ESCAPE PROBABILITY OF ELECTRONS IN TOTAL ELECTRON YIELD EXPERIMENTS. Horst Ebel, Robert Svagera, Wolfgang S.M. Werner and Maria F.

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1 Copyright (C) JCPDS International Centre for Diffraction Data ESCAPE PROBABILITY OF ELECTRONS IN TOTAL ELECTRON YIELD EXPERIMENTS Horst Ebel, Robert Svagera, Wolfgang S.M. Werner and Maria F. Ebel Institut Rir Angewandte und Technische Physik Technische Universitat Wien Wiedner Hauptstralje 8-1, A 14 Vienna (Austria) INTRODUCTION The photoelectric absorption of x-ray photons of energy hv in an atomic level of electron binding energy E, is characterized by the emission of photoelectrons with kinetic energy hv-e,. In the course of their de-excitation the ionized atoms emit with a probability O<p<l Auger electrons with known kinetic energies. Thus, an irradiation of a solid specimen by monochromatic x-rays causes free electrons with well defined kinetic energies after their release from the atoms. The photoelectric absorptions occur in various depths of the specimen. Some of the corresponding photo and Auger electrons reach the surface after elastic and inelastic collisions. These electrons can be detected. Whereas the energy of the electrons at their origin is described by discrete values, we observe after their escape from the surface, a continuous energy distribution with a superposition of the original line spectrum of kinetic electron energies. The continuum is caused by inelastic collisions and the subsequent loss of kinetic energy. The electron range decreases with decreasing kinetic energy and therefore only a relatively small amount of the electrons from greater depths is able to reach the surface and to escape from there. When measuring the total electron yield (TEY) the detection of the electrons is performed without energy dispersion. Only the detection of low energy secondary electrons is suppressed by a retarding potential of typically 5OV in front of the electron detector. A systematic variation of the photon energy from below to above an absorption edge of one of the chemical elements in the solid gives rise to an increase of the TEY signal. The characteristic quantity in our application of TEY is this jumplike increase. Fig.1 depicts the TEY signal of GaAs in dependence on the photon energy from below the Ga K-edge to above the As K- edge. The size of the TEY jump depends on the x-ray flux, the concentration of the element in the specimen, the photoelectric absorption edge jump (K, L, M), the fluorescence yield of the corresponding atomic level and the escape probability. The following considerations deal with the escape probability of electrons in dependence on i. the chemical element, ii. the depth from where the electrons have to migrate to the specimen surface and the original kinetic energy of the electrons.

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 I I I I,I I I,,I I,,,I #_ IO,5 II, II,5 12, Photon Energy [kevj Fig.1 Measured TEY response of GaAs versus photon energy and comparison with the computed response. MONTE CARLO APPROACH The depth dependent emission characteristics for TEY have been investigated by means of Monte Carlo model calculations. Our model closely follows the one described in detail by Shimizu and Ding Ze-jun and will only be outlined here briefly. The basic model assumption usually made for medium energy electron transport in random solids is that an electron trajectory consists of linear steps between scattering processes. The distribution of steplengths is assumed to obey Poisson statistics allowing for a simple generation of random value for the steplengths. The only types of collisions regarded here are elastic electron deflection in the screened Coulomb field of the nucleus and (inelastic) excitations of the sea of valence electrons and lower shell electrons in the framework of the dielectric response approach. Depending on the type of collision, a characteristic of the process (i.e. a scattering angle or energy loss) is determined by drawing a random value from the corresponding distribution and updating either the electron direction, via some spherical trigonometry, or its energy. The distribution of scattering angles, or differential elastic scattering cross section was calculated with the relativistic partial wave expansion method after Yates2 employing a Thomas-Fermi-Dirac potential specified by the parameters given by Bonham and Strand3. For the present purpose, the differential inelastic inverse mean free path provides all necessary information concerning the inelastic electron solid interaction. This quantity was calculated with Penn s formalism4 employing a quadratic plasmon dispersion relation and using the required optical data compiled in the Handbook of Optical Constants of Solids. Generation and transport of secondaries is entirely disregarded.

4 Copyright (C) JCPDS International Centre for Diffraction Data Dependences of escape probabilities versus generation depth of Au for the case of isotropic emission, two electron energies (1 and 12keV) and two cones of electron acceptance (O-2 and O-8 with regard to the surface normal) are displayed in Figs. 2 to 5. An escape energy of at least 5eV was chosen. Apart from a pronounced energy and acceptance cone angle dependence, a quite striking feature is seen especially for smaller acceptance cone angles: the depth dependence deviates from exponential attenuation. This is a well known effect in the quasi elastic case6,7 and has been successfully explained by increasing isotropization of the escaping particle flux density as the generation depth is increased. Since elastic scattering is more intensive in the slowing down regime, we may conclude that the same mechanism is responsible for the non-exponential emission characteristics observed here. Erbil and coworkers* already suggested a deviation from Beer-Lambert type absorption law for TEY on the basis of a geometric argument. We describe the Monte Carlo results by a superposition of two exponential responses. P escape = ampl,aexp(-t/h,) - ampl,.exp(-t/h,) The sampling depth is defined by the depth A where the integral over pescape+dt from to A becomes l-l/e=.63 of the complete area beyond the escape probability - depth response. This is the usual definition under the assumption of an exponential law..8 MC results and approximation (Au 1 kev, cone O-8) ampl(l)=1.8 lambda(l)=2.29 ampl(2) =.316 lambda(2)= R._ E.5 n :.4 t; Q) :.3 P depth (nm) Fig.2 Escape probability of 1 kev electrons from different depths in Au. The cone of electron acceptance covers take-off angles of to 8 with regard to the surface normal. The sampling depth A becomes 4.24nn-r. In spite of the completely different escape probability - depth responses the agreement between the sampling depths of Figs.2 and 4 and Figs.3 and 5 is within 5%. In other words, the sampling depth depends primarily on the electron energy and the escape probability, but

5 37 additionally on the solid angle of electron detection (cone of electron acceptance, electron take-off angle)..9.8 MC results and approximation (Au IPkeV, cone O-8) ampl(l)=1.19 lambda(l)=555 ampl(2) =.394 lambda(2)= >,.6.Z s Q.5! h.4 E ti depth (nm) Fig.3 As Fig.2 with electron energy of 12 kev and sampling depth A=12.7nm..12 MC results and approximation (Au 1 kev, cone O-2).ampl(l)=.344 lambda(l)=2.19 ampl(2) =.242 lambda(2)=1.4 I.1 h -2 Q.8 % h.6 E ri g depth (nm) Fig.4 Escape probability of 1keV electrons from different depths in Au. The cone of electron acceptance covers take-off angles of to 2 with regard to the surface normal. The sampling depth A becomes 4.5nm.

6 Copyright (C) JCPDS International Centre for Diffraction Data MC results and approximation (Au IZkeV, cone O-2) ampl(l)=.353 lambda(l)=52.9 ampl(2) =.24 lambda(2)= z - % %.6 h g depth (nm) Fig.5 As Fig.4 with electron energy 12keV and sampling depth A=97.9mn. W OS Ir Pt AU Table 1 Investigated chemical elements with atomic number, atomic weight and density

7 372 GENERAL FORMULA FOR ESCAPE PROBABILITIES The Monte Carlo calculations were performed on 26 chemical elements (table l), 19 electron energies from 1keV to 3keV and electron acceptance angles with regard to the surface normal of O-lo, lo-2, 2-3, 3-4, 4-5, 5-6, 6-7 and 7-8. The following development of a general formula is based on our experimental setup. We use a conical channeltron for electron detection. Its front diameter is 13.7mm. The channeltron is mounted with its axis parallel to the surface normal of the specimen and the distance between the front of the channeltron and the specimen is 22mm. An x-irradiation of the specimen close to the intersection of the channeltron axis with the specimen surface allows to define the acceptance cone by O-2. Fig.6 displays the values of amplitude(l) of the 26 elements versus log(electron energy). A slight increase with increasing electron energy and an averaged scatter of the numerical values of +O.l allows for an approximation of amplitude(l) by a linear or a quadratic dependence versus log(electron energy). r r.6 - s.= 3 z Ej O-4 t ' log(electron energy (kev)) Fig.6 Presentation of the ampl(l)-values energies of 26 chemical elements and 19 kinetic electron We concentrated our investigations on the elemental range Z>2. As the number of elements is reduced to these 2 elements with Z>2 a comparably smaller scatter is obtained (Fig.7). The least squares fit through the data points is given by with the numerical A(i)-values of Fig.7. It has to be mentioned that the least squares fits of Figs.6 and 7 are nearly identical.

8 .8.6 i!.= E E.4 m A() = , A(1) = , A(2) = log(eleli:on eneriy (kev)) Fig.7 ampl( 1)-values of 2 chemical elements with Z>2 and 19 kinetic electron energies Similar considerations led us to the description of ampl(2) by ampz(2) = iio C(i) * (log EkiJi 1.8 w.6 i.z z 5.4 C() = , C(1) = , C(2) = log(eleli:on eneriy (kev)) Fig.8 ampl(2)-values of 2 chemical elements with Z>2 and 19 kinetic electron energies.

9 374 Now log(lambda(1)) is plotted versus log(electron energy) (Fig.9). The values of log(lambda(1)) increase with increasing kinetic electron energy. The wide scatter of ordinate values for different chemical elements at given electron energies can be reduced by multiplying lambda(l) with p.z/a (Fig.1). This factor is directly proportional to the number of electrons per cm3. =: 8 E 6 7 i x E 4 m = B 8. l ; t I l :. : : i.. : ;. l. : s.*ee. l. l. *:1:.*- l a l 8. : :.*t8. l **.. *:*. l I I _ I. *. l : *. l 8.: 8% :: ii :t 8 * a t b i I If f t f t 8g i f;i( id l atfi l a I log(electron energy (kev)) Fig.9 log(lambda( I.))-values of 26 chemical elements and 19 kinetic electron energies B() = , B(1) = , B(2) = log(ele/i:on eneriy (kev)) Fig.1 log(lambda( l).p.z/a)-values with quadratic least squares fit of 26 chemical elements and 19 kinetic electron energies

10 375 The approximations for lambda( 1) and lambda(2) respectively, are log(zambda(1) P-Z 7) =,io B(i) (log Ekin)i log(zambda(2) * P-Z 7) = iio D(i). (log EkJ Numerical values of coefficients B(i) and D(i) are given in Figs. 1 and 11. Or ene& (kev)) 2.5 Fig.1 1 log(lambda(2).pz/a)- va 1 ues of 26 chemical elements and 19 kinetic electron energies with quadratic least squares fit CONCLUSIONS An evaluation of the results of Monte Carlo calculations led us to an universal description of the escape probability of electrons with defined kinetic energy which start in matter in depth t under an arbitrary direction. The universal algorithm has been obtained from the evaluation of the results from Monte Carlo calculations performed on 26 chemical elements and 19 kinetic electron energies. This is valid for an electron acceptance cone of O- 2 with regard to the surface normal of the specimen. In order to perform a comparison with,,electron ranges from literature we transform our escape probabilities into sampling depths A. As already mentioned A depends only to a minor degree on the acceptance cone. We plot log(a.p+z/a) versus log(electron energy) of our 26 elements and 19 energies (Fig. 12) and use again the least squares fit for the description of the sampling depth in matter in dependence on the kinetic electron energy.

11 376 l%w P*Z -) =,io E(j) * (lo!3 E,kin)i A i3 k 6 L *a x 5 4 A Ei,o 2- E() = , E(1) = , E(2) = O-.5 -I 1 log(ele%n enet& (kev)) Fig.12 log(a.p.z/a)-values quadratic least squares fit of 26 chemical elements and 19 kinetic electron energies with In comparison with Erbil et al* and Martens et al9 who published an electron range of 1OOmn for 7keV electrons in Cu, we obtain A=72.6nm. Abbate et al gave 2.5nt-n for O.SkeV electrons in Tb and our value is h=.75. Finally, Vogel et al found l.lnm for.8kev electrons in Dy and our value is A=O.72nm. There exists no information on the accuracy of the experimental results of the different authors. Another possibility to check the validity of our universal description of the escape probability is an evaluation of TEY experiments performed on different substrate layer combinations. One example is depicted in Fig. 13. Ti substrates were covered with Cr layers with thicknesses from 1 to 5nm Normalized jumps are the ratios of Ti K-jumps from Ti substrates with Cr layer and an uncovered Ti specimen. Data points of Fig. 13 are from experiments and the curve is from our theoretical concept 12,13 under inclusion of the numerical values of the escape probability of this work. Thicknesses of the Cr layers were measured during sputter deposition and by XRFA. An agreement of better than +5% between the different values of the layer thicknesses could be found. The standard deviation o of the normalized jumps is better than 5% of the jump value. Thus, the deviations of the data points from the curve in Fig.13 are within the described error intervals. A second example is depicted in Fig.14. Fe substrates were covered with Cr layers with thicknesses from 1 to 5OOnn-r. Normalized jumps are the ratios of Cr K-jumps from Cr layers and a thick Cr layer.data points of Fig.14 are from experiments and the curve is from our theoretical concept. The other details are comparable to the discussion of Fig. 13.

12 377 Our earlier investigations14 15 were concentrated on exponential description of the emission depth distribution. A comparison with our present results from 26 elements and 19 electron energies on the basis of sampling depth A gives a fairly good agreement Cr layer thickness (nm) 5 6 Fig.13 Measured Ti K-jumps of Ti substrates covered with thin Cr layers (data points) and theoretical response (curve) calculated with the escape probabilities of this paper exp l theory thickness of chromium layer (nm) Fig.14 Theoretical response of the normalized Cr K-jump versus thickness of the Cr layer and results of our experiments from 1 chromium layers

13 378 REFERENCES Ul lj1 WI WI WI [I41 WI R.Shimizu and Ding Ze-jun, Rep.Prog.Phys. 487 (1992) A.C.Yates, Comp.Phys.Comm. 2: 175 (1971) R.A.Bonham and T.G.Strand, J.Chem.Phys. 39: 22 (1963) D.R.Penn, Phys.Rev. B35: 482 (1985) E.D.Palik ed., Handbook of Optical Constants of Solids (Academic Press, N.Y. 1985) W.S.M.Werner, W.H.Gries and H.Stiiri, Surf.Interface Anal. 17: 693 (1991) I.S.Tilinin and W.S.M.Werner, Phys.Rev. B46: (1992) A.Erbil, G.S.Cargill III, R.Frahm and R.F.Boehme, Phys.Rev. B37: 245 (1988) G.Martens, P.Rabe, G.Tolkiehn, and A. Werner, phys.stat.sol. (a)55: 15 (1979) Abbate, J.B.Goedkoop, F.M.F.de Groot, M.Grioni, J.C.Fuggle, S.Hofmann, H.Petersen, and M.Sacchi, Surf.Interface Anal. 18: 65 (1992) J.Vogel, and M.Sacchi, J.Electron Spectrosc.Relat.Phenom. 67: 181 (1994) M.F.Ebel, R.Svagera, M.Lindner, M-Baron and H.Ebel, this volume H.Ebel, R.Svagera and M.F.Ebel, this volume H.Ebel, R.Svagera, M.F.Ebel, N.Zagler, W.S.M. Werner, H.Stiiri and M.GrGschl; Proc. ECASIA 95 (edited by H.J.Mathieu, B.Reihl and D.Briggs) J.Wiley&Sons (1996) TD4, H.Ebel, R.Svagera, M.F.Ebel, N.Zagler, W.S.M. Werner, H.Stdri and M.Griischl; Advances in X-ray Analysis, Vo1.39, in print