QUANTITATIVE TEY (TOTAL ELECTRON YIELD) - THEORY, INSTRUMENTATION AND EXPRIMENTAL RESULTS

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1 732 QUANTITATIVE TEY (TOTAL ELECTRON YIELD) - THEORY, INSTRUMENTATION AND EXPRIMENTAL RESULTS Horst Ebel, Robert Svagera, Maria F. Ebel and Matthias Baron Institut fiir Angewandte und Technische Physik Technische Universitat Wien Wiedner Hauptstrafie S- 1, A 14 Vienna (Austria) INTRODUCTION In 1994 we published for the first time the analytical application of TEY,2 which is based on a fundamental parameter approach similar to XRF. Quantitative analyses of binary alloy systems and layer thicknesses of elemental layers and compositions and thicknesses of ternary layers on binary substrates were the subjects of further papers, to be continued by the evaluation of measured TEY responses, considerations on the statistical significance of measured results and the influence of secondary electrons on analytical results. A further consideration is the sampling depth of the method. In the present paper we report on the application of a new description of the escape probability of electrons in solid matter to the determination of layer thicknesses, a new description of an effective TEY jump and the influence of the x-ray detection efficiency of the electron detector on the description of measured TEY jumps versus layer thickness. THEORY OF THE SUBSTRATE METHOD a. Effective layer thickness TEY deals with the release of electrons in matter due to the interaction of x-rays with atoms. In the energy interval from 1 to 3keV the photoelectric absorption is dominating. Thus, we expect photoelectrons from the absorption processes and Auger electrons from the de-excitation of the atoms. We demonstrate the derivation of the equation for the signal strength in dependence on the layer thickness by the combination of V as substrate element and of Au as layer element and use the TEY information from the V K-jump. The depth distribution of photoelectric absorptions in the substrate is given by t dt dzvk = x,. e-z-w pt,,,,.-. cos a %,VK f? *e AALL -ZE,Au PAu cosa ze,v describes all possible photoelectric absorptions of x-ray photons with energy E in the different atomic shells and subshells j with electron binding energies BE, of V (~~, =I=~:E,vj). xe is the flux of monochromatic x-rays of energy E in photons/s. pv is the density and a the angle of incident x-rays with regard to the surface normal. The second exponential expression describes the absorption of incident x-rays in the Au layer. An exponential decrease with

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 -

3 733 depth t characterizes the depth distribution of the number dzv, of photoelectric absorptions in the V K-shell. Photoelectrons of kinetic energies E,i =E-BE,, and Auger electrons of known kinetic energies E,,(VK,kl) are released. A certain percentage of these electrons reaches the surface of the solid after inelastic collisions and can be detected. The detection probability Pdetection depends on the element i, the depth t, the kinetic energy Ekin and the solid angle R of electron acceptance. Fig.1 displays the detection probability for vanadium, E,i,,=SkeV and a detection cone of k2 with regard to the surface normal. The data have been obtained by Monte Carlo calculations under the assumption of an arbitrary direction of the electrons after their start in depth t and are valid for an escape energy from the surface of at least 5eV. We describe the response by a sum of two exponential functions. A systematic investigation of the energy and element dependences of the constants K,, K2, h,, and h,, led to the following general description KI = ln(E,,) -.32.[ln(II?kjn)]2 K, = ~ln(E,)-.31~[ln(E,,)]2 Ai is the atomic weight and Zi the atomic number of element i. K, and K, only depend on Eki,,, whereas h,,l and hi,2 depend on both the element i and Ekin. The equations have been obtained from least squares fits to the results of Monte Carlo calculations3 which have been performed on 2 chemical elements from Z=22 to Z=79 at 19 electron energies from 1 to 3keV. We compared the results from 6 further chemical elements from Z=3 to 19 and found a reasonable agreement with the above given description..2 MC results and approximation (V BkeV, cone O-2).15 * 2 Q z.1 h 4 P depth (nm) 15 2 Fig.1 Depth dependence of the escape (detection) probability of 5keV electrons in electron acceptance of +2 with regard to the surface normal V for an

4 734 A similar distribution is obtained for Au. The resultant amplitudes are nearly identical, but the depth range is different. The amplitudes K, and K, do not depend on the chemical element, but the corresponding values of the electron ranges hv,l, h,,, are approximately three times the values hau,l and hau,2. MC results and approximation (Au SkeV, cone O-2) 1 depth (nm) Fig.2 Depth dependence of the escape (detection) probability of 5keV electrons in Au for an electron acceptance of +2 with regard to the surface normal An integration of dn,, =dzvk.pelectron.pesca,,e,v from depth t=o to t+m cc nvk = xe.e -ze,v b p t cosa E VK =x * A - Per&on Pv E cosa % VK * A * Peiecmn * Pv * cosa M %,I -K2.e r I _ A A 1 TE,V * Pv 1 t+b 1 4lL Iv,2. e-ze,au pau COStXdt = - -K2- e VJ _ E,Au PAu,~ cosa.e re,v * Pv 1 cos a + &,I cos a + 4,* I defines the contribution tc I the measured TEY signal from VK-electrons. pelectron is the probability for the release of either a photo or an Auger electron after photoelectric absorption. For photoelectrons pelectron =l and for VK,kl-Auger electrons pelectron=l-qk (qk is the fl&~rescence yield). Thus, we replace the Au layer by an jnactive V layer of thickness A which does not contribute to the TEY signal. This replacement asks for a transformation of the thickness da,, into A. A comparison between Figs.1 and 2 shows that for V substrate and thickness d,=loonm the escape probability is approximately.2, whereas an identical escape probability for Au at thickness d,,~4nm is observed. An Au layer of approximately 4nm causes an identical attenuation as an jnactive V layer of 1OOnm. AU

5 735 In order to derive an equation for the transformation of thicknesses from V to Au we plot the escape probabilities of V and Au versus reduced depth scales (p,~z,/a,)-t and (p,,~z,,,/a,jt and compare again the escape probabilities (Figs.3 and 4). MC results and approximation (V 5keV, cone O-2) depth*rho*zla 6 Fig.3 As Fig. 1 but versus pv-z,-t/a, MC results and approximation (Au 5keV, cone O-2) depth*rho*zia 6 Fig.4 As Fig.2 but versus pau-z,;t/a,, The responses are now nearly identical and the transformation A A==----- PAU Au dau h V AAu can be performed by

6 736 Consequently, the expression nvk for V substrate and Au layer of thickness d, becomes E VK P.Z.d P.Z.d I, Aa, Au -K2. TE,V e A AU f2 Ekin ZV 1 _ E,Au PAu,~ cosa.e Au OSa + AV *f2(ekin) We used the pair V and Au due to their well pronounced difference of electron ranges at a given electron energy Ekin. b. Effective TEY jumps The following considerations are performed on thin Cr layers on Ti substrates and Ti K-edge jumps were evaluated for Cr layer thicknesses. Thus, we deal with the TEY responses from 25eV below to 25eV above the Ti K-edge. Incident photons with an energy of less than BE,ik=4.965keV are able to ionize the L and M -shells of Ti and of Cr. Therefore, photoelectrons and LMM-Auger electrons from Ti and Cr form the TEY signal in this energy interval and still contribute at photon energies of more than 4.965keV to the TEY responses versus photon energy. The principle of the theoretical treatment with our earlier description of the electron ranges in matter,2 can be adopted to the new concept of escape (detection) probablities by a comparison to the development of the equation for nvk in the foregoing chapter. Fig.5 gives the TEY responses versus photon energy for and 5nm Cr layer thickness. Negative contributions to jumps are from the increase of ZE,Ti from 3.33 to 71.4cm2/g at the Ti K-edge..3 Onm Cr - 5nm Cr -.25 z 5.2 Jz iii s g.15 ii 3 z.$ photon energy (kev) Fig.5 TEY responses due to photoelectrons from L and M-shells and LMM-Auger electrons of Ti and Cr for and 5Onm Cr layer At photon energies E24.965keV it becomes possible to additionally ionize the Ti K-shell. Ti K-radiations and Ti KLL and Ti LMM-Auger electrons are from de-excitation. Ti K- radiations can cause secondary excitations in Ti L and Ti M of the substrate and in Cr L and Cr M of the layer. These secondary ionization processes are responsible for further photo and Auger electrons. The contribution of the photoelectron from photoelectric absorption of

7 Copyright (C) JCPDS-International Centre for Diffraction Data incident x-rays in the Ti K-shell to the TEY signal can be neglected due to the small kinetic energy. Fig.6 gives the complete TEY signal and the,,background corresponding to Fig.5 without Cr layer. In the experiments we measure the sawtooth like response and were not able to recognize the negative jump of the,,background. The loss of the jump is approximately 2%. In our earlier evaluations we used just the jump of Ti K photoelectric absorption and introduced an error of a few percent. Now the evaluations are performed under recognition of the negative background jump. For the sake of completeness the response of Ti with 5nm Cr layer is given in Fig backgr. - Ti K -?? s g. Tii 5 5. P 3 iii g.4 In J A energ; photon 5.5 (kev) Fig.6 TEY signal versus photon energy and,,background for Ti without Cr layer backgr. - Ti K g.35 - c $.3 - s $ s 2 ;.2 -.E *.15 - z t 1 I photon energy (kev) Fig.7 TEY signal versus photon energy and,,background for Ti with 5nm Cr layer. c. X-ray detection efficiency of the electron detector The photon flux of characteristic Ti K-radiations is given by

8 73 R F Ti-K 1 TiK = detector.-.l. -e 4x cosa ETi! TiK,Ti, cosa cosp _ E,Cv + TiK.Cv cosa cosp %Pb with the solid angle R of x-ray detection (in our system R/4x=.226). ZTiK,Cr is the coefficient of photoelectric absorption of Ti K-radiation in Cr, ~TiK,Ti for Ti K-radiation in Ti and re,ti_k for radiation of energy E in the Ti K-shell. For photon energies of 4SkeV (Ti K-radiation) Wiza4 published a detector efficiency of channel electron multipliers sdetecto~=.4. Fig. displays the contribution from the detection of characteristic Ti K-radiation to the measured TEY signals. o-ooo2 I Cr layer thickness (nm) 5 6 Fig. Detection of Ti K-radiation by the electron detector A slight decrease with increasing Cr layer thickness comes from the absorption of incident monochromatic radiation and Ti K-fluorescence radiation in the Cr layer. The contribution to the measured jump of Ti without Cr layer of approximately O.Olelectrons/photon is less than 2% and nearly compensates the negative jump of the,,background (see Figs.5 and 6). The jumplike increase at the Ti K-absorption edge is evaluated for quantitative applications. The main contribution of O.Oelectrons/photon comes from primary excitation and subsequent de-excitation by the emission of Ti KLL and Ti LMM-Auger electrons (see Fig.9, at d,,=onm). Secondary excitations with photoelectrons from photoelectric absorption of characteristic Ti K-radiation in the Cr layer and subsequent Auger electron emission (see dotted curve in Fig. 1) start at d,,=o from zero followed by an increase towards the maximum of.15 electrons/photon at d,,=9nm and a decrease to,9electrons/photon at d,f6nm. Therefore, only the detection of x-rays by the electron detector and the secondary excitations in the layer are responsible for measured Ti K-jumps at Cr layer thicknesses of more than 2nm. Secondary excitations with photoelectrons from photoelectric absorption of characteristic Ti K-radiation in the Ti substrate and subsequent Auger electron emission (see full curve in Fig. 1) are responsible for contributions of O.O13electrons/photon at d,,=o followed by a decrease towards zero at approximately d,,=15nm. We form the sum of these

9 739 contributions under recognition of the breakdown of the,,background and compare our computed results with measured results. It is usual to normalize the computed and the measured signals with regard to a reference - in our application this is the Ti K-jump at d,,=o Cr layer thickness (nm) Fig.9 Contribution from primary excitation of Ti K and de-excitation by emission of Ti KLL and subsequent Ti LMM-Auger electrons to the measured Ti K-jumps sec.1 - sec ' ;.1 ie s 5 e-5 Y 3 1 6e-5.s u) 2 4e-5 2e Crlayerthickness(nm) 5 6 Fig.1 Contributions to the measured Ti K-jumps from secondary excitation processes. sec. 1 describes the substrate contribution from photoelectrons Ti K-radiation+Ti L-shell absorption and Ti K-radiation+Ti M-shell absorption and Ti LMM-Auger electron emission from de-excitation of Ti L sec.2 describes the layer contribution from photoelectrons Ti K-radiation+Cr L-shell absorption and Ti K-radiation-+Cr M-shell absorption and Cr LMM-Auger electron emission from de-excitation of Cr L

10 =I:1 IOnmCr,,._ (-- _ 12 substrate Ti E WI 16, I 4- A, I I I WeV1 1 I I I I 4, 53 5,2 E WI, 4-w,.. I I I 4 5,O 5,2 EWI I I I I 4 5,O 5,2 4tL 4, 5,O 5,2 16 WeV1 WeV1 16, I I, I 4, 59 5,2 WeV1 16, I I I I I 4, 5 52 WeVJ 4-- v I I I 4, 5,o 5,2 EWfl Fig.1 1 Measured TEY responses in the Ti K-region 1 I I I I 4 5,o 532 WeV1

11 741 INSTRUMENTATION AND EXPERIMENTAL RESULTS The measurements were performed employing a ROKAPPA Q-EDP-1 instrument. The x-ray source consists of either a Cu or an Ag target and the desired photon energy is tuned by means of a monochromator assembly, in which several crystals are placed to give best reflection for different energies. We used in general either Si(ll1) or Ge(ll1). The monochromator chamber is purged with He for low absorption at low photon energies. The specimen chamber is separated from the monochromator chamber and pumped to approximately 1m6mbar. A channeltron is used as electron detector. All settings of the instrument are computer controlled. The specimens were prepared by sputter deposition of Cr on Ti substrates and the layer thicknesses were measured by quartz crystal monitor. After deposition we performed thickness determinations by XRF and found reasonable agreement with the monitor values, For the characterization of the specimens we use the monitor values. Ti K-jumps were measured in an energy interval from -25eV to +25eV with regard to the Ti K-absorption edge. Fig.1 1 gives 11 measured TEY responses for Cr layer thicknesses from to 5OOnn-r. Fig.12 displays our theoretical response of normalized Ti K-jumps (Ti K-jump=1 at d,,=o) versus Cr layer thickness and the normalized experimental results of Fig. 11. The theoretical thickness dependence (curve) has been computed under neglection of a possible detection of characteristic Ti K-radiation by the electron detector Y._ c.5 -z.e 3.4 E g.3 I I L-l meas. -theory Cr layer thickness (nm) 5 6 Fig.12 Theoretical and experimental normalized Ti K-jumps An agreement between theory and experiment is only given at Cr layer thicknesses from to Onm. This indicates an additional contribution to the measured signal which has not been included in our theoretical concept. Considering the detection of characteristic Ti K- radiations by the electron detector the curve of Fig. 13 is obtained. This result confirms our theoretical approach, the evaluation procedure of measured TEY responses and the concept of escape probabilities.

12 Copyright (C) JCPDS-International Centre for Diffraction Data Y.- l-.5 m It).4 E g Cr layer thickness (nm) 5 6 Fig13 Experimental (data points) and theoretical normalized Ti K-jumps (curve) considering the detection of x-rays by the electron detector. CONCLUSION We introduce a new description of electron ranges in matter and demonstrate the application by the development of a new theoretical approach for the determination of layer thicknesses by the substrate method. A careful investigation of the TEY responses in dependence on photon energy and layer thicknesses recommends the consideration of a breakdown of the background signal at the absorption edge and of x-ray detection by the electron detector. The new approach is verified by an investigation on thin Cr layers on Ti substrates. REFERENCES [l] M.F.Ebel, R.Svagera, H.Ebel, R.Hobl, M.Mantler, J.Wernisch, and N.Zagler, Adv.X-Ray Ana1.3: 127 (1995) [2] H.Ebel, R.Svagera, M.F.Ebel, and N.Zagler, Adv.X-Ray Anal. 3: 325 (1995) [3] H.Ebel, R.Svagera, W.Werner and M.F.Ebel, this volume [4] J.L.Wiza, Nucl.Instr. and Methods. 162: 57 (1979)