-rameters. A common mistake leading to singular matrix is to try to fit parameters having no impacton χ2 ! Fit is performed either up to a maximum number of iterations (Num. iterations; from 2 to100) or if the decrease of χ2 over 9 iterations in a row is below a given threshold (Tolerance; from0.1 to 0.00001). At the end of a fit, information about convergence status is given in the commandline. Two warning messages (Lower/Upper limits) are displayed if some of the fit parameters arereturned ”very” close to the limits or the epsilon values are too large compared to the fit results(both thresholds of 1 %). A list of the parameters leading to warnings is shown in the commandwindow history.


The Write Fit Report button updates the I4P Fit/FIT REPORT notebook with a summaryof the last fit. It includes also reliance factors and the matrix of correlation between parameters. Ac-tual peak areas, positions of maximum and FWHMs are calculated numerically on the used bindingenergy range since for asymmetric peaks; these parameters may differ from those of the input file.Areas with/without satellites/spin-orbit split components are also given. A backup of the I4PFitfolder is also created in the folder of data. Change its name to avoid overwriting at the next call.From an existing I4PFit type folder, the commands plot i4pfit() and report i4pfit() allow to vi-sualize at any time the fit graph result and the fit report. The command reload i4pfit() will reloadthe old fit in the I4P Fit panels; be careful that the running panels will be overwritten.

Starting from a satisfactory fit, batch fit can be performed for all spectra in the current datafolder using Bath fit menu. Spectra which names contain a given character string are processedin the way they appear in the folder. The fit is performed (i) either from the initial guessed valuesor (i) from the results of the previous fit step. On output for each spectrum, the I4PFit folder iscopied in the current data folder with the same name as the fitted spectrum, and fitted values, peakcharacteristics (area, extremum value, extremum position, FWHM) and reliance factors are storedin waves fitted values, peak carac and reliance. Row, column and chunk meanings are given inthe corresponding wave info. During batch fit, all graphs can be plotted (or not) as well as the fitresults.

5.6 List of peak profiles

• Polynomial background:

Bpol(E) = Ap +Bp∆E + Cp∆E2 +Dp∆E

3 with ∆E = E − 〈E〉 (5.2)

• Shirley background [39]:

BShirley(E) = Sh

∫ E

E0

I∗(E′)dE′ (5.3)

I∗(E) = I(E)− I(E0) with I(E), the primary spectrum, namely the sum of all peaks withoutbackground [13,46]. E0 is chosen on the low binding energy side of the peaks.

• Generalized Shirley background [11]:

BGenShir(E) = Sh

∫ E

E0

I∗(E′)dE′ + Sl

∫ E

E0

dE′∫ E′

E0

I∗(E′′)dE′′

+ Sc

∫ E

E0

dE′∫ E′

E0

dE′′∫ E′′

E0

I∗(E′′′)dE′′′ (5.4)

Same remark as for the Shirley background.

• Two (C > 0) or three (C < 0) parameters Tougaard background [43]:

BTougaard(E) =

∫ E

E0

K(E − E′)M∗(E′)dE′

or K(T ) =B(T −G)

[C + (T −G)2]2ΘH(T −G) (5.5)

or K(T ) =B(T −G)

[C − (T −G)2]2 +D(T −G)2ΘH(T −G)

M∗(E) = S(E) − S(E0) is the measured spectrum i.e. the sum of primary spectrum andbackground S(E) = I(E) + B(E) [13, 46]. When only primary spectrum P (E) is known as incase of simulation/fit, BTougaard is calculated iteratively [13, 46] up to a relative accuracy of0.005.


• Distorted Shirley [46,47]:

BDistortedShirley(E) =

∫ E

E0

K(E − E′)M∗(E′)dE′ (5.6)

with K(T ) =B [1− exp [−D(T −G)]]

C + (T −G)2ΘH(T −G)

Same remark as for the Tougaard background.

• Lorentzian:

ILorentz(E) =1

π

Aσ

(E − E0)2 + σ2

with FWHM = 2σ (5.7)

• Gaussian:

IGauss(E) =A

σ√

2πexp

[− (E − E0)2

2σ2

]with FWHM = 2

√2 ln(2)σ (5.8)

• Voigt:IV oigt(E) = IGauss(E)⊗ ILorenzt(E) (5.9)

• Pseudo-Voigt:

IPseudo−V oigt(E) = ηIGauss(E) + (1− η)ILorentz(E)

with FWHMLorentz = FWHMGauss = FWHM

0 ≤ η ≤ 1 (5.10)

• Lorentzian X Gaussian:

ILorXGauss(E) =AσL

π exp[σ2L

2σ2G

]Erfc

[σL√2σG

] exp[− (E−E0)

2

2σ2G

](E − E0)2 + σ2

L

with FWHML = 2σL,FWHMG = 2√

2 ln(2)σG (5.11)

• Oscillator:

IOscillator(E) =ALπ

4E20σ

(E2 − E20)2 + σ2

LE2

with FWHM = σL (5.12)

• Doniach-Sunjic [7]:

IDoniach−Sunjic(E) =1

π

AΓ[1− α]

[(E − E0)2 + σ2](1−α)/2 cos

[πα

2− (1− α) arctan

(E − E0

σ

)]with FWHM = 2σ; 0 ≤ α < 1 (5.13)

• Generalized Doniach-Sunjic:

IGenDoSu(E) =2µσA

π2(µ+ 2)

π2 + π

µ + arctan(Eσ )

[(E − E0)2 + σ2]γ

with FWHM = 2σ; γ > 0;µ > 0 (5.14)


• Mahan [27]:

IMahan(E) =

{A

ξαΓ(β)(E − E0)β−1 exp

[−E − E0

ξ

]}⊗ ILorentz(E)

with FWHM = FWHMLorentz;β > 0; ξ > 0 (5.15)

• Post-collision interaction [45]:

IPCI(E) =1

π

Aσ

[(E − E0 + δσ)2 + σ2]× exp

[2δ arctan

(E − E0 + δσ

σ

)]with FWHM = 2σ; δ ≥ 0 (5.16)

• Asymmetric Voigt:

IAsym−Lorenzt(E) =A

π(σ1 + σ2)

{[1 + sign(E − E0)]σ2

1

(E − E0)2 + σ21

+[1− sign(E − E0]σ2

2

(E − E0)2 + σ22

}with FWHMHighBE = 2σ1; FWHMLowBE = 2σ2 (5.17)

• Asymmetric pseudo-Voigt [35]:

Same as Eq. 5.10 with (5.18)

FWHMPseudo−V oigt =2FWHM

1 + exp [−ε(E − E0 − Esf )]; ε ≥ 0

• Step function (reversed direction between Fermi and Work function steps):

Istep(E) =Hs

2Erfc(−E−E0

σErf

) +Hs

[1

2+

1

πarctan

(E − E0

σarctan

)]+

Hs

1 + exp(−E−E0

kBT

) (5.19)

with σErf = FWHMErf/2√

ln 2;σarctan = 2√π ln 2FWHMArctan

with decay Istep(E)× exp

[−E − E0

λd

]×[1 +Bs(E − E0) + Cs(E − E0)2 +Ds(E − E0)3

]• Fano:

IFano(E) =Aσ

π(1 + q2σ2)

(E − E0 + qσ)2

(E − E0)2 + σ2

with FWHM = 2σ; q =1− νν

;−1 < ν < 1 (5.20)

• Plasmon [14]:

IPlasmon(E) =A

π

∞∑n=1

[(1− a)an−1 +

1

eb − 1

bn

n!

]σ0 + nσP

(E − E0 − nEP )2 + (σ0 + nσP )2

with FWHM = 2σ; 0 ≤ a < 1; 0 ≤ b < 1 (5.21)

• Band bending lorentz [3]:

IBandBending(E) =1

λbb

∫ +∞

0

exp(−z/λbb)ILorentz[E0(z)]dz

E0(z) = E0 − Vbb[1− z2

W 2

]if z < W

E0(z) = E0 if z > W

W > 0 ; λbb > 0 (5.22)


• Gadzuk-Sunjic [9]:

IGadzuk−Sunjic(E) =A

π

(1

η2c+

1

ω2c

)α/2exp

(−E − E0

ηc

)Γ(1− α)

[(E − E0)2 + σ2](1−α)/2cos θ

− ηα−1c δI(E − E0)

θ = (1− α) arctan

(E − E0

σ

)− 1

2πα− σ

ηc

δI(E − E0) = A cos(σ/ηc)−B sin(σ/ηc)

A =

∫ 1

0

z−α exp

(zE − E0

ηc

)sin(zσ/ηc)dz

B =

∫ 1

0

z−α exp

(zE − E0

ηc

)cos(zσ/ηc)dz

with FWHM = 2σ; 0 ≤ α ≤ 1; 0 < ηc; 0 < ωc (5.23)

• Peak pair due to spin-orbit splitting:

Ipair(E) = I(E) +BrI(E + Eso)

Br > 0;Eso > 0 (5.24)

• Gaussian broadening of I(E):

IGaussBroad(E) = IGauss(E)⊗ I(E) (5.25)

The following notations are used the description of the line shapes:

• Ap, Bp, Cp, Dp : polynomial background coefficients (centred on the middle of the bindingenergy range 〈E〉);

• Sh, Sl, Sc : the generalized Shirley background coefficients;

• B,C,D : Tougaard background parameters (for universal background B ' 3006 eV2, C =1643 eV2);

• Bs, Cs, Ds : the distorted Shirley background coefficients;

• G : band-gap of the material;

• A : peak area (actual area ONLY for symmetric profiles such as Gaussian or, Lorentzian; foractual peak areas, see the numerical integration over the fit range in the fit report);

• E0 : peak central value (actual peak maximum ONLY for symmetric profiles such as Gaussianor Lorentzian; for actual peak maximum position, see the fit report);

• FWHM : Full-Width at Half-Maximum (actual FWHM ONLY for symmetric profiles such asGaussian or Lorentzian; for actual peak FWHM, see the fit report);

• η : mixing ration in the pseudo-Voigt function (0 ≤ η ≤ 1);

• ⊗ : convolution product;

• α : asymmetry parameter of Doniach-Sunjic (α = 0 for pure Lorentz function);

• γ, µ : asymmetry parameters of generalized Doniach-Sunjic (γ = 1;µ = 0 for pure Lorentzfunction);

• β, ξ : asymmetry and width of Mahan peak (ξ → +∞ for Doniach-Sunjic with α = β);

• δ : asymmetry parameters of post-collision interaction function (δ = 0 for pure Lorentz func-tion);


• ε : asymmetry parameter of the asymmetric pseudo-Voigt (ε = 0 for pure Lorentz function);

• Esf : sigmoidal shift of the asymmetric pseudo-Voigt;

• Hs : the step height times the number of functions with FWHMs different from zero;

• kBT : Boltzmann constant times temperature (K);

• λd : exponential decay coefficient of step function;

• Bs, Cs, Ds : polynomial coefficients of step function decay;

• EP : plasmon energy;

• σP : plasmon width;

• aP : plasmon extrinsic damping;

• bP : plasmon intrinsic damping;

• Vbb : band bending amplitude;

• ηc : damping amplitude of core-hole potential;

• ωc : cut-off amplitude of the order of the Fermi energy;

• W : width of the space charge layer (nm);

• λbb : escape depth of the photoelectron (nm);

• Eso : spin-orbit splitting;

• Br : branching ratio;

• Γ(x) : Gamma function;

• Erfc(E) : complementary error function;

• ΘH(E) : the Heaviside function (ΘH(E) = 0 if E < 0; ΘH(E) = 1 if E > 0);

• sign(E) : the sign function (sign(E) = −1 if E < 0; sign(E) = +1 if E > 0).

5.7 Manage fit from an existing I4PFit folder

Data, fit and template can be fully reloaded from an existing I4PFit folder of the current Igor Proexperiment into the two windows I4P Fit/PEAK MANAGER and I4P Fit/DATA FIT usingthe menu Reload from folder of I4P Fit; be careful the existing windows will be overwritten.Similarly, data fit graph and fit report can be displayed using the menus Plot from folder andReport from folder.

CHAPTER 6THE I4P HELP MENU

6.1 Clean all

The menu Clean all deletes all windows and folders created by I4P.

6.2 Help Command

The menu Help Command displays a list of commands available in I4P.

6.2.1 Background corrected area

Background corrected area (see Sect. 3.6) of a given core level can be obtained from the commandline:

Area BGS(spectrum name,BackType,BElow,BEhigh,wBE,posBGS,keepback,Sh,Sl,Sc,B,C,D,Bs,Cs,Ds,G,Ls])

where:

• spectrum name : name of the spectrum wave;

• BackType : type of background (Shirley; Generalized Shirley; Tougaard; DistortedShirley; Blend; Linear; None); background is pinned on given binding energy values exceptfor a blend; default or user given parameters are used;

• [BElow, BEhigh] : optional; low and high binding energy (eV); (default values set to minimumand maximum of EB of spectrum);

• [wBE] : optional; half-window in binding energy for averaging (eV); (default value 0.4 eV);

• [posBGS] : optional; 1 = force positive background subtracted spectrum; 0 = do not; (defaultvalue 0);

• [keepback] : optional; 1 = keep intermediate waves (* BG; * BGS); 0 = do not; (default value0);

• [Sh,Sl,Sc] : optional; generalized Shirley parameters (eV−1,eV−2,eV−3); (default value [0.01, 0.001, 0.0001]);

• [B,C,D] : optional; Tougaard background parameters (eV2); (default values [3006, 1643, 0]);

27

CHAPTER 6. The I4P Help menu

• [Bs,Cs,Ds] : optional; Distorted Shirley background parameters (eV, eV2, eV−1); (defaultvalues [17.5, 750, 0.1])

• [G] : optional; gap (eV); (default value 0 eV)

• [Ls] : optional; linear slope (eV−1); (default value 50 eV−1)

• example :print Area BGS(”O1s”,”Shirley”)print Area BGS(”O1s”,”Tougaard”,BElow=525,BEhigh=540,wBE=0.8,posBGS=1)print Area BGS(”O1s”,”Blend”,Sh=0.01,Sl=0.001,Sc=0.0001,B=3006,C=1643,D=0,Bs=17.5,Cs=750,Ds=0.5,G=0,Ls=0)

6.2.2 Correction from analyzer transmission function

A spectrum can be corrected from the analyzer transmission function with the command line:

CorrectFromAnalyzerTF(spectrum name,[exponent,getTF])

where:

• spectrum name : name of the spectrum wave;

• [exponent] : optional; the exponent of the transmission function in FAT/CAE mode (defaultset to 1.0);

• [getTF] : optional; 1=generate the transmission function wave, 0=do not (default set to 0);

• example :CorrectFromAnalyzerTF(”O1s”,exponent=1,getTF=0).

6.2.3 Photo-ionization cross section

Photoionization cross section (Mbarn) corrected from asymmetry [49] for an unpolarized source isavailable from the command line:

CoreLevel2PICS(TagElement,core level,Xray source,[PrintInfo,Angle])

where:

• TagElement : element symbol;

• core level : the considered core level;

• Xray source : the used X-ray source (Al, Mg);

• [PrintInfo] : optional; 1=print the content of database; 0=do not (default set to 0);

• [Angle] : optional; the angle in degrees between the X-ray source and the analyzer (defaultset to the magic value ψm = 54.74◦ );

• example :print CoreLevel2PICS(”C”,”1s”,”Al”,PrintInfo=0,Angle=75).


6.2.4 List of closest core levels and Auger transitions

A list of the closest transitions to a given binding energy can be displayed with the command:

BE2Peaks([Xray source,BE,dBE])

where:

• [Xray source] : optional; the used X-ray source (Al,Mg) (default value read from wave notes);

• [BE] : optional; the binding energy (eV) (default value is the position of cursor A on the topgraph);

• [dBE] : optional; the binding energy windows of the search (EB ± dEB) (eV) (default dEB =±1.5 eV);

• example :print BE2Peaks(Xray source=”Al”,BE=285,dBE=1).Without arguments, the function returns the information for the cursor A position of the topgraph (accounting from trace X-offset) within dEB = ±1.5 eV.

6.2.5 Inelastic mean free path from ”universal” equation

Inelastic mean free path (A) of a photoelectron calculated with universal equation [10,38,40,41] canbe obtained from the command line:

Material2IMFP(type,material,E,[Xray source])

where:

• type : 0=non-relativistic TPP2M; 1=relativistic TPP2M; 2=Gries;

• material : material name in the available database;

• E : kinetic/binding energy (eV);

• [Xray source] : optional; the used X-ray source (Al,Mg). If present, E is defined as thebinding energy (default kinetic energy);

• example :print Material2IMFP(0,”Ag”,368,Xray source=”Al”).

6.2.6 Transport mean free path from Jablonski’s databases

Transport mean free path (A) of a photoelectron calculated with the universal formula of IMFP [10,38,40,41] and the Jablonski’s databases [15,17,21] can be obtained from the command line:

Material2TRMFP(typeIMFP,typeTRMFP,material,E,[Xray source])

where:

• typeIMFP : 0=non-relativistic TPP2M, 1=relativistic TPP2M;2=Gries;

• typeTRMFP : 1=database 1, 2=database 2; 3=database 3;



• [Xray source] : optional; the used X-ray source (Al,Mg). If present, E is defined as thebinding energy (default kinetic energy);

• example :print Material2TRMFP(0,1,”Ag”,368,Xray source=”Al”).


6.2.7 Effective attenuation lengths or emission depth distribution function

The effective attenuation lengths (A), mean escape depth (A) or emission depth distribution function(normalized) [19] can be obtained from the command line:

MED : Get MED(typeChandra,IMFP,Omega,Alpha,Psi,Theta,aBeta)EAL(bulk) : Get EALb(typeChandra,IMFP,Omega,Alpha,Psi,Theta,aBeta)

EAL(film) : Get EALf(typeChandra,IMFP,Omega,Alpha,Psi,Theta,aBeta,Thick)EAL(marker) : Get EALm(typeChandra,IMFP,Omega,Alpha,Psi,Theta,aBeta,Thick)

EDDF : Get EDDF(typeChandra,IMFP,Omega,Alpha,Psi,Theta,aBeta,Depth)

where:

• typeChandra : choice of Chandrasekhar’s function, 0: integral, 1=approximate 1, 2=approx-imate 2, 3=approximate 3; 4=approximate 4

• IMFP : inelastic mean free path (A);

• Omega : albedo;

• Alpha : sample normal/analyzer angle (deg);

• Psi : analyzer/X-ray angle (deg);

• Theta : sample normal/X-ray angle (deg);

• Beta : asymmetry factor of core level;

• Thick/Depth : thickness/depth (A).

• example :print Get EALf(2,20,0.2,0,54.7,54.7,2,10)

6.2.8 Surface excitation parameter

The surface excitation parameter [32,33] can be obtained from the command line:

Material2SEP(material,E,Alpha,[Xray source])

where:



• Alpha : sample normal/analyzer angle (deg);

• [Xray source] : optional; the used X-ray source (Al,Mg). If present, E is defined as thebinding energy (default, kinetic energy);

• example :print Material2SEP(”Ag”,368,0,Xray source=”Al”).

6.3 Help Plot Command

The menu Help Plot Command displays a list of commands available in I4P for plotting.

6.3.1 I4P Fit command

Data fit and report can be simply displayed or fully reloaded from an existing I4PFit folder usingthe commands:

plot i4pfit(); report i4pfit(); reload i4pfit()


6.3.2 Load a Vamas file from command line

A Vamas (*.vms) [6] file can be loaded directly from the command line:

Load VAMAS(fileNameStr,[pathNameStr,getBE,getTF])

where:

• fileNameStr : full path to *.vms file or only *.vms file name if path option is present;

• [pathNameStr] : optinal; partial path to *.vms file (default path included in fileNameStr);

• [getBE] : optional; 1 = make binding energy waves; 0 = do not (default set to 0);

• [getTF] : optional; 1 = read transmission function waves; 0 = do not (default set to 0).

• example :Load VAMAS(”C\\XPS\\XPSfile.vms”)Load VAMAS(”XPSfile.vms”,pathNameStr=”C\\XPS”,getBE=1,getTF=1)Data are stored in the current data folder; the command overwrites existing data folder.

6.3.3 Resize a spectrum

A spectrum from the current folder or pointed by cursor in the top graph can be resized from thecommand line:

Resize Spectrum([spectrum name,BElow,BEhigh,dBE,getBE])

where:

• [spectrum name] : optional; name of the spectrum wave (default is the wave pointed bycursor A on the top graph);

• [BElow, BEhigh] : optional; low and high binding energy (eV) (default values given by cursorson the top graph);

• [dBE] : optional; step in binding energy (eV) (default is the energy step of the spectrum);

• [getBE] : optional; 1 = make binding energy waves; 0 = do not (default set to 0);

• example :Resize Spectrum(spectrum name=”O1s”,BElow=525,Behigh=535,dBE=0.1,getBE=1)Resize Spectrum(dBE=0.1)The resized spectrum (* CUT) is stored in the wave spectrum data folder and append to thetop graph if present.

6.3.4 Convert a spectrum

A (X,Y) pair of waves in the current folder can be converted to a spectrum suitable for I4P usingthe command line:

Convert XY(wave energy,wave counts,WorkFunction,Energy scale,Excitation source,Excitation energy,dBE,Analyzer mode)

where:

• wave energy : name of the energy X-wave;

• wave counts : name of the count Y-wave;

• WorkFunction : work function of the analyzer (eV) (EB = hν − EK −WF )


• Energy scale : scale in energy (Binding energy; Kinetic energy; Energy loss);

• Excitation source : source of excitation (Al Kalpha; Mg Kalpha; He I; He II; Synchrotron;Ion Scattering Spectroscopy; Electron Energy Loss Spectroscopy);

• Excitation energy : energy of the excitation source (eV);

• dBE : step in energy (eV);

• Analyzer mode : mode of the analyzer (FAT, FRR);

• example :Convert XY(”O1s BE”,”O1s”,”Kinetic energy”,”Synchrotron”,450,0.1,”FAT”)The converted spectrum (* CON) is stored in the current folder.

6.3.5 Shift the binding energy scale of a spectrum

The binding energy or energy loss scale of a spectrum (and the corresponding * BE) can be shiftedusing the command line:

ShiftBE Spectrum(spectrum name,BEShift,[ExcEner])

where:

• spectrum name : name of the spectrum;

• BEShift : the applied shift in binding energy or energy loss (eV);

• [ExcEner] : optional, the new excitation energy (eV) (otherwise not modified);

• example :ShiftBE spectrum(”O1s”,233,ExcEner=1486.6)

6.3.6 Convert a spectrum from usual binding energy scale to kinetic en-ergy scale

A spectrum stored in binding energy or energy loss scale can be converted to a kinetic energy scalefrom the command line:

BE2KE Spectrum(spectrum name,[derivative,removeWf])

where:

• spectrum name : name of the spectrum;

• [derivative] : optional, 1 = calculate the derivative spectrum (otherwise not generated);

• [removeWf] : optional, 1 = remove the analyzer work function correction (otherwise kept);

• example :BE2KE Spectrum(”Auger”,derivative=1,removeWf=1)A new * XKE spectrum in kinetic energy and, optionally a derivative * DIFF, spectrum isgenerated.


6.3.7 Parameters of all background corrected spectra in the top graph

The parameters (Position, FWHM, Area) of all background-corrected core levels plotted in the topgraph can be obtained from the command line:

Graph2Peaks(BackType,[BElow,BEhigh,wBE,posBGS,keepback,Sh,Sl,Sc,B,C,D,Bs,Cs,Ds,G,Ls]

where:

• same inputs as Area BGS command (see Sect. 6.2.1);

• example :Graph2Peaks(”Shirley”)Graph2Peaks(”Tougaard”,BELow=524,BEhigh=540,keepback=1,C=2000)Data are stored into waves (Peaks Name,Peaks BE,Peaks Area,Peaks FWHM) in the currentdata folder; spectra order corresponds to plot.

6.3.8 Plot of the inelastic electron scattering cross section

Plot the inelastic electron scatetring cross section versus energy loss for Tourgaard [43] (Eq. 5.5) orDistorted Shirley [47] (Eq. 5.6) cases

Plot IESCS([Type, B, C, D, G, Estep])

where:

• [Type] : optional; 1=Two-parameters Tougaard; 3=Three-parameters Tougaard; 3=Distorted-Shirley (default set to 1);

• [B] : optional; B-parameter (eV2 or eV) (default set to B = 3006);

• [C] : optional; C-parameter (eV2) (default set to C = 1643);

• [D] : optional; D-parameter (eV2 or eV−1) (default set to D = 0);

• [G] : optional; gap of the material (eV) (default set to G = 0);

• [Estep] : optional; step in energy loss (eV) (default set to Estep = 0.5);

• example :Plot IESCS(Type=1,B=3006,C=1643,D=0,G=0,Estep=0.5).

6.4 Help I4P

The menu Help I4P opens the present pdf manual.

C:\Users\UserName\Documents\WaveMetrics\Igor Pro 6 User Files\UserProcedures\I4P\I4P help\templates.

6.5 About I4P

The Igor Pro Paris Photoemission Package can be obtained freely upon request to the author([email protected]). It is given as such without any warranty about accuracy, reliability,completeness and fitness for purpose. The author can not be held responsible of inaccurate results ormisuse of the present package. An acknowledgement about its use in any kind of publication wouldbe appreciated.The present package is based on strongly revised versions of:

• XPSmania set of Igor Pro procedures by F. Bruno [1];


• PTSelector.ipf by D. Niles, J.J. Weimer and R. Knochenmuss [31];

• Load Omicron.ipf and XPS Bakcground.ipf by J. Mudd [29];

• VAMAS parser.ipf by Chozo [4].

CHAPTER 7ANNEX

7.1 List of wave extension used in I4P

• BE : binding energy wave;

• BG : background spectrum;

• BGS : background subtracted spectrum;

• CON : spectrum created from (X,Y) waves;

• CUT : cut-out or resized spectrum;

• GL : ghostlines spectrum;

• GLS : ghostlines subtracted spectrum;

• ISS : mass scale interpolated ISS spectrum;

• MS : mass scale of ISS spectrum;

• SA : satellites spectrum;

• SAD : satellites deconvoluted spectrum;

• SAS : satellites subtracted spectrum;

• SUB : difference spectrum after overlap;

• TF : transmission function spectrum;

• TFC : transmission function corrected spectrum;

• XKE : spectrum in kinetic energy;

• DIFF : derivative spectrum;

35

CHAPTER 7. Annex

7.2 Spin-orbit splitting of atomic levels

Subshell l j-value Area ratio

s 0 1/2 n/ap 1 1/2− 3/2 1 : 2 = 0.5d 2 3/2− 5/2 2 : 3 = 0.66f 3 5/2− 7/2 3 : 4 = 0.75

Table 7.1: Degeneracy due to L-S coupling : [2(l − 1/2) + 1]/[2(l + 1/2) + 1]

7.3 Spectroscopic notations of atomic levels

n l m Auger notation XPS notation

1 0 1/2 K 1s1/22 0 1/2 L1 2s1/22 1 1/2 L2 2p1/22 1 3/2 L3 2p3/23 0 1/2 M1 3s1/23 1 1/2 M2 3p1/23 1 3/2 M3 3p3/23 2 3/2 M4 3d3/23 2 5/2 M5 3d5/24 0 5/2 N1 4s1/24 1 5/2 N2 4p1/24 1 5/2 N3 4p3/24 2 5/2 N4 4d3/24 2 5/2 N5 4d5/24 3 5/2 N6 4f5/24 3 5/2 N7 4f7/25 0 5/2 O1 5s1/25 1 5/2 O2 5p1/25 1 5/2 O3 5p3/25 2 5/2 O4 5d3/25 2 5/2 O5 5d5/26 0 5/2 P1 6s1/26 1 5/2 P2 6p1/26 1 5/2 P3 6p3/2

CHAPTER 7. Annex

7.4 Quantification in photoemission

The peak areas from a substrate Is and from a film If core level are given by [8]:

• for a continuous film of thickness t (Fig. 4.4-a):

Is ∝ nsσsTsλebss cos(α) exp

(− t

λefsf cosα

)

If ∝ nfσfTfλebff cos(α)

[1− exp

(− t

λefff cosα

)]; (7.1)

• for a film of pancakes of height H covering a fraction Θ (0 < Θ < 1) of the surface (equivalentthickness t = ΘH) at a α = 0◦ emission (Fig. 4.4-b):

Is ∝ nsσsTsλebss

[1−Θ + Θ exp

(− H

λefsf cosα

)]

If ∝ nfσfTfλebffΘ

[1− exp

(− H

λefff cosα

)]; (7.2)

• for a film of hemispheres of radius R covering a fraction Θ of the surface (t = 23ΘR) at a α = 0◦

emission (Fig. 4.4-c):

Is ∝ nsσsTsλebss

{1−Θ +

2(λefsf )2Θ

R2

[1−

(1 +

R

λefsf

)exp

(− R

λefsf cosα

)]}(7.3)

If ∝ nfσfTfλebffΘ

{1−

2(λefff )2

R2+

2λefff (R+ λefff )

R2exp

(− R

λefff cosα

)};

• for an homogeneous alloy S1−xAx (Fig. 4.4-d):

Is ∝ σsTsλebs(s+a) cos(α)(1− x)

If ∝ σfTfλeba(s+a) cos(α)x; (7.4)

where:

• ns, nf are the atomic concentrations of the substrate/film;

• σs, σf are the photoionization cross sections of the substrate/film corrected from asymmetry;

• Ts, Tf are the transmission functions of the analyzer at the kinetic energy of the substrate/filmcore levels;

• λepq = λeff , λess, λ

esf are the effective attenuation lengths of the photoelectron for core level p in

the material q; the superscripts (eb, ef) correspond to bulk or practical film EAL [18, 19] (inprinciple averaged over thickness up to the information depth), respectively;

• α is the take-off angle between analyzer and surface normal.

Eqs. 7.2-7.3 are valid only in normal emission. If the substrate is covered by a continuous overlayer of

thickness tl, a damping factor exp(− tlλefsl cosα

)should be accounted for in the previous equations for

Is. λefsl is the corresponding effective attenuation length. A further ”effective” damping exp(−Spq)

due to surface excitations can be added for each electrons going through the interface between materialp and q (p, q = (s, l, a)). Spq is the corresponding interface excitation parameter [32,33].

CHAPTER 7. Annex

7.5 Tougaard background parameters

Material B (eV2) C (eV2) D (eV2) Gap (eV)

”universal” [43] 2866 1643 0 n.a.”universal” [36] 3006 1643 0 n.a.

Fe,Pd,Ti,Cu,Ag,Au [43] 4210 1000 13300 0Polymers [43] 434 551 436 n.a.

SiO2 [43] 325 542 275 n.a.Si [43] 132 325 96 n.a.Ge [43] 73 260 62 n.a.Al [43] 16.5 230 4.5 0

Table 7.2: Parameters of the Tougaard background (Eqs. 5.5) for various materials. From Refs. [36,43].

7.6 X-ray satellite and ghost-lines

Source α1,2 α3 α4 α5 α6 β

Mg ∆E (eV) 0 8.4 10.2 17.5 20.0 48.5Mg Irel 100 8.0 4.1 0.55 0.45 0.5Al ∆E (eV) 0 9.8 11.8 20.1 23.4 69.7Al Irel 100 6.4 3.2 0.4 0.3 0.55

Table 7.3: X-ray satellite energies and relative intensities. From Ref. [48]. FWHM(Kα1,2 − Mg) = 0.68 eV;FWHM(Kα1,2 − Al) = 0.83 eV are used in I4P.

Source α1 α2 α′ α3 α′3 α4 α5 α6

Mg ∆E (eV) 0. -0.265 4.740 8.210 8.487 10.095 17.404 20.430Mg Irel 100 50 2.099 7.868 4.712 9.071 1.129 0.538Mg FWHM (eV) 0.541 0.541 1.1056 0.6264 0.7349 1.0007 1.4311 0.8656Al ∆E (eV) 0. -0.415 5.452 9.526 9.958 11.701 20.072 23.576Al Irel 100 50 1.928 7.774 2.373 6.139 0.634 0.276Al FWHM (eV) 0.58 0.58 1.3366 0.6922 0.6623 1.1557 1.495 0.877

Table 7.4: X-ray satellite energies, relative intensities and FWHM. From Ref. [25].

Source He I α He I β He I γ He II α He II β He II γ

∆E (eV) 0 1.87 2.52 19.59 27.15 29.8Irel 100 1.5 0.5 1 0.1 0.

Table 7.5: He I satellite energies and relative intensities. A FWHM = 0.01 eV and a He II/He I ratio of 0.01are arbitrarily used in I4P. From Ref. [2].

CHAPTER 7. Annex

0.6

0.5

0.4

0.3

0.2

0.1

0.0

Re

lative in

tensity

3020100-10

Relative photon energy (eV)

Kα1

Kα2

Kα'

Kα3

Kα3'

Kα4

Kα5

Kα6 10-6

10-5

10-4

10-3

10-2

10-1

-30 -20 -10 0 10 20 30

0.6

0.5

0.4

0.3

0.2

0.1

0.0

Re

lative

inte

nsity

3020100-10


Kα1,2

Kα3

Kα4

Kα5

Kα6

Kβ

10-7

10-6

10-5

10-4

10-3

10-2

10-1

-80 -40 0 40 80

10-7

10-6

10-5

10-4

10-3

10-2

10-1

-40 -20 0 20 40

0.8

0.6

0.4

0.2

0.0

Rela

tive inte

nsity

3020100-10


Kα1,2

Kα3

Kα4

Kα5

Kα6

Kβ

0.6

0.5

0.4

0.3

0.2

0.1

0.0

Re

lative

in

ten

sity

3020100-10


Kα1

Kα2

Kα'

Kα3

Kα3'

Kα4

Kα5

Kα6

10-7

10-6

10-5

10-4

10-3

10-2

10-1

-30 -20 -10 0 10 20 30

(a) (b)

(c) (d)

Mg

Mg

Al

Al

Figure 7.1: X-ray emission lines (a)(b) from Ref. [48] (Tab. 7.3; FWHM(Kα1,2 − Mg) = 0.68 eV;FWHM(Kα1,2 − Al) = 0.83 eV) and (c)(d) from Ref. [25] (Tab. 7.4). Plots on logarithmic scale is shown ininset.

Source O(Kα) Cu(Lα) Mg(Kα) Al(Kα)

Mg ∆E (eV) 728.7 323.9 0 -233Mg Irel 5 0.1 100 3Al ∆E (eV) 961.7 556.9 233 0Al Irel 5 0.1 3 100

Table 7.6: X-ray ghost line relative displacements and intensties. Relative intensities depend on the anodeageing. The given values are those used in I4P for plotting purpose. From Ref. [48].

7.7 Portfolio of fits

A list of examples of fits of core level spectra is provided in the I4P Help subfolder of the I4Pinstallation (see Chap. 1). No claim of accuracy is put forward; their purpose is only to clarify theuse of fit in I4P.

CHAPTER 7. Annex

80x103

60

40

20

0

Inte

nsity

AgBulk plasmon

420 400 380 360

Binding Energy (eV)

-5

5

∆I/

σ

Ag 3d of Ag(001)

unmonochromated Al Kα140x10

3

120

100

80

60

40

20

0

Inte

nsity

AgBulk plasmon

380 375 370 365

Binding Energy (eV)

-20

-10

10

∆I/

σ

Ag 3d of Ag(111)

monochromated Al Kα

6000

5000

4000

3000

2000

1000

0

Inte

nsity

Si(0)Si(4+)-SiO2

125 120 115 110 105 100

Binding Energy (eV)

-15-10

-5

5

∆I/

σ

Si 2p of SiO2/Si

monochromated Al Kα 8000

6000

4000

2000

0

Inte

nsity

O1s-SiO2

540 535 530 525 520

Binding Energy (eV)

42

-2

∆I/

σ

O 1s of SiO2/Si

monochromated Al Kα

140x103

120

100

80

60

40

20

0

Inte

nsity

Pt 4f Pt 5pPlasmon

120 100 80 60

Binding Energy (eV)

-15-10

-5

510

∆I/

σ

Pt 4f of Pt(111)

unmonochromated Mg Kα

6000

4000

2000

0

Inte

nsity

Ti(4+)3/2Ti(4+)1/2Shakeup-1Shakeup-2

480 470 460 450

Binding Energy (eV)

-2.0

-1.0

1.0

∆I/

σ

Ti 2p of TiO2(110)

unmonochromated Mg Kα

Shirley background

6000

4000

2000

0

Inte

nsity

Ti(4+)3/2Ti(4+)1/2Shakeup-1Shakeup-2

480 470 460 450

Binding Energy (eV)

4

2

-2

∆I/

σ

Figure 7.2: Fits of selected core level spectra performed with the I4P package.

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