Self-consistent calibration of TixC1-x auger spectra

SURFACE AND INTERFACE ANALYSISSurf. Interface Anal. 26, 590È596 (1998)

Self-consistent Calibration of AugerTixC

1—xSpectra

Wolfgang S. M. Werner,1,* Paul J. M. Schmo� lz,1 Horst W. Wagner,1 Herbert Sto� ri1 andJohann Kiefer21Institut fu� r Allgemeine Physik, Vienna University of Technology, Wiedner 8È10, A 1040 Vienna, AustriaHauptstra�e2TCE, Werk Deuchendorf, A-8605 Kapfenberg, Austria

Auger sputter depth proÐling was performed on a specially prepared TiC sample with carbon concentration varyingwith depth. This resulted in a series of Auger spectra corresponding to with x varying between 0.1 andTi

xC

1—x,

0.95. Although the carbon concentration gradient is not known a priori, there exists a method to associate any ofthese spectra with a given stoichiometry, utilizing the smooth relationship between the C and Ti signal for a largerange of stoichiometries and imposing the constraint of atomic fractions adding up to unity. In this way thestoichiometry of each spectrum has been determined, leading to a large series of standard spectra, that allow thestoichiometry of any unknown specimen to be calibrated on the basis of its Auger spectrum. SensitivityTi

xC

1—xfactors and calibration curves established in this way are given for peak areas, while it was found that it isimpossible to establish meaningful calibration curves for Auger peak-to-peak heights owing to chemical e†ects inthe spectra. 1998 John Wiley & Sons, Ltd.(

KEYWORDS: auger spectrometry ; carbicle ; titanium calibration ; electron scattering ; background correction

INTRODUCTION

Thin Ðlm of borides, carbides, nitrides and oxides showpromising applications in protective and decorativeapplications due to their high hardness, chemical stabil-ity and optical properties, and also in semiconductorproduction due to their electric and thermal properties.These properties are highly dependent on stoichiometry,which is difficult to infer by classical methods such aselectron probe microanalysis (EPMA) and Auger elec-tron spectroscopy (AES). Although measurements viax-ray photoelectron spectroscopy (XPS) and high-energy Rutherford backscattering (RBS) are easier toevaluate, they have their own difficulties and lack thespatial resolution of AES.

Quantitative analysis of refractory compounds bymeans of AES is complicated for several reasons : Ðrst ofall it is difficult to extract an intensity from an experi-mental spectrum that is representative for the stoichi-ometry because the peak shape strongly varies withcomposition. This is illustrated in Fig. 1, which shows anumber of spectra covering a broad range ofTi

xC1~xstoichiometries. The changes in the shape and position

of the carbon peak are clearly observable.Furthermore, the characteristic Auger peaks in the

energy spectrum are superimposed on a broad back-ground of secondaries and backscattered primaries. Theshape of this background also depends on the stoichi-ometry. Also, the characteristic peaks are accompaniedby a tail of inelastically scattered Auger electrons at thelow kinetic energy side. Finally, for many refractory

* Correspondence to : W. S. M. Werner, Institut fu� r AllgemeinePhysik, Vienna University of Technology, Wiedner 8È10,Hauptstra�eA 1040 Vienna, Austria.Email : werner=IAP.TUWIEN.AC.AT

materials, the features due to the Auger process (peakand inelastic tail) exhibit a considerable overlap.

In addition to the problem of quantitative spectruminterpretation, another serious problem exists : it isextremely difficult to prepare adequate standards in abroad range of stoichiometries for cross-calibration.

In the present paper, a simple calibration procedureis proposed to overcome these problems. The problemof peak intensity determination is tackled by applica-tion of a recently developed method to eliminate theinelastic tail that also strongly suppresses the back-ground due to secondaries and backscattered pri-maries.1 This allows accurate peak area determinationto be performed, which is assumed to eliminate theinÑuence of chemical e†ects on the extracted signalbecause the Auger peak area is governed by the innershell ionization cross-section while the chemical sur-rounding of the atoms merely a†ects the outer shellsparticipating in the chemical binding. Thus, althoughthe peak shape will vary strongly with the chemicalcomposition, the peak area still carries a quantitativesignature of the stoichiometry.

The problem of standard preparation is dealt with inthe following fashion : instead of preparing a smallnumber of standards and carefully cross-calibratingthem with an independent technique, we have used alarge number (D400) of unknown spectra correspond-ing to a broad range of stoichiometries. Acquisition ofsuch a data set and preparation of the required sampleis simple : a single specimen with a concentration gra-dient is used and spectra are acquired while the layercontaining the gradient is sputtered away.

All these unknown spectra are subsequently cali-brated by establishing a semi-empirical model for theAuger intensities of the constituents and self-consistently evaluating the entire data set to give thestoichiometry of every single spectrum.

CCC 0142È2421/98/080590È07 $17.50 Received 21 January 1998( 1998 John Wiley & Sons, Ltd. Accepted 16 March 1998

CALIBRATION OF TixC1~x

AUGER SPECTRA 591

Figure 1. Several spectra for values of x covering a large range of stoichiometries. These spectra have been corrected for the energyTixC

1Éxdependence of the analyser transmission.

This calibration procedure, to be outlined in moredetail below, was applied to the system, leadingTi

xC1~xto a large set of calibrated reference spectra along with

calibration curves and sensitivity factors. As a test, theAES spectra of two stoichiometric (and homogeneous)

TiC standards were evaluated using the establishedsensitivity factors. The analysis gave deviations of \4%in both cases, proving that the proposed method is con-sistent with the more involved conventional calibrationschemes.

Figure 2. Example of application of the background subtraction technique ÍEqn (1)Ë.

( 1998 John Wiley & Sons, Ltd. Surf. Interface Anal. 26, 590È596 (1998)

592 W. S. M. WERNER ET AL .

DETERMINATION OF PEAK AREAS FROMEXPERIMENTAL SPECTRA

The method to extract peak areas from the experimen-tal data is described in detail in Ref. 1 and will be out-lined brieÑy only here. In order to extract peak areasfrom experimental spectra, it is necessary to eliminatethe contribution of multiply scattered electrons from thedata. This can be achieved by applying the deconvolu-tion formula1,2

f (E) \ y(E)[ iPE

=dE@y(E@)w(E@[ E) (1)

where f (E) is the intrinsic spectrum of unscattered elec-trons and y(E) is the experimental spectrum. The nor-malized di†erential inelastic inverse mean free path(DIIMFP) w(T ) describes the probability for an energyloss T in a single inelastic event. Very often, the univer-sal DIIMFP proposed by Tougaard is used for thispurpose3

w(T ) \ 2CT(C] T 2)2 (2)

where C\ 1643 eV2. The parameter i describes,amongst other things, the inÑuence of elastic scatteringon the electron escape process and is in the range 0.9È1.0, depending on the sample composition and thegeometry. In accordance with the results in Ref. 1, wehave chosen a value of i \ 0.95 corresponding to acylindrical mirror analyser (CMA) geometry for theenergies and elements considered.

Application of Eqn (1) to the raw spectra not onlyeliminates the inelastic tail, but in addition stronglysuppresses the background of secondaries and inelas-tically backscattered primaries, thereby greatly facili-tating peak area determination. An example of thisprocedure applied to experimental spectra is shown inFig. 2. The hatched areas give the peak intensities. Aminor uncertainty in this procedure is introduced by thefact that the Ar and C peaks cannot be resolved prop-erly by our spectrometer. It can, moreover, be observedthat the Ti peak is not entirely free of multiple scatteredelectrons. This is attributable to the fact that the univer-sal DIIMFP [Eqn. (2)] is not appropriate for all stoi-chiometries in the case of In fact, the DIIMFPTi

xC1~x

.changes considerably with composition (see, forexample, the optical data for C and Ti and their com-pounds in Ref. 4). This is a problem that needs furtherinvestigation.

CALIBRATION PROCEDURE

As explained in the introduction, we have self-consistently evaluated our comprehensive data set usinga model for the Auger intensities of the constituents ofthe graded sample. In this model, the following assump-tions were made :(1) The length scale, over which the concentration

varies appreciably, greatly exceeds the escape depthof the Auger electrons so that each spectrum corre-sponds to a homogeneous sample. ThisTi

xC1~x

assumption was well fulÐlled at any depth of thesample used in the present work.

(2) It is assumed that the sensitivity factors can be fac-torized into an elemental factor that does notdepend on the stoichiometry (ionization cross-section, Ñuorescence yield) and a composition-dependent factor (escape depth, Augerbackscattering factor). The composition-dependentfactor is taken to be identical for all constituents ofthe sample. Because this factor is entirely deter-mined by the electron transport and therefore onlydepends on the primary energy (Auger backscatter-ing factor) and Auger electron energy (escape depth),this assumption is reasonable for sufficiently highprimary energies and for suffi-E0? ECKLL , ETiLMMciently similar Auger energies ECKLL [ ETiLMM .

(3) It is assumed that the relationship between the Tiand C signals is smooth over the entire range ofstoichiometries and can be described by a poly-nomial of low order.

Taking into account the aforementioned assumptions,we write for the Ti and C signals

IC\ ap(x)Cc (3)

ITi\ bp(x)CTiHere, a and b are proportional to the elemental sensi-tivity factors and p(x) is the dependence of these factorson the stoichiometry x. We impose the trivial constrainton the atomic concentrations of C and Ti

CC] CTi\ 1 (4)

by introducing the parameter

m \ (12 [ CC) \ [(12 [ CTi) (5)

for the stoichiometry, and transform Eqn (3) as follows

IC\ (12 [ m)ap(m) (6)

ITi \ (12 ] m)bp(m)

Next, an appropriate parameterization must be chosenfor p(m). Anticipating the results to follow (see Fig. 3), wechoose a linear composition dependence for p(m)

p(m) \ 1 ] cm (7)

because the Ti signal was found empirically to dependquadratically on the carbon signal. Using Eqn (6), onecan express m in terms of a/b and ITi/IC

mk\ m(a/b, ITi/IC) (8)

where the index k refers to a particular measurement.Thus the sensitivity factors a, b and c can be establishedby minimizing the function

s2\;k[ o IC, k [ IC(a, c, m

k) o2] o ITi,k [ ITi(b, c, m

k) o2]

(9)

which provides the self-consistent calibration of theentire set of spectra through the sensitivity factors a, band c (or m

k).

At this point it should be noted that the sensitivityfactors a and b also contain the experimental sensitivityand are therefore neither universal nor transferablebecause we did not measure the spectra in absoluteunits. A transferable sensitivity factor for the intensity

Surf. Interface Anal. 26, 590È596 (1998) ( 1998 John Wiley & Sons, Ltd.


AUGER SPECTRA 593

(a)

(b)Figure 3. Empirical relationship between the Ti and C signals : (a) peak intensities determined by means of Eqn (1), where the solid lineindicates the quadratic relationship of the Ti and C signals as per Eqn (7) using the value of c retrieved by solving Eqn (9) ; (b) peakintensities given by the APPH method.

ratio can be derived by transforming EqnRTiC \ ITi/IC(6) into

m \ [12(1[ STiCRTiC)/(1 ] STiC RTiC) (10)

where is the sensitivity factorSTiC\ a/b \ 1/RTiC(m \ 0)for the intensity ratio.

EXPERIMENTAL

The uncalibrated graded Ðlm was deposited by meansof ion plating in an argon plasma on a refractory metalsubstrate. Titanium was evaporated using an electron



beam; carbon was introduced in the form of acetyleneAfter depositing a layer of pure titanium, the(C2H2).partial pressure of acetylene was slowly ramped up. On

reaching the maximum sustainable level of acetylene,the energy of the electron beam was slowly rampeddown, reducing titanium evaporation. The result was agraded Ðlm, ranging from amorphous carbon on top viatitanium carbide to titanium (from the interface to thesubstrate). The thickness of the resulting Ðlm was D3lm. The concentration gradient was not fully predeter-mined and thus presumably not constant : deposition ofcarbon was not proportional to the partial pressure ofacetylene because the deposition rates of carbondropped at higher concentrations due to the reducedavailability of titanium atoms, which are preferredbonding sites.

The sample was analysed using a double-pass CMAelectron spectrometer with 0.6% energy resolution. Thesample was mounted at an angle of 45¡ with respect tothe axis of the electron gun and the CMA, and 65¡ withrespect to the ion gun. Over D48 h the Ðlm was sput-tered away, using 2 keV krypton ions with an intensityof the order of 10~7 A mm~2. The energy of theprimary electron beam was 8 keV, its intensity wasD10~6 A and the spot diameter was D20 lm. Becausethe intensity was expected to vary during the session,the molybdenum clip that held the sample was used tomeasure the variations in beam current : for everysample measurement, a molybdenum reference spec-trum was taken. Integral intensity was used to normal-ize the spectra of the sample. Due to the thickness of theclip and the sampleÏs inclination, the distance from theanalyser was nearly the same for both locations ; bothwere well inside the area of maximum sensitivity of theCMA. All spectra were sampled from 25 to 625 eV,using a step width of 1 eV and a measurement time of0.1 s. Thus and lines were covered.CKLL , TiLMM OKLLMaximum intensities were in the range of 107 countss~1. Spectra were corrected by a factor E~1 correspond-ing to the energy dependence of the sensitivity of theCMA.

RESULTS AND DISCUSSION

The D400 spectra acquired at di†erent depths of thesample were subjected to the background subtractionprocedure and their C and Ti peak areas were deter-mined by numerical integration. In addition, peakintensities were established on the basis of the Augerpeak-to-peak height (APPH) method. The result isshown in Fig. 3 for the peak areas and APPHs, respec-tively. The arrow in Fig. 3(a) indicates the intensity ratiofound for the two stoichiometric TiC standards. It canbe seen in Fig. 3(a) that a smooth relationship betweenthe Ti and C signals does indeed exist over the broadrange of intensities covered by our experiment, inaccordance with the model assumptions. The relation-ship between the Ti and C signals is found to be quad-ratic, as indicated by the solid line in Fig. 3(a). Asmooth interdependence of the C and Ti signals is notobserved at all when the spectra are evaluated with theAPPH method [Fig. 3(b)]. Thus, it can be concludedthat the evaluation method described here conforms

with the assumption made in the outlined calibrationtechnique : that it is essential to use an evaluationmethod that eliminates the inÑuence of chemical e†ectsfor proper calibration.

The intensities shown in Fig. 3(a) were used to self-consistently calibrate the acquired spectra via Eqn (9),yielding the calibration curves shown in Fig. 4. Thedata points are the experimental (normalized) intensitiesand the solid lines are the calibration curves [Eqn (6)].It can be seen that Eqns (6) and (7) properly describethe experimental intensities. The values for the sensi-tivity factors determined in this way are : STiC \ 0.53and c\ 0.59. Using this result and Eqn (6), along withthe intensities and for the stoichiometric TiC stan-ITi ICdard [marked by the arrow in Fig. 3(a)], one Ðnds mst\for the stoichiometry of the standard, which[0.03agrees with the expected value of to within a fewmst\ 0per cent.

At this stage, it should be noted again that the sensi-tivity factor can be derived from one single mea-STiCsurement of a stoichiometric standard [cf. Eqn (10)].Within our model assumptions, in particular the con-straint of Eqn (4), such a single measurement also pro-vides a calibration for the entire stoichiometric range.This is only true, however, if it is ascertained that asmooth relationship between the signals of the constitu-ents does actually exist. As the results in Fig. 3 show,this depends critically on the way in which the signalsare extracted from the raw data and whether the inÑu-ence of chemical e†ects is properly eliminated. In otherwords, the method proposed here not only allows anyunknown TiC spectrum to be calibrated without anycross-calibrated standard, but it also provides a consis-tency check for the data evaluation method.

The composition dependence of the sensitivity factorp(m) is obviously quite strong, as can be judged from therather high value for c. Physically, this compositiondependence should match the dependence of the escapedepth and Auger backscattering factor (i.e. the surfaceionization). The inÑuence of additional ionization ofprimary electrons that are backscattered in the bulk aswell as the electron escape process have been assessedindependently to perform another consistency check ofour model by comparing the theoretical sensitivityfactor p(m) with the value of c determined empirically.For the surface ionization this was done by means ofMonte Carlo model calculations using the modeldescribed recently.5 The inÑuence of the stoichiometryon the escape depth was estimated via the approx-jaimate formula6

ja ^ji jtr

ji ] jtr(11)

where and are the inelastic and transport meanji jtrfree paths, respectively : the former was taken from thevalues of Ref. 7 ; the latter was calculated via the partialwave expansion method.8 For both quantities thevalues for pure C and Ti were interpolated linearly togive the estimated composition dependence for[0.5O m O 0.5. It was found both for the surface ion-ization and the escape depth that the compositiondependence for both Ti and C is identical to a verygood approximation, providing support for the validityof one of the main assumptions underlying the present



AUGER SPECTRA 595

Figure 4. Calibration curves (solid lines) established by minimizing the functional Eqn (9) for all Ti and C intensities (open circles).

work. Furthermore, the composition dependence of theAuger backscattering factor (or surface ionization) wasfound to be quite strong (increasing by D45%), whilethe escape depth decreases by D5%. These results aredisplayed graphically in Fig. 5 and compared with thecomposition dependence of the sensitivity factor foundin our experiment (solid line). The open and closedcircles are the Ti and C surface ionizations (normalized

at m \ 0), which are seen to be almost perfectly identi-cal. The dashed line is the product of these results withthe escape depth compositional dependence, giving thetheoretical composition dependence of p(m). The theo-retical result is seen to deviate slightly from linearity.This may be due to the fact that ionization due to fastsecondaries was neglected in the Monte Carlo calcu-lations. Nonetheless, the agreement between theory and

Figure 5. Composition dependence of the sensitivity factor p(y) compared with the composition dependence of the Ti La and C Ka surfaceionizations determined by the Monte Carlo method.



experiment is satisfactory, providing evidence for thevalidity of the assumptions that the composition depen-dence is the same for all constituents of the sample.

These Ðndings support our model assumptions thatthe sensitivity factors can be factorized into elemental (aand b) and stoichiometry-dependent [p(m) or c] factorsand the fact that the latter factor is identical for all con-stituents in a sample. This has important consequencesfor the transferability of our results. As outlined above,the factor p(m) is mainly determined by the transport ofprimaries and signal electrons. Therefore, this factorwill, in general, depend on parameters such as theprimary energy, the experimental geometry, etc. and isnot simply transferable to other experimental set-ups.However, according to our model assumptions, whichare supported by the present results, the values of a andb and particularly do not depend on theSTiC\ a/bexperimental details and should therefore be trans-ferable directly.

When interpreting our data, it should be kept inmind that there are several sources of error that cannotbe estimated simply and might a†ect the calibrationprocedure :(1) preferential sputtering may lead to an inhomoge-neous surface composition ;(2) the DIIMFP varies with composition ;(3) the constraint of atomic fractions adding up to unitymay not be satisÐed strictly due to the presence of aslight amount of process gas in the specimen.The Ðrst two e†ects suggest a modiÐcation of our pro-cedure to include the intensity determination in the cali-bration procedure, rather than separately determining

peak intensities and subsequently performing the cali-bration, as was done in the present work. Then theDIIMFP depends on and the signal extraction mustm

kbe carried out when solving Eqn (9). This can also aid intracing or eliminating the inÑuence of surface inhomo-geneities by peak shape analysis.9

CONCLUSIONS

A model to self-consistently calibrate a set of unknownstandard spectra has been proposed and applied to theTiC system. An essential aspect of such a method is asmooth dependence of the signal of all constituents ofthe sample on composition. It has been shown that,in the case of Auger spectra, this can be achieved evenin the presence of strong chemical e†ects by using peakareas for the representative signal and properlyaccounting for the electron escape process and multiplescattering in the peak area extraction. The compositiondependence of the sensitivity factor agreed reasonablywell with the theoretical expectation, while the methodwas shown to be consistent with conventional cali-bration techniques that require cross-calibration via oneor more standards. The fact that cross-calibration is notneeded for the proposed method makes its prospectiveapplication, particularly for ternary systems, quiteattractive. In this case, two graded samples (again withunknown gradient) suffice to calibrate the entire stoi-chiometric range.

REFERENCES

1. W. S. M. Werner, Surf . Interface Anal . 26, 455 (1998).2. I. S. Tilinin and W. S. M. Werner, Surf . Sci . 290, 119 (1993).3. S. Tougaard, Surf . Interface Anal . 11, 453 (1988).4. E. D. Palik (ed.), Handbook of Optical Constants of Solids .

Academic Press, New York (1985).5. H. W. Wagner and W. S. M. Werner, X-Ray Spectrom. (1998),

in press.

6. I. S. Tilinin and W. S. M. Werner, Mikrochim. Acta 114/115,485 (1994).

7. S. Tanuma, C. J. Powell and D. R. Penn, Surf . Interface Anal .11, 577 (1988).

8. A. C. Yates, Comp.Phys.Commun. 2, 175 (1971).9. W. S. M. Werner, Surf . Interface Anal . 23, 737 (1995).


Self-consistent calibration of TixC1-x auger spectra

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