COMPARISON OF THREE UNIVERSAL CURVES FOR THE ESCAPE PROBABILITY OF X-RAY EXCITED ELECTRONS - I. THEORY

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1 Copyright(c)JCPDS-International Centre for Diffraction Data 2001,Advances in X-ray Analysis,Vol COMPARISON OF THREE UNIVERSAL CURVES FOR THE ESCAPE PROBABILITY OF X-RAY EXCITED ELECTRONS - I. THEORY ABSTRACT Horst Ebel, Robert Svagera, Maria F. Ebel and Wolfgang S.M. Werner2 Technische Universittit Wien, Wiedner HauptstraJe 8-l 0, A 1040 Wien, Austria An essential quantity in quantitative surface analysis by x-ray induced electron emission is the sampling depth or escape probability of electrons. In his investigations of a universal curve for escape probabilities in total electron yield XAS Schroeder describes the escape probability P(x) of electrons from a depth x in units of the Bethe range RB by The expression holds for an electron emission into a 2x-geometry, electron energies from 2.96 to 7.40 kev and elements from K to Zn. Ebel et al2 describe the escape probability by P(x) = A,. exp[-2]-a2.exp[-:] whith amplitudes Al, AZ and mean free paths 21 and & obtained from least squares fits to the results of Monte Carlo calculations The solid angle of electron acceptance 0 is also recognized in this concept. This approach covers electron energies from 0.5keV to 30keV and elements from Z=l 1 to Z=79. For practical applications we propose the following algorithm for escape probabilities P(x) = A1. exp[-2. p)- A,.exp[-k.p] The dimension of I/p/z is cm2/g and the meaning is identical with the usual mass attenuation coefficient,l@ in x-ray analysis. The least squares fits of log(l/p/l) and log(l/@z) versus log(eki,) of the electron energy do not depend on A, 2 and L? PHOTOELECTRIC ABSORPTION In the course of photoelectric absorption of monoenergetic x-rays, electrons of kinetic energy Ekin=h I+E~ are released from the atoms. The probability w describes the first step of the rearrangement of the atoms towards the original electronic configuration by emission of characteristic x-radiation. Further electrons can be released from the atoms with probability l-u by an emission of one or even more Auger electrons. Auger electrons are characterized by defined kinetic energies. Thus, photoelectric absorption of monochromatic x-rays is responsible for the emission of a series of monoenergetic electrons from atoms. Besides photoelectric absorption, Compton scattering causes an additional contribution to electron emission. This kind of interaction of x-rays with matter is neglected due to the comparably small probability in the photon energy range from 0.5 kev up to approximately 30 kev. I Institutfir Angewandte und Technische Physik Institutfiir Allgemeine Physik

2 This document was presented at the Denver X-ray Conference (DXC) on Applications of X-ray Analysis. Sponsored by the International Centre for Diffraction Data (ICDD). This document is provided by ICDD in cooperation with the authors and presenters of the DXC for the express purpose of educating the scientific community. All copyrights for the document are retained by ICDD. Usage is restricted for the purposes of education and scientific research. DXC Website ICDD Website -

3 Copyright(c)JCPDS-International Centre for Diffraction Data 2001,Advances in X-ray Analysis,Vol.44 2 Copyright(c)JCPDS-International Centre for Diffraction Data 2001,Advances in X-ray Analysis,Vol Copyright(c)JCPDS-International Centre for Diffraction Data 2001,Advances in X-ray Analysis,Vol hv PE &in w 1 vacancy in K QJK 1 t$ = hv - EbK 1 vacancy in L 2 vacancies in L Fig.1 Photoelectric absorption in the K-shell, emission of K-photoelectron, followed by emission of either characteristic K radiations or KLL Auger electrons, followed by emission of characteristic L radiations and/or LMM Auger electrons. Tuning the x-ray photon energy causes a systematic variation of the energy of photoelectrons, whereas the energy of Auger electrons remains unchanged. L WV) Fig.2 Dependence of kinetic energy of photo- and Augerelectrons of copper on the photon energy of incident x-radiation TRANSPORT OF ELECTRONS IN MATTER The following considerations are dedicated to solid matter. An exponential law describes the depth distribution of the number of monoenergetic electrons released by photoelectric absorption. Depending on the composition of the specimen, the kinetic energy of the electrons, the initial direction of the electrons and the distance between the point of origin and the surface only few electrons reach the surface without any kind of scattering in the specimen. Much more electrons leave the surface after numerous scattering events and consequently, with reduced kinetic energy, and most of the electrons do not reach the surface.

4 Copyright(c)JCPDS-International Centre for Diffraction Data 2001,Advances in X-ray Analysis,Vol.44 3 Copyright(c)JCPDS-International Centre for Diffraction Data 2001,Advances in X-ray Analysis,Vol Copyright(c)JCPDS-International Centre for Diffraction Data 2001,Advances in X-ray Analysis,Vol C Fig.3 A. Escape of electron without scattering event B. Escape of electron after numerous scattering events C. No escape of the electron. In our experiments we use nondispersive electron detection. The production of secondary electrons is not within the frame of our theoretical concept and therefore, the detection of electrons with kinetic energies of less than 50 ev is suppressed in our experiments by a dc-bias between specimen and detector. Consequently, photoelectrons with energies of less than 50 ev are also excluded from detection. In order to describe measured electron signals from solids irradiated with monochromatic x-radiation, the transport of electrons with given start energy has to be quantified. Monte Carlo calculation offers an excellent tool for the solution of this problem. Our mode closely follows the one described in detail by Shimizu and Ding Ze-jun3. Since most of the detected electrons are detected after multiple scattering we assume an isotropic angular distribution of directions of the trajectories from the point where the electron starts. Escape energies of at least 25, 50 and 100 ev were chosen. Our electron detector is a channeltron and allows us to detect only electrons within a given solid angle. Thus, the solid angle of electron detection L? asks for an additional variable in the Monte Carlo algorithm. Typical results of the Monte Carlo calculations can be seen from Figs.5 to 11. Fig.4 Description of the solid angle of electron detection L2 by angles LX~ and a~ MC l fit - global Fig.5 Escape probability of electrons versus depth for Cu, 5 kev, bias -50 V, acceptance angle 0 to 20 (data points give MC, full response gives 1.s.f. of data points and broken curve is the global description of the escape probability).

5 Copyright(c)JCPDS-International Centre for Diffraction Data 2001,Advances in X-ray Analysis,Vol.44 4 Copyright(c)JCPDS-International Centre for Diffraction Data 2001,Advances in X-ray Analysis,Vol Copyright(c)JCPDS-International Centre for Diffraction Data 2001,Advances in X-ray Analysis,Vol a 0.4 MC fit - global l Fig.6 As Fig.5 for an acceptance angle 0 to iril~ Fig.7 As Fig.5 for an acceptance angle of 0 to Fig.8 As Fig.5 with kinetic electron energy 0.5 kev. depth (nm) Fig.9 As Fig.5 with kinetic electron energy 30 kev

6 Copyright(c)JCPDS-International Centre for Diffraction Data 2001,Advances in X-ray Analysis,Vol.44 5 Copyright(c)JCPDS-International Centre for Diffraction Data 2001,Advances in X-ray Analysis,Vol Copyright(c)JCPDS-International Centre for Diffraction Data 2001,Advances in X-ray Analysis,Vol a ST 0.14 MC l fit - ( , I global - -. Fig.10 As Fig.5 for Na instead of cu. depth (nm) MC. fir - global Fig.11 As Fig.5 for Au instead of cu We describe the escape probability by P(x)= A1.exp[---&.pr)-dz.exp[---&a-) with amplitudes Al and AZ, and cross sections l/& and l/p/22 in cm /g. The values of Al, AZ, l/,&l and l/p/22 have been evaluated by least squares fits (1.s.f.) of P(X) to the results of Monte Carlo calculation for elements Li, Be, Na, Al, Si, K, V, Cr, Fe, Co, Ni, Cu, Se, Nb, MO, Rh, Pd, Ag, Te, Ta, W, OS, Ir, Pt, Au, kinetic electron energies 0.15, 0.20, 0.25, 0.30, 0.40, 0.50, 0.60, 0.70,0.80, 0.90, 1.00, 1.20, 1.40, 1.60, 1.80,2.00, 3,4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19,20,21,22,23, 24,25,26, 27,28, 29, 30 kev, bias -25, -50, -100 V and acceptance angles 0 to lo, 20, 30, 40, 50, 60, 70, 80 and 90. The total number of combinations is = A systematic investigation of the results led to the following conclusions: 1 The bias dependence ofal, AZ, l/p/z1 and l/p/zz is only significant at Ekin < 0.5 kev. 2 Amplitudes Al and A2 depend on 0 and on Ekin. 3 Amplitudes A1 and AZ do not depend on 2. 4 l/p/z1 and l/p/22 depend primarily on Ekin. 5 Cross sections l/p/z1 and l/p/22 do not depend on 2. 6 A first restriction for a global fit is the exclusion of the low 2 elements Li and Be. 7 A second restriction is the exclusion Of Ekin < 0.5 kev. A, = exp C C,,j. azi- + log(e,,). C C,,j. a~ - j=1+4 j=

7 Copyright(c)JCPDS-International Centre for Diffraction Data 2001,Advances in X-ray Analysis,Vol.44 6 Copyright(c)JCPDS-International Centre for Diffraction Data 2001,Advances in X-ray Analysis,Vol Copyright(c)JCPDS-International Centre for Diffraction Data 2001,Advances in X-ray Analysis,Vol A, = exp c C,,i. azi- + log(e,, ). c C,, j * j=1+4 q=o", a2 is given in degrees and can be chosen from 10 to 90 $ = exp C Cl,j log(e,, ) - 7 C1.i C2.i C3.i C4.i C5.i C6.i 1 j=1+4 j=1+4 + = exp C C2, j l g(e& >j- 2 j=1+4 a- J-1 a- J-2 J-3 -- J-4 a E+O E+OO -l.l18e E E+Ol E+OO -l.o86e E E+OO 1.529E E-03 l.o74e E E E E E+OO 1.858E E E E E E E-07 Table 1 Coefficients Cij for the global description of Al, AZ, l//al and lipa2 The global fits of A1 and A2 and of l/p/z1 and l/p/22 enable us to describe escape probabilities of electrons by a universal curve. The quality of the global fits can be seen from the comparison of the escape probabilities from Monte Carlo calculation (dots) with the broken curves (global) in Figs. 5 to 11. COMPARISON OF UNIVERSAL CURVES Schroeder describes the escape probability P(X) of electrons from a depth x for an electron emission into a 2x-geometry, electron energies from 2.96 to 7.40 kev and elements from K to Zn in units of the Bethe range Rg. P(x)=O.,,(,-,,)exp;-2.7.:) We describe P(x) for electron energies from 0.5 kev to 30 kev, elements from Z=l 1 to Z=79 and variable solid angle of electron acceptance by the much more general approach P(x)= A1.exp[-&.p]-A.exp[-2-p) whith amplitudes A and cross-sections I/p/ (expressed in cm2/g) obtained from least squares fits to the results of Monte Carlo calculations Since the meaning of I/p/ is identical with the usual mass attenuation coefficient,a@ in x-ray analysis we propose our approach for an application in the field of quantitative analysis by x-ray excited electron emission REFERENCES [l] Schroeder, S.L.M., Solid State Comm. 1996,98, [2] Ebel, H., R. Svagera, W.S.M. Werner, M.F. Ebel, Adv.X-Ray Anal. 1999,41, [3] Shimizu, R., Ding Ze-jun, Rep.Prog.Phys. 1992,55, [4] Ebel, H., R. Svagera, M.F. Ebel, N. Zagler, W.S.M. Werner, H. St&i, M. Griischl, Proc. ECASIA 95 (edited by H.J.Mathieu, B.Reihl and D.Briggs) J.Wiley &Sons 1996 TD4,99 l-998 [5] Werner, W.S.M., Phys.Rev., 1997, B55, [6] Wagner, H.W., W.S.M.Wemer, X-Ray Spectrom. 1998,27,