Reference-free GIXRF-XRR as a methodology for independent validation of XRR on ultrathin layer stacks and a depth-dependent characterization
Philipp Hönicke, Blanka Detlefs, Yves Kayser, Uwe Mühle, Beatrix Pollakowski, Burkhard Beckhoff
RReference-free GIXRF-XRR as a methodology for independent validation ofXRR on ultrathin layer stacks and a depth-dependent characterization
Philipp H¨onicke, a) Blanka Detlefs, Yves Kayser, Uwe M¨uhle, Beatrix Pollakowski, and Burkhard Beckhoff Physikalisch-Technische Bundesanstalt (PTB), Abbestr. 2-12, 10587 Berlin,Germany CEA-LETI, 17 rue des Martyrs, 38054 Grenoble, France. TU Dresden, Inst. of Material Science, Helmholtzstr. 7, 01062 Dresden, Germany. (Dated: 5 March 2019)
Nanolayer stacks are technologically very relevant for current and future applications in many fields of research.A non-destructive characterization of such systems is often performed using X-ray reflectometry (XRR). Forcomplex stacks of multiple layers, low electron density contrast materials or very thin layers without anypronounced angular minima, this requires a full modeling of the XRR data. As such modeling is using thethicknesses, the densities and the roughnesses of each layer as parameters, this approach quickly results ina large number of free parameters. In consquence, cross-correlation effects or interparameter dependenciescan falsify the modeling results. Here, we present a route for validation of such modeling results whichis based on the reference-free grazing incidence X-ray fluorescence (GIXRF) methodology. In conjunctionwith the radiometrically calibrated instrumentation of the Physikalisch-Technische Bundesanstalt the methodallows for reference-free quantification of the elemental mass depositions. In addition, a modeling approachof reference-free GIXRF-XRR data is presented, which takes advantage of the quantifiable elemental massdepositions by distributing them depth dependently. This approach allows for a reduction of the free modelparameters. Both the validation capabilities and the combined reference-free GIXRF-XRR modeling aredemonstrated using several nanoscale layer stacks consisting of HfO and Al O layers.PACS numbers: 61.05.cm, 78.70.En, 68.55.jd, 07.85.Qe I. INTRODUCTION
Nanoscale material systems are a relevant topic inmany fields of current materials research, especiallyin nanoelectronics and energy storage applications .Driven by the search for novel material functionalitiesand improved performance, the variety of investigatedmaterial combinations with respect to their elementaland structural composition is steadily growing . Also,the desired single layer thicknesses are in the low nanome-ter regime, which results in a strong additional influenceof interfacial properties between adjacent materials onthe integral functionality of the system. One methodol-ogy that is widely used for the characterization of suchnanomaterials is X-ray reflectometry (XRR). This tech-nique is easily available also on laboratory tools and is of-ten used to derive thicknesses, densities and roughnessesof nanolayer stacks.XRR is a well-established technique for sample systemswith sufficiently high electron density contrast and thick-nesses larger than a few nanometers , where the angularoscillations in XRR provide a direct and traceable accessto the thickness of the thin layer. However, for more com-plex stacks of multiple layers, low electron density con-trast or very thin layers without any pronounced angularminima, it may not be sufficient to perform XRR only assuch systems require a careful modeling of the experimen-tal data. The modeling of XRR data is usually performed a) [email protected] by using assumed structure and the thickness, the densityand the surface roughness of each layer in the stack asthe optimization parameters. Remaining discrepanciesdue to interfacial mixing are often taken into accountby adding interfacial layers with additional parameters.Therefore, these modeling approaches quickly rely on alarge number of free modeling parameters if samples withmultiple nanolayers are to be investigated. This kind ofapproach can easily suffer from cross-correlation effectsor interparameter dependencies limiting stand-aloneXRR data interpretation. A validation to which extentany parameter cross-correlation effects reduce the relia-bility of the derived modeling results is usually missingas it is not straightforward.This issue can be addressed with the reference-free X-ray fluorescence spectrometry methodologies of thePTB, Germany’s national metrology institute. By rely-ing on radiometrically calibrated instrumentation andreliable knowledge of the atomic fundamental parame-ters, no certified reference material or calibration stan-dards are needed for a quantitative analysis of the massdeposition of an element of interest. In fact, reference-free X-ray fluorescence spectrometry can even be usedto qualify reference materials or calibration samples .As the mass depositions are the product of each mate-rials density and thickness, they can be used to inde-pendently validate any XRR modeling result. In addi-tion, reference-free grazing incidence X-ray fluorescence(GIXRF) is capable to provide also depth dependentinformation about the sample structure .GIXRF is based on the angular and depth dependent a r X i v : . [ phy s i c s . a pp - ph ] M a r changes of the intensity distribution within the X-raystanding wave (XSW) field arising from the interferenceof incident and reflected X-rays on a flat surface or inter-face. Due to the complementary nature of the analyticalinformation provided by GIXRF and the dimensional in-formation provided by X-ray reflectometry (XRR), also acombined analysis of GIXRF and XRR data is possible.This was already identified to be a promising method-ological approach to reliably characterize nanostructuresby DeBoer et al in the early 1990s.In this work, we will demonstrate how the results ofa conventional XRR modeling can be validated usingthe quantification capabilities of reference-free GIXRFat higher incident angles, where the XSW can beneglected . In addition, we present an alternative mod-eling approach based on a hybrid reference-free GIXRF-XRR methodology. It takes advantage of the quantifiedelemental mass depositions for each element which canthen be used as modeling constraints in order to reducethe amount of free parameters in both GIXRF and XRRevaluations. This is basically achieved by distributing theelemental mass depositions in depth into several layers,which can also intermix at interfaces.In this work, we use the reference-free GIXRF method-ology of PTB in order to gain access to the massdepositions, but of course any other first-principle orSI traceable technique which can provide this informa-tion at reasonably low uncertainties could be used. Soeven though we used rather sophisticated synchrotronradiation based instrumentation a very similar approachcan be performed using well characterized laboratoryGIXRF-XRR equipment as long as the relevant mass de-positions can be derived absolutely. II. EXPERIMENTAL
In this work, thin Al O /HfO /Al O layer stackswith individual thicknesses in the nanometer range havebeen deposited on silicon wafers with a native oxidelayer.We specifically chose these two oxides as they pro-vide a very high electron density contrast. The layerswere fabricated at CEA-LETI using atomic layer deposi-tion (ALD), which is a technique that provides very welldefined and uniform layers. For both metal oxides, wa-ter vapor was used as the oxygen source during the ALDdeposition process. Trimethylaluminium and HfCl wereused as precursors and the processing temperature duringALD deposition was 300 ◦ C. In addition to varying indi-vidual layer thicknesses, also one sample with an oppositelayer sequence as well as one sample with three repeti-tions of the single three layer sequence was deposited. Intable I on overview of the used samples can be found.At a later stage, one pieces of the S4 wafer was ther-mally annealed in N atmosphere for 40 s at 800 ◦ C. Theannealing conditions were chosen to be identical to thework of Lan et al. in order to obtain comparable results. TABLE I. Description of the different layer sequences of thenanolaminate samples used in this work.Sample Layer sequenceS1 Al O / HfO /SiO on SiS2 HfO / Al O / HfO / SiO on SiS3 [Al O / HfO ] / SiO on SiS4 Al O / HfO / Al O / SiO on SiS4 800 ◦ C annealed for 40 s at 800 ◦ CS5 Al O / HfO / Al O / SiO on SiFIG. 1. Comparison of the measured XRR using Cu-K α ra-diation on the different samples. A. XRR characterization
Directy after deposition, each sample was character-ized at LETI by means of XRR measurements. Theseexperiments were performed using a Bruker D8 Fablineinstrument handling 300mm wafers. A Cu-K α X-raysource was used for this laboratory XRR characeriza-tion. The data was modeled using the Bruker LEPTOSsoftware and GenX , an XRR analysis code, based onthe differential evolution algorithm. Both modelings wereperformed by using the densities, the thicknesses and theroughnesses of each layer as the modeling parameters. Inaddition, also the roughness of the silicon substrate wasvaried. In fig. 1, the different XRR curves for the varioussamples are shown. The modeling results from the LETIXRR experiments are shown in table II. B. GIXRF-XRR characterization
The reference-free GIXRF-XRR experiments were car-ried out in the PTB laboratory at the electron storagering BESSY II, employing the plane grating monochro-mator (PGM) beamline for undulator radiation as wellas the four-crystal monochromator (FCM) beamline forbending magnet radiation . At both beamlines, PTB’sin-house built instrumentation for reference-free XRFand XRR experiments was used. The setup is installedin an ultra-high vacuum (UHV) chamber equipped witha 9-axis manipulator, allowing for a very precise samplealignment with respect to all relevant degrees of freedom.The emitted fluorescence radiation is detected by meansof a calibrated silicon drift detector (SDD) mountedat 90 ◦ with respect to the incident beam. Additionalcalibrated photodiodes on a separate 2 θ axis allow forXRR measurements simultaneously with the reference-free GIXRF measurements as well as for the determina-tion of the incident photon flux.To optimize the excitation conditions for the Al-K andthe fluorescence lines originating from the Hf-L3 shell,the nanolaminate samples were measured at two incidentphoton energies E inc (1.622 keV and 10.0 keV). The exci-tation energy of 10 keV presents the advantage that onlythe L3 shell of Hf can be ionized and that Coster-Kronigtransitions do not occur. The excitation energy of 1.622keV (which is below the Si-K absorption edge) results ina drastically reduced spectral background for the Al-Kline and in the suppression of any secondary excitationchannels. Thus, the selection of these excitation condi-tions allows for the lowest achievable uncertainties in theAl and Hf quantification. For each photon energy, botha reference-free GIXRF and a XRR measurement wereconducted in parallel. III. RESULTS AND DISCUSSIONA. Validation of XRR modeling results
TABLE II. Overview on the various parameters as determinedfrom a modeling of the XRR data shown in fig. 1. The resultsof sample S3 are not shown.
S1 S2 S4 S5
Unit Al O HfO Al O Al O Thickness
Density − Roughness
HfO Al O HfO HfO Thickness
Density − Roughness — HfO Al O Al O Thickness — 0.74 1.30 2.34 nm
Density — 6.98 3.57 2.97 gcm − Roughness — 0.23 0.28 0.39 nm
SiO Thickness
Density − Roughness
Substrate Roughness
In table II, the obtained modeling results from the LETI XRR experiments are shown. As already men-tioned, the densities, the thicknesses and the roughnessesof each layer as well as the substrates roughness servedas the modeling parameters. The XRR results are in linewith expectations, e.g. that the derived material den-sities are somewhat lower than the corresponding bulkdensities and that the roughnesses are in the order ofhalf a nanometer. In addition, also the achieved agree-ment between the experimental and the modeled XRRcurves (not shown here) is very good and does not indi-cate any issues. However, as there are at least ten in-dependent modeling parameters and the features in theexperimental XRR data are not always very pronounced,one may expect parameter correlation effects. The re-maining question is now how one can evaluate how severethey influence the results.One way to perform a validation of such modelingresults is to calculate each materials mass deposition(= product of material density and thickness) from thethicknesses and densities as determined by the XRR dataevaluation. These mass depositions can then be com-pared to mass depositions obtained from e.g. quantita-tive GIXRF experiments. In the following, we have calcu-lated the corresponding total elemental mass depositionsof Al, Hf and O from each resulting parameter set bymultiplying the respective modeled densities and thick-nesses assuming stoichiometric materials and then usereference-free GIXRF experiments for an independentvalidation. At incident angles far above the critical an-gle for total external reflection the fluorescence intensitymodulations due to the interplay of the XSW field andthe nanolayer stack vanish and a direct quantification ofthe mass depositions can be performed without any struc-tural modeling. To do so in reference-free GIXRF experi-ments, the recorded fluorescence spectra are deconvolvedusing the known detector response functions for therelevant fluorescence lines as well as for the backgroundcontributions. A direct and traceable quantification ofthe mass depositions can then be performed as presentedin ref. using Sherman’s equation. The necessary in-strumental parameters, e.g. the solid angle of detectionor the incident photon flux are known due to the usage ofthe well-known physically calibrated instrumentation .The relevant fundamental parameters are partially takenfrom databases or derived from dedicated experimentsin the case of the oxygen and aluminum K-shell aswell as the Hf-L3 shell (according to ref. ) fluorescenceyields. The derived mass depositions for Al, O and Hfare shown in figs. 2 and 3 as black stars. A relative ex-perimental uncertainty between 8 % and 9 %, which isdominated by the relative uncertainties of the fundamen-tal parameters involved in the quantification is achieved.The calculated mass depositions for the XRR modelingresults are also shown in figs. 2 and 3 as red stars.The direct comparison of the XRR modeling and thereference-free GIXRF derived mass depositions revealsdiscrepancies for some samples. With respect to Al, theresults only agree within the corresponding uncertainties FIG. 2. Comparison of quantified elemental mass depositions for Al (left) and O (right) versus the calculated data using themodeling results of the LETI-XRR data. The reference-free GIXRF quantification was performed for incident angles above 4 ◦ .FIG. 3. Comparison of quantified elemental mass depositionsfor Hf versus the calculated data using the modeling resultsof the LETI-XRR data. The reference-free GIXRF quantifi-cation was performed for incident angles above 4 ◦ . for sample S4. For all other samples, there is a largermismatch. For oxygen, only sample S5 shows a signif-icant mismatch but on all samples, the XRR modelingresults yield too much oxygen. For Hf, the agreement issimilar as for Al. These deviations show, that despite thehigh electron density contrast between HfO and Al O and despite the superior deposition capabilities of ALD,the XRR modeling still results in substantial deviations.The main reason for these differences originates in the fact that both the material densities and thicknesses arefree model parameters and, thus, the materials mass de-position can be varied by the modeling. Consequentlyany shortcomings of the used layer model, e.g. surfacecontamination or interface diffusion or uncertainties ofthe used optical constants, e.g. due to missing fine struc-ture close to absorption edges will be compensated tosome extent by a wrong adjustment of the densities andthicknesses. If there are enough free parameters this isnot easy to detect, as the overall agreement between cal-culated XRR and the experimental data is often verygood.For these reasons, the need for an external validation ishigh especially for cases, where multiple very thin layersare to be characterized as shown here. It should also benoted that the experimental XRR data for the samplesin this work shows rather prominent features (see fig. 1).Still, the deviations between modeled mass depositionsand the real ones is relatively large as shown. So oneshould expect this to be even more of an issue if theXRR data has less prominent features due to even thinnermaterials or less electron density contrast. B. Modeling of reference-free GIXRF-XRR data
In addition to such a validation of XRR modeling re-sults, the reference-free GIXRF-XRR data measured atthe two incident photon energies E inc (1.622 keV and10.0 keV) also allows for a depth dependent combinedmodeling of the layer structure. Here, the total mass de-positions and, thus, the products of the respective layerthicknesses and densities are known from the reference-free quantification at high incident angles as describedearlier. Thus, the densities and thicknesses are not al-lowed to vary independently because the information onthe elemental mass deposition can be used by distribut-ing them in depth into separate layers. Each layer densityis a modeling parameter and the corresponding thicknessis then derived from the respective mass deposition. Inaddition, the optical constants of a given material alsoscale with its density. As a result, the number of freeparameters is reduced.In addition, some corrections to take into account therespective uncertainties of the quantified mass deposi-tions or of the used tabulated optical constants for thebulk materials are necessary. This is realized by applyingscaling factors, which are allowed to vary by the respec-tive parameters’ relative uncertainty around unity. Totake into account any interfacial mixing of two adjacentlayers, additional intermixing coefficients for each inter-face are implemented. They determine the width wherethe materials change symmetrically from one to the otherand can range from zero (no intermixing) to 1 (fully in-termixed layers).The hybrid modeling routine for reference-free GIXRF-XRR is modeling the full data set of two XRR and twoGIXRF curves at once (see fig. 4) in order to take fulladvantage of the complementary nature of GIXRF andXRR. It first assumes density values for each layer in thestack (including a carbonaceous surface contaminationlayer). Using the previously quantified mass depositions,the resulting thickness values for each layer are calcu-lated. With these layer thicknesses, concentration depthprofiles for each layer are defined. Depending on the re-spective intermixing coefficient, these depth profiles canoverlap at the interfaces. The concentration depth pro-files are then used to calculate depth profiles for eachoptical constant ( δ and β ) at the two used photon ener-gies. Here, bulk optical constants for Al O , HfO , SiO and Si from were used and also scaled with the mod-eled material densities. If an intermixing is present, theeffective optical constants are calculated accordingly bymeans of a linear combination.The full layer stack is then separated into thin sublay-ers in order to calculate both the resulting XRR curvesfor both photon energies as well as the XSW for each pho-ton energy. A PTB in-house developed software package(XSWini ) was used here, as it could be directly imple-mented into the modeling routine. The derived intensitydistribution within the XSW is then numerically inte-grated in conjunction with the calculated concentrationdepth profiles and all other relevant instrumental andfundamental parameters to calculate the angular fluores-cence profiles for Al and Hf as shown in reference .Using this procedure, the samples S4 and the annealedS4 800 ◦ C have been analyzed and the correspondingconcentration depth profiles obtained are shown in fig.5. The solid lines correspond to the layer stack of sam-ple S4 whereas the dotted lines to sample S4 800 ◦ C (an-nealed for 40 s at 800 ◦ C). An increase of the interfacial intermixing for the annealed sample is clearly visible forall interfaces. The non-annealed sample shows no rele-vant intermixing, which is in line with the expectations for such ALD depositions. The observed diffusion-drivensymmetric intermixing for the annealed sample is veri-fied by the findings in the work of Lan et al. . Oneshould also note the increase in the modeled thickness ofthe SiO layer on the annealed sample, which is in lineboth with the increase of the quantified oxygen mass de-position shown in fig. 2 and also with TEM images (notshown) of the annealing sample series. The growing oxidelayer at the interface to the Si substrate is a known effectduring annealing when HfO is present and very smalloxygen contaminations within the annealing atmosphereare sufficient to result in the observed SiO growth .In summary, the combined modeling approach usingeach materials concentration depth profile instead of dis-tinct layers with additional interface layers allows to de-rive information about the intermixing due to the ther-mal annealing even on such thin layers. As this wouldnot be easily possible with GIXRF alone or with conven-tionally modeled XRR, the present approach provides animproved strategy for the characterization of ultrathinlayers and layer stacks. IV. CONCLUSIONS
In summary, this work demonstrates how the widelyused conventional modeling approach for XRR data ob-tained on very thin layers can suffer from parametercross-correlation effects which can mask unexpected sam-ple changes or incomplete model assumptions. This canbe a crucial issue when characterizing ultra-thin layeredsamples and it occurs due to the resulting large numberof free model parameters. As a result, these modelingstrategies often provide very well reproduced experimen-tal data but still erroneous results, which are then hardto be revealed. As many software implementations forboth commercial and research tools are using this con-ventional approach, this issue must be addressed. Usingthin nanolaminate layer stacks with Al O and HfO aslayer materials, we have uncovered these unfavorable ef-fects and also present both a validation scheme and anew hybrid modeling scheme. The external validation ofthe modeled elemental mass depositions helps to bench-mark the conventional modeling results and, thus, to re-veal the negative cross-correlation effects. For a morereliable modeling, the mass depositions are directly usedin the presented hybrid GIXRF-XRR approach in orderto reduce the risk of such hindering parameter cross-correlations.In this respect, we derived the total elementalmass depositions using our reference-free quantifica-tion scheme to set-up a hybrid reference-freeGIXRF-XRR modeling. It uses the information aboutthe elemental mass depositions, which can be used to re-duce the degrees of freedom within the modeling. This FIG. 4. Comparison of the full experimental data set, consisting of an XRR (black stars and axes) and a GIXRF curve (redstars and axes) for each photon energy and the respective modeling results (blue solid lines) for sample S4 800 ◦ C.FIG. 5. Comparison of the concentration depth profiles de-termined using the reference-free GIXRF-XRR modeling ofsamples S4 (solid lines) and the annealed S4 800 ◦ C (annealedfor 40 s at 800 ◦ C, dotted lines). can lead to a more reliable interpretation of the exper-imental data as compared to the conventional modelingapproaches and compared to single XRR or GIXRF anal-ysis.It also should be noted, that the presented methodol-ogy does not require synchrotron radiation sources andis transferable also to laboratory instruments. These in-struments can also provide an access to the elementalmass depositions if they are well calibrated or one sim-ply uses other quantitative methods, e.g. Rutherfordbackscattering spectrometry in order to determine themass depositions. These can then be brought into themodeling of the laboratory GIXRF-XRR experimentaldata. Thus, the presented quantitative hybrid GIXRF-XRR approach combines the non-destructive and in-linecapable GIXRF and XRR techniques with sufficient reli-ability to reveal unexpected changes to the sample struc- ture as it has a reduced amount of degrees of freedom. ACKNOWLEDGMENTS
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