Horst Ebel, Robert Svagera, Christian Hager, Maria F.Ebel, Christian Eisenmenger-Sittner, Johann Wernisch, and Michael Mantler

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1 DETECTION OF SUBMONOLAYERS BY MEASUREMENT OF THE TOTAL ELECTRON YIELD (TEY) OF X-RAY EXCITED ELECTRON EMISSION Horst Ebel, Robert Svagera, Christian Hager, Maria F.Ebel, Christian Eisenmenger-Sittner, Johann Wernisch, and Michael Mantler Technische Universitat Wien Institut Rir Angewandte und Technische Physik A 14 Vienna (Austria), Wiedner Hauptstralje 8-1 INTRODUCTION We described in earlier papers1,2,3 the theoretical concept for the determination of thicknesses and compositions of thin layers and the composition of bulk specimens by TEY. An essential feature in quantitative TEY is the statistical significance of the measured TEY jumps. The present investigations are dedicated to the detection limit of TEY for extremely thin layers and consequently, on the minimum detectable mass by TEY. For this purpose we have to quantify the statistical significance of the measured TEY jumps. This statistical concept is developed by an explanation of the procedure. TEY measurements are performed and evaluated. Another application is the possibilibilty to quantify the significance of quantitative analyses by TEY. EXPERIMENTAL We investigated bulk Al,Ga,_,As, GaAs and thin Cr layers on Si wafers and measured the Ga K and the Cr K jumps. We mounted the specimens in the specimen chamber (1m6 mbar) of the x-ray station ROKAPPA Q-EDP 1 on a grounded specimen holder allowing a total of six specimens. X-radiation of a rotating Cu anode system (3 kv, 1 ma) was monochromatized by either a Ge (111) or a Si (111) crystal. The photon energy was scanned in steps of 1 ev from 25 ev below to 25 ev above the Ga K absorption edge and from 35 ev below to 35 ev above the Cr K absorption edge, respectively. The total electron emission of the specimen was detected by a channeltron detector. In front of the channeltron a biased grid (-4 V with regard to ground) was mounted. Thus, we suppressed the detection of low energy secondary electrons, Besides the electron emission we measured the x-ray flux by a gas proportional counter, following the sequence: Copyright JCPDS-International Centre for Diffraction Data 1997

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 I TEY 1 (cps) n E reduced TEY (e-/photon) photon energy (kev) Fig.1 Measured flux of monochromatized x-rays for photon energies from below the Ga K edge to above the As K edge Measured TEY response of pure GaAs Comparison of the normalized TEY response to the theoretical response 72 3 Copyright JCPDS-International Centre for Diffraction Data 1997

4 x-ray spectrum - TEY-spectrum of specimen 1 - TEY-spectrum of specimen TEYspectrum of specimen 6 - x-ray spectrum. This sequence helps to detect drifts of the x-ray flux and to reject the corresponding TEY results from further evaluation. The first step of the evaluation of measured responses of TEY signals in dependence on the photon energy is the elimination of the influence of the x-ray flux. We calculate x-ray fluxes after correction of the measured data for deadtime losses of the detector in dependence on the photon energy and form the ratio of the TEY and the x-ray flux spectra. Whereas the measured spectra are given in units of electrons per second and photons per second, the normalized TEY spectra give electrons per photon. An example of the data reduction is given in Fig.1. The response on top is the flux of monochromatic x-rays in the photon energy range from 1.1 kev to 12.2 kev. The W L lines are from surface contamination of the Cu target due to evaporation from the tungsten filament. The measured TEY response of pure GaAs contains the Ga K edge at approximately 1.4 kev and the As K edge at approximately 11.9 kev. The normalized TEY response is the ratio of TEY and x-ray flux. This normalized experimental result (thick line) is compared to our theoretical response (thin line)1,2,3. The interesting quantities are the jumps at the two absorption edges. Thus, the jump at the Ga K edge is the difference.12-.5=.7 and the jump at the As K edge is =.6. We express the result of quantitative TEY measurements by the ratio of the jumps of an unknown specimen and a standard of known composition and thickness. A quantitative analysis of Al,Ga,_,As is performed by using the ratio of the Ga K jumps of Al,Ga,_,As and of pure GaAs. A thickness determination of thin Cr layers asks for the ratio of the Cr K jumps of the thin layer and a thick reference. Examples are given in this paper. Two essential features of the reduced responses have to be mentioned: i The responses are influenced by counting statistics ii It is possible to approximate them close to an absorption edge by a linear fit to the normalized TEY response. QUANTIFICATION OF TEY JUMPS A first result of the theoretical treatment of TEY signals is the proportionality of the normalized TEY signal with the photoelectric absorption coefficients. TEY is frequently used for the quantification of EXAFS structures. On our responses we expect EXAFS structures too. This explains the description of the intrinsic response by a superposition of an EXAFS structure with the sawtooth response of the photoelectric absorption coefficient (Figs.2a and 2b). The TEY response is obtained by an energy scan with monochromatic x-rays. An important feature of a crystal monochromator is the spectral FWHM of the monochromatic energy distribution. A narrow setting of the monochromator allows for FWHMs of a few ev and less. Since the TEY response is the result of a convolution of the photoelectric absorption coefficient response with the spectral distribution function of the monochromator, we are able to depict the EXAFS structures of the specimen only for narrow monochromator setting. As it can be seen from Fig.2a a FWHM of 5 ev enables a nearly perfect reproduction of the intrinsic response. On the other hand a narrow monochromator setting causes weak fluxes of monochromatic x-rays. But, our analytical TEY application asks only for the jump of the sawtooth response. Therefore, a comparably great FWHM of 1 ev allows much greater x-ray fluxes and the EXAFS structure disappears in the TEY response of Fig.2b. Copyright JCPDS-International Centre for Diffraction Data 1997

5 4 b) - intrinsic edge structure afler convolution I monochromator resolution 93 IO, IO,2 IO,4 IO,6 IO,8 II, 93 IO, IO,2 IO,4 IO,6 IO,8 II, E Wfl E Wfl 4 d) 4 3 L I ,8 IO, IO,2 IO,4 IO,6 IO,8 II, E Ffl 93 IO, IO,2 IO,4 IO,6 IO,8 II, E [keyi Fig.2 Detailed description of the development of a measured TEY response from the intrinsic response its convolution with the energy distribution of the monochromator separation of the curve into discrete data points addition of counting statistics by a random number generator. Our measurements are performed by step scans of the photon energy. With a step width of 1 ev the TEY response is represented by discrete data points (Fig.2c). Adding counting statistics by a random number generator one obtains the synthesized TEY response of Fig.2d. Below and above the edge there exist two energy ranges, where the data points allow for two linear least squares fits. The evaluation is performed by an extrapolation of the linear fits to the vertical line at the position of the absorption edge. The distance of the intersections of the linear fits on the vertical line is the TEY jump. Counting statistics govern the numerical value of the jump. Copyright JCPDS-International Centre for Diffraction Data 1997

6 A numerical treatment4 of the standard deviation (3, of the intersection of a least squares fit through statistically scattering data points (xi, yi) with the ordinate axis in (, a) asks for the knowledge of the standard deviation O(yi) of the individual data point. Since our reduced TEY responses are ratios, we need the standard deviations o(teyi) of the TEY signal - it is the square root of the total number of measured electrons at energy position Ei - and o(fluxi) of the x-ray flux - it is the square root of the total number of measured x-ray photons at energy position Ei. o(y,)is found by an application of the law of error propagation to ratios. The abscissa xi is measured with regard to the absorption edge at energy Eedge and is given by Xi=Ei- E edge. The error quantity Vi in the least squares fit is defined by v. = Yi -a-b xi 1 O(Yi) with the intersection a and the slope b of the linear fit. The chi-square merit function becomes From the minimum follow X2(a,b) = 2~: i=l conditions of the chi-square merit function ax2 - ax2 =O and - a Lb a= b= with the abbreviations S xx S, -Sx Sx, A S*S, -s, *s, A The standard deviation, of the intersection Sxx of =- A N is the number of data points. a is obtained from ERROR ANALYSIS AND DETECTION LIMIT An error analysis is possible as the standard deviations of the lower and the higher intersections of the jumps for both, the unknown and the reference specimen, have been determined. Error propagation has to be applied to two differences - higher minus lower intersection - and one ratio - jump of the unknown divided by the jump of the reference specimen. The resulting standard deviation is used to define for example a o-interval around the measured jump ratio. Fig.3 contains the measured normalized Ga K TEY responses of pure GaAs and of a thick Al,Ga,_,As specimen. Both responses include the linear fit procedure, the intersections with the vertical line at the Ga K edge and the width of the error intervals expressed by an interval of *to, where CJ is the resulting standard deviation. A comparison of the Copyright JCPDS-International Centre for Diffraction Data 1997

7 experimental TEY ratio with the theoretical x-dependence at x=.33 shows an excellent agreement between theory and experiment. IO 8 t; I- 6 4 & IO 8 4 :pq&qjq... - if-- 2 :: IO,2 IO,4 IO,6 IO,2 IO,4 Photon energy [kevj Photon energy [key IO,6 17 iz % a E b,4 c z % 32 S i!! w , concentration of Al (x) Fig.3 Normalized TEY responses of GaAs and of Al,Ga,_,As (x=.33) measured in steps of 1 ev at photon energies from 25 ev below to 25 ev above the Ga K edge. From linear extrapolation the intersections on the vertical line at edge position are determined. The intervals at the intersections describe fo, intervals. The ratio of the two measured jumps is the data point in the theoretical x-dependence of this ratio. The error bars have been set to fo. Copyright JCPDS-International Centre for Diffraction Data 1997

8 4:lI InmCr 3 substrate Si & 2 - l- & 2 - l- 1 - A A % I I I 5, EWI, I I E Wfl > 2 - P,p /,, I I I WeV1 H--- 1 I II I E WI t 2 - F 1; 2 l- 1-1 I I I 5,6 5, EWI I I I 5, EWI 64 Fig.4 Normalized TEY responses of thin Cr layers on Si wafers Copyright JCPDS-International Centre for Diffraction Data 1997

9 Defining the detection limit DL by with the background signal n,, we have a quantity DL equal to three times the standard deviation of the background signal. When replacing 3. J-- nb by 3., of the lower intersection in the reduced TEY response we obtain the height of the jump which can be distinguished from the TEY response without the chemical element of interest. Thus, we performed measurements on thin Cr layers on Si wafers and measured the Cr K TEY responses. Fig.4 shows the reduced TEY responses of six Cr layers of thicknesses.5, 1, 2, 4, 1 and 5 nm measured in steps of 1 ev in the photon energy interval from 35 ev below to 35 ev above the Cr K edge. An averaged standard deviation of the lower intersection of.5 has been found. According to theory a Cr layer of 5 nm is of infinite thickness for TEY. We need the ratios of the Cr K jumps of an unknown thin Cr layer and the infinite thick reference layer. The theoretical dependence of this ratio (Fig.5) helps us to determine the detection limit of Cr. It follows from the initial slope of the curve at layer thickness t=o. The initial slope m of the broken curve in Fig.5 is.4/6. We express in case of extremly thin Cr layers the ratio r of the measured layer jump (jumpl,,,) and the jump of the 5nm layer (jumpsoo) by r= JUmPlayer t jump5-6 and the minimum detectable layer thickness tmin by r _- jump,i, -- O-4. t. m1n jump5oo - 6 m1n Cr on Si t P-d Fig.5 Theoretical TEY ratios of thin Cr layers on Si wafers in dependence on the layer thickness for layers with and without an Al overlayer of 2 run. Copyright JCPDS-International Centre for Diffraction Data 1997

10 5 4 3 iti I nm Al.5nm Cr substrate Si I 5, WeV , t1 2nm Al 4 Inm Cr substrate Si 3 2i I- 2 k--t E WI 5 I I I I I I , E WI E [keel D 2nm Al 1 Onm Cr substrate Si cl I- 2 2nm Al 5OOnm Cr substrate Si 1 I II I ,O E Pvl 58 6 WeV Fig.6 Normalized TEY responses of thin Cr layers on Si wafers with an Al overlayer of 2 nm Copyright JCPDS-International Centre for Diffraction Data 1997

11 The corresponding measured jttmp,i, jumpmin = bin * jump5 has to be equal to 3.,=3*.5. From Fig.4 follows jumpsoo=37-7=3. Thus, tmin is found from jumpmin = $ * tmin 3= 3..5 t min =.75nnI This is a submonolayer and with the density of Cr of 6.93 g/cm3, an observed surface area of.12 cm2, a minimum detectable mass of 5.8 ng is the result of our investigations. Comparing this detection limit of TEY to XRF and EPMA the minimum detectable Cr layer thickness has been 1 nm. This means that the detection limit of TEY is more than one order of magnitude better. XPS offers a detection limit of less than.1 nm which is one order of magnitude better than TEY. But, TEY offers another applicability. When covering the thin Cr layer with an Al layer of 2 nm and repeating the experiments, the responses of Fig.6 were measured. The minimum detectable Cr layer thickness becomes.3 nm. This is approximately a monolayer of Cr and this monolayer is buried under 2 nm Al. Such a layer thickness is out of the detection range of XRF, EPMA and does not even appear in the spectra of electron spectroscopies like XPS or AES. The standard deviation (T, becomes smaller increasing the time of data accumulation and/or the x-ray flux. Then it becomes possible to detect buried submonolayers by TEY. CONCLUSION TEY is a powerful analytical tool with detection limits between the values of XRF, EPMA on the one side and XPS on the other side. We found for Cr layers a minimum detectable thickness of,7 nm and we were able to detect a buried monolayer of Cr. REFERENCES 1 M.F.Ebel, R.Svagera, H.Ebel, R.Hobl, M.Mantler, J. Wernisch, and N.Zagler, Adv.X-Ray Ana1.38: 127 (1995) 2 H.Ebel, RSvagera, M.F.Ebel, and N.Zagler, Adv.X-Ray Anal. 38: 325 (1995) 3 H.Ebel, R.Svagera, M.F.Ebel, and N.Zagler, Adv.X-Ray Anal. 39: (1996) in press 4 Numerical Recipes in C, Cambridge University Press Eds. W.H.Press, S.A.Teukolsky, W.T.Vetterling, and B.P.Flannery (1992) Copyright JCPDS-International Centre for Diffraction Data 1997