Copyright(c)JCPDS-International Centre for Diffraction Data 2001,Advances in X-ray Analysis,Vol

Transcription

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 II. EVALUATION OF LAYER THICKNESSES AS DETERMINED BY TOTAL ELECTRON YIELD (TEY) ABSTRACT Horst Ebel, Robert Svagera, Maria F. Ebel and Wolfgang S.M.Werner2 Technische UniverszXit Wien, Wiedner Hauptstraje 8-l 0, A 1040 Wien, Austria The validity and limitations of the concept of universal curves for the escape probability of x-ray excited electrons 192*3 were investigated by a series of TEY-measurements performed on thin pure element layers and ternary layers on GaAs-wafers. Layer thicknesses were chosen from a few nanometers up to several hundred nanometers and the electron energies covered a range from approximately 1 kev up to 20 kev. The essential result of TEY-measurements is that the layer thicknesses from TEY and from other methods are in very good agreement. Thus, the experiments are besides a confirmation of the analogy of the theoretical approaches of quantitative x-ray analysis4 and TEY analysis5 an excellent verification of the concept of universal curves for the escape probability of x-ray excited electrons 2. EXPERIMENTAL The measurements were performed employing a ROKAPPA Q-EDP-100 instrument. The x-ray source consists of either Cu or Ag target and the photon energy is tuned by means of a monochromator assembly, in which several crystals are arranged to give best reflection for different energies. We used in general either Si( 111) or Ge( 111). For low x-ray absorption at low photon energies the monochromator chamber is purged with He. The specimen chamber is separated from the monochromator chamber and evacuated to approximately 10m6 mbar. As electron detector a channeltron is used. All settings of the instrument are computer controlled. Thin films were prepared by sputter deposition or by evaporation and layer thicknesses were measured by quartz crystal monitor. We performed additional thickness determinations by XRF and electron probe micro analysis. For further details on the evaluation of data see ref.5. THEORY OF THIN FILM TEY Equations for TEY signals have been derived similar toxrf6. Whereas in XRF the escape of the fluorescence signal from depth x to the surface is expressed by exp(-y,t,.px/cosp) we use in TEY the escape probability3 with cross sections l/pa. -(~~~~) -A P(x)= A, ae *,(p&) Theory is demonstrated in GaAs-wafers with a variety of layers of different thicknesses. In the following selection of typical equations we took for primary processes the excitation of GaKLL Auger electrons in the substrate and in an Al(x)Ga( 1-x)As layer of thickness t. Examples of secondary excitations in the substrate and in an Al(x)Ga(l-x)As layer are the excitations of AsLMM Auger electrons by Ga K-radiation from the substrate and of Al KLL Auger electrons in the layer by Ga K-radiation from the substrate. For secondary excitation by layer radiation in 1 Institut ftir Angewandte und Technische Physik 2 Institut ftir 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 layer element excitation of Al KLL Auger electrons in the layer by Ga K-radiation from the layer has been chosen. Indices a and b in ra,b represent the energy of x-ray photons and the absorber, respectively. Cross sections l/&p are abbreviated by Ci and densities of either layer or substrate material are pi and ps. Concentrations and fluorescence yields are given by c and o. It is assumed that secondary excitation is performed by the complete series of characteristic K-radiations. Consequently, the radiations are replaced by an effective K-radiation of averaged photon energy and the transition probabilities are replaced by px=l. The angle of incident x-radiation with regard to the surface normal is a. primary excitation in substrate (Ga KL.L) ngakll (substr, prim) = 1. cos a -1 i+la, exp(--p, teci) *kc > I. i=l z A+Cj cos a cga,s. r,,,. (1- acak ). exp(- 2. t >. cos a primary excitation in layer (Ga KLL) 1 n,,(hy,prim)=----c cosa Gil,1 * E,GaK *(1-wGuK)- i=l L?L+c, cosa secondav excitation (As LMT from substrate by Ga K-radiation from substrate) n,s,w(substr,sec(gaks -+ A&)) =. 1 1 =-.-.c 2 cosa GaJ E GaK i+l. Ai +exp(-tep,.ci) TE, ---+cj cos a GaK AS,8 zguk,a, 6 z E,s secondary excitation (Al KLL in layer by GaK-radiation from substrate) naiel (Zay, sec(gak, + AEK, )) = =-.-.c 1 1 t * E,GaK - cr)gak CAl,i =G,,AIK.(l-WAIK).exp -z,,,.p, - 2 cosa Ga,s cosa 1. Ai.. tany.dy

4 Copyright(c)JCPDS-International Centre for Diffraction Data 2001,Advances in X-ray Analysis,Vol secondary excitation (Al KLL from layer by Ga K-radiation from layer) AIKLL (lay,sec(gu~, + AIK, >) = + * ---& cga,/ *,,,a, u)gok cal,i,,,a,.( - u)a/k > *p$c -1 > i+. Aj.tr.i *tarry.@.jko i=l j=l with ril = exp[-[&+ci) p.&tci).(&~) p, et) RESULTS Results of theory and experiment are expressed in relative edge jumps. In Figs.1 to 10 full curves have been computed. The curves are typically the sum of 10 to 50 contributions. Experimental data are the data points in the diagrams and can be distinguished by symbols cm for crystal monitor, xfu for x-ray fluorescence analysis and epma for electron probe micro analysis. Figs. 1 to 5 are from investigations performed on chemical elements of the layer, Figs. 6 to 9 from elements of the substrate and Fig.10 from Ga in both, substrate and layer. Theoretical substrate responses of Figs. 6 to 9 contain besides the resultant response the contributions from the substrate (substr), the layer (al, CU, au) and from characteristic x-rays (x~ays). The electron yield characterizes the number of measured electrons per incident photon. 3

5 Copyright(c)JCPDS-International Centre for Diffraction Data 2001,Advances in X-ray Analysis,Vol GaAs-CrK (theor. ~3084, exp..0075) the& - Ma-m x Fig.1 Relative Cr K-edge jumps of thin Cr the layers. The response is primarily defined by the attenuation of Cr KLL Auger electrons in Cr. Electron yie1d:theor-y Experiment Cr layerthickness (nm) Y P L 0.2 GaAs-CuK (theor exp..ooss) theor - *cm* l z&-m x Fig.2 Relative Cu K-edge jumps of thin Cu the layers. The attenuation of Cu KLL Auger electrons in Cu is primarily responsible for the observed thickness dependence of the relative Cu K jumps. Electron yield: Theory Experiment Cu&hickness (nm) GaAs-AuLl (theor..0017, exp..60,4) Fig.3 Relative Au Ll-edge jumps of thin Au the layers. The response is primarily defined by attenuation of Au LlMM Auger electrons in Au. Electron yield: Theory Experiment GaAs-AuL2 (theor..0039, exp..0025) wl8op - cm* l xfa-m x Fig.4 Relative Au L2-edge jumps of thin Au the layers. The response is typical for the attenuation of Au L2MM Augerelectrons in Au. Electron yield: Theory Experiment Au layerthickness (nm)

6 Copyright(c)JCPDS-International Centre for Diffraction Data 2001,Advances in X-ray Analysis,Vol l- GaAs-Ag. K-th= K-ex=.0003, LSth=.0143, LJex=,001 II 4.2 I Ag layer thickness (nm) Fig.5 Relative Ag K-edge- and Ag L3-edge jumps of thin Ag layers on GaAs substrates versus thickness of the layers. The two responses demonstrate the attenuation of Ag KLL- and Ag L3MM Auger electrons in Ag. Electron yield (K-edge) Theory Experiment (L3-edge) Theory Experiment G&As-AI (theor..0033, exp..0031) the.9 - epma + xfa 0. al - xrays - SUbsW - Fig.6 Relative Ga K-edge jumps from the substrate, GaAs wafers covered with Al layers of different thicknesses. The response demonstrates the attenuation of Ga KLL Auger electrons in Al. Electron yield: Theory Experiment \ = _ - - _ ml 1000 Al layerthickness (nm) Fig.7 For comparison to Fig.6 the relative As K-edge jumps from the substrate. GaAs wafers covered with Al layers of different thicknesses. The response demonstrates the attenuation of As KLL Auger electrons in Al. Electron yield: Theory Experiment Al glthbkness (nm) GaKAs-Cu (theor..0033, exp..0031) 800 IWO the& - Tf$ : _ x&m CU - xrays - SUbstr -.. X Fig.8 Relative Ga K-edge jumps from the substrate. GaAs wafers covered with Cu layers of different thicknesses. The response demonstrates the attenuation of Ga KLL Auger electrons in Cu. Electron yield: Theory Experiment

7 Copyright(c)JCPDS-International Centre for Diffraction Data 2001,Advances in X-ray Analysis,Vol theof - epma + Xfa Q. *fern x all* - ways - subsb Fig.9 Relative Ga K-edge jumps from the substrate. GaAs wafers covered with Au layers of different thicknesses. The response demonstrates the attenuation of Ga KLL Auger electrons in Au. Electron yield: Theory Experiment Au layerthicd~m) Fig.10 Ga K-edge jumps of GaAs wafers covered with Al(x)Ga( 1 -x)layers of different thicknesses (from 1.4 pm at x=0.69 to 2.4 pm at x=0.14) versus concentration x of Al. CONCLUSIONS A comparison of escape probabilities published by Schroeder, our earlier description2 and the presentation by an electron cross-section3 gave within the certainty of the experimental results no pronounced differences between the theoretical responses of Figs. 1 to 10. Advantages of crosssections are the ease of transformation of algorithms for quantitative x-ray fluorescence to quantitative total electron yield analysis and the computation of numerical values by polynomials in depence on electron energy and solid angle of electron acceptance. The agreement between experiment and theory confirms the theoretical approach and the numerical presentation of the escape probabilities of electrons from matter over a wide range of electron energies and chemical elements. 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] Ebel, H., R. Svagera, M.F. Ebel W.S.M. Werner, Adv. X-Ray Anal. (this volume) [4] Sherman, J., Spectrochim.Acta 1955, 7, [5] Ebel, H., R.Svagera, M.F.Ebel, Adv.X-Ray Anal. 2001,43, [6] Hobl, R., PhD Thesis, 1996 Techn.Univ.Wien