Shape- and element-sensitive reconstruction of periodic nanostructures with grazing incidence X-ray fluorescence analysis and machine learning
Anna Andrle, Philipp Hönicke, Grzegorz Gwalt, Philipp-Immanuel Schneider, Yves Kayser, Frank Siewert, Victor Soltwisch
SShape- and element-sensitive reconstruction of periodic nanostructures with grazingincidence X-ray fluorescence analysis and machine learning
A. Andrle, ∗ P. H¨onicke, Y. Kayser, and V. Soltwisch
Physikalisch-Technische Bundesanstalt (PTB), Abbestr. 2-12, 10587 Berlin, Germany
G. Gwalt and F. Siewert
Helmholtz Zentrum Berlin f¨ur Materialien und Energie (HZB),Department Optics and Beamlines, Albert-Einstein-Str. 15, 12489 Berlin, Germany
P.-I. Schneider
JCMwave GmbH, Bolivarallee 22, 14050 Berlin, Germany andZuse Institute Berlin, Takustrasse 7, 14195 Berlin, Germany
The characterization of nanostructured surfaces with sensitivity in the sub-nm range is of high im-portance for the development of current and next generation integrated electronic circuits. Moderntransistor architectures for e.g. FinFETs are realized by lithographic fabrication of complex, wellordered nanostructures. Recently, a novel characterization technique based on X-ray fluorescencemeasurements in grazing incidence geometry has been proposed for such applications. This techniqueuses the X-ray standing wave field, arising from an interference between incident and the reflectedradiation, as a nanoscale sensor for the dimensional and compositional parameters of the nanos-tructure. The element sensitivity of the X-ray fluorescence technique allows for a reconstruction ofthe spatial element distribution using a finite-element method. Due to a high computational time,intelligent optimization methods employing machine learning algorithms are essential for a timelyprovision of results. Here, a sampling of the probability distributions by Bayesian optimization isnot only fast, it also provides an initial estimate of the parameter uncertainties and sensitivities.The high sensitivity of the method requires a precise knowledge of the material parameters in themodeling of the dimensional shape provided that some physical properties of the material are knownor determined beforehand. The unknown optical constants were extracted from an unstructured butotherwise identical layer system by means of soft X-ray reflectometry. The spatial distribution pro-files of the different elements contained in the grating structure were compared to scanning electronand atomic force microscopy and the influence of carbon surface contamination on the modelingresults were discussed.
I. INTRODUCTION
Since nanotechnology and thus nanostructures of dif-ferent kind are relevant in many areas of science andtechnology, metrology techniques that can support de-sign, research and fabrication of such nanostructures areof high importance. Especially in the semiconductor in-dustry, which is probably the most popular field of appli-cation for nanotechnology as well as a very strong driverfor research in this field, complex 2D and 3D nanos-tructures with feature sizes in the single-digit nanome-ter regime [1, 2] are employed in order to keep Moore’slaw [3] alive. The performance of these nanostructurescrucially depends on a well-controlled fabrication, bothin terms of targeted dimensional parameters and 3D el-ement compositions (e.g. dopant distributions). Thus,there is a strong need for metrology techniques which al-low to characterize these parameters with sufficient sen-sitivity [4].Typical analytical or dimensional techniques used inthis context are scanning and transmission electron mi-croscopy (SEM, TEM) [5, 6], atomic force microscopy ∗ [email protected] (AFM) [7] and techniques that also address elementaldistributions such as secondary ion mass spectroscopy(SIMS) [8], atom probe tomography (APT) [9] andenergy-dispersive X-ray spectroscopy (EDX) combinedwith scanning electron microscopy (STEM) [10]. Allthese techniques have different advantages and disad-vantages regarding sample preparation and consumption,achievable spatial resolution, required duration and otherexperimental parameters (e.g. tip sizes). Optical metrol-ogy based on light-matter interaction has a significant ad-vantage in terms of measurement speed (with respect toslow techniques, e.g. APT and STEM) and the ability tostatistically measure large areas in contrast to scanningtechniques. Optical reflectometry also known as opticalcritical dimension (OCD) [11] metrology is still used andcontinuously improved despite the resolution limits thathave been reached. In order to keep pace with shrink-ing structures, intensive research is being carried out toreduce the wavelength of the employed radiation and toincrease the sensitivity via the dispersion of the periodicnanostructured surface. This is called deep ultraviolet(DUV) or extreme ultraviolet (EUV) scatterometry andcan be extended into the X-ray spectral range. In X-ray scattering techniques, a distinction is made betweenmeasurements in transmission, also known as critical di- a r X i v : . [ phy s i c s . a pp - ph ] F e b mension small angle X-ray scattering (CDSAXS) [12],and reflection mode known as grazing incidence small an-gle X-ray scattering (GISAXS) [13, 14]. Both techniqueshave already shown that they allow for the dimensionalreconstruction of nanostructures with an uncertainty inthe sub-nm range [15, 16], but both require a specialsample thinning or sample design, which limits the ap-plication possibilities [17]. Usually, these techniques alsoemploy rather high photon energy X-rays, which limitsthe optical contrast between different materials withinthe investigated nanostructures.In this paper, we employ the grazing incidence X-rayfluorescence analysis (GIXRF) [18] method and soft X-rays ( < II. EXPERIMENTAL
As an example of two-dimensional nanostructures, alithographically patterned silicon nitride grating on a sil-icon substrate was investigated. It was manufacturedby means of electron beam lithography (EBL) at theHelmholtz-Zentrum Berlin. The nominal pitch of thegrating is p = 100 nm, the nominal height is h = 90 nmand the nominal line width of the sample is w = 50 nm.For the manufacturing of the gratings, a silicon substratewith a 90 nm-thick Si N layer was used. ZEP520A, a positive resist (organic polymer), was spin coated on thesubstrate and developed with a Vistec EBPG5000+ e-beam writer, operated with an electron acceleration volt-age of 100 kV. The grating was etched via reactive ionetching using CHF and to remove the remaining resistan oxygen plasma treatment was applied. A sketch of thecross-section is shown in Fig. 1 a). The total structuredarea of the grating was 1 mm x 15 mm and the samplearea outside the patterned region consists of the origi-nally deposited Si N layer. Directly after fabrication,cross-section SEM images have been recorded on a sistersample.We performed GIXRF and X-ray reflectometry (XRR)measurements in PTB’s laboratory [27] at the BESSY IIelectron storage ring using the plane-grating monochro-mator (PGM) beamline [28] for undulator radiation. Thesample was mounted in an ultrahigh-vacuum (UHV)measurement chamber [29], where a 9-axis manipulatorallows for an accurate sample alignment with respect tothe direction of incident X-ray beam. The incidence an-gle θ is defined as the angle between the X-ray beam andthe sample surface. The azimuthal angle ϕ is defined asthe angle between the incident beam and a plane, whichis normal to the sample surface and parallel to the direc-tion of the grating lines such that ϕ = 0 ◦ is defined asthe orientation parallel to the plane of incidence. Bothsample rotation axes can be aligned with an uncertaintybelow 0.01 ◦ .As we have employed radiometrically calibrated X-ray fluorescence (XRF) instrumentation, we can performreference-free GIXRF [30] and gain a quantitative ac-cess to the elemental mass depositions present on thesample [31]. At each angular position for θ and ϕ , afluorescence spectrum is recorded with a calibrated sil-icon drift detector (SDD) [32] and the incident photonflux is monitored by means of a calibrated photodiode.The GIXRF-measurements were performed at an inci-dent photon energy of E i = 680 eV, allowing for theexcitation of N-K α as well O-K α fluorescence radiation,which mainly originates from the surface oxide layer onthe grating structure. In Fig. 4 the obtained and nor-malized N-K α a) and O-K α b) fluorescence intensitiesfor different angles θ and ϕ are shown.In addition, we have performed XRR experiments onthe non-structured Si N layer next to the grating at thesame photon energy ( E i = 680 eV). From this we candetermine the optical constants of the SiO layers andthe Si N layer, which are expected to be more reliablein the soft X-ray spectral range than using only tabulateddata as in [33].For an independent validation of the dimensionalGIXRF reconstruction results, additional AFM measure-ments were performed with an Nanosurf Nanite 25x25.The sample was measured under tapping mode condi-tion and a standard pyramidal shaped silicon probe witha tip radius <
10 nm was used, as it is commonly ap-plied for the inspection of diffraction gratings [34]. TheAFM-probe is characterized by a resonance frequency of190 Hz and force constant of 48 N / m. The inspectedsample area was 500x500 nm in size covering about 5grating lines. The height profile, obtained by averagingtwo in juxtaposition located AFM line profiles, is shownin Fig. 6. III. SIMULATION AND OPTIMIZATION OFFLUORESCENCE INTENSITIES
The GIXRF signals are directly related to the XSWfield intensity distribution which, besides the incidentphoton energy and the incidence and azimuthal angles,depends on the shape and material composition of the il-luminated nanostructured surface. To reconstruct thesesample features from the experimental data, we applied afinite-element method (FEM) based forward calculationof the XSW and optimized the structural parameters toreproduce the experimental data.In Fig. 1, the basic principle of the FEM procedureis shown. The mesh grid and the model parameters aredisplayed in Fig. 1 a). The FEM solver calculates theelectric near-field for a given structure (Fig. 1 b)). Theamount of fluorescence photons generated at a given co- ordinate depends on the local electric near-field intensity( E ( x, y )) and the compositional and fundamental param-eters of the respective material (mass fraction of the flu-orescent element in the material W k , photo-ionizationcross section for the incident photon energy τ ( E i ) andthe fluorescence yield ω k , taken from databases [35] ordedicated experiments [36]). These photons can be re-absorbed on the path through the sample towards thedetector (Fig. 1 b)) with a probability depending on thematerials mass attenuation coefficient µ ( E f ) for the flu-orescence photon energy E f , the density ρ of the mate-rial and the distance to the surface of the nanostructure y dis ( x, y ). Eventually, the fluorescence photon will bedetected with a given detection efficiency (cid:15) ( E f ) if it isarriving within the effective solid angle of detection Ω.The overall emitted fluorescence intensity of course alsodepends on the incident photon flux N .Thus, the measured emitted fluorescence intensityΦ( θ, ϕ, E i ) (derived from the detected count rate F ( θ, ϕ, E i )) can be modeled using the integration overthe full area of the fluorescent material of the nanos-tructure as described by the modified Sherman equa-tion [21, 23]:Φ( θ, ϕ, E i ) = 4 π sin θ Ω F ( θ, ϕ, E i ) N (cid:15) ( E f ) (cid:124) (cid:123)(cid:122) (cid:125) I exp = W k ρτ ( E i ) ω k (cid:80) dx · (cid:88) x (cid:88) y | E ( x, y ) | · exp [ − ρµ ( E f ) y dis ( x, y )] dxdy (cid:124) (cid:123)(cid:122) (cid:125) I model . (1)The equation 1 is applied for nitrogen and oxygenfluorescence and has been implemented directly in theMaxwell solver to eliminate errors due to conversion toa regular cartesian grid. The calculated emitted fluores-cence intensities I model are then compared against theexperimental value I exp . By using a global optimizationalgorithm such as Bayesian optimization (BO) [24, 25],an optimal set of the model parameters can then bedetermined. BO uses a stochastic model, a Gaussianprocess, of an unknown objective function to be mini-mized in order to determine promising parameter val-ues [24, 37]. In a previous work [25, 38], it was shown thatthe BO performs much better than other meta-heuristicoptimization approaches with respect to the computingtime needed to find the global minimum. Since BO con-siders all previous function evaluations, it can be moreefficient than other meta-heuristic global optimizationstrategies [25] and local optimization strategies [39]. Thisis a crucial benefit here, as one model calculation takesseveral minutes on a standard desktop computer. Here,we use an implementation of BO which is part of theJCMsuite software package [40]. The error function χ χ ( (cid:126)gp ) = (cid:88) θ,ϕ ( I exp ( θ, ϕ ) − I model ( (cid:126)gp, θ, ϕ )) σ N ( θ, ϕ ) (2)was minimized with respect to the different model pa-rameters of (cid:126)gp described earlier (see Fig. 1 a)) and modelerrors for the nitrogen (cid:15) N and the oxygen fluorescence sig-nals (cid:15) O ). These model error parameters are introducedto consider potential errors e.g. the uncertainty of theemployed atomic fundamental parameters or the influ-ence of a thin surface contamination layer into account.Even though material dependent parameters like opticalconstants or material densities deviate most likely fromthe tabulated bulk data for the grating materials (SiO and Si N ), we do not include these as free parametersin the model. Indeed, as this would drastically increasethe number of model parameters and thus prolong thenecessary calculation times, we rather determine theseparameters separately by XRR (described in the nextsection). σ N is the calculated experimental error consist-ing of an error estimation for the effective solid angle ofdetection σ Ω ( θ ), the error contributions originating fromcounting statistics √ FF for the respective fluorescence line FIG. 1. a) Cross-section with the finite-element mesh-grid showing the layout used for the simulation. The height h , thewidth w , the sidewall angle swa , the oxide layer thicknesses in the groove t g and the on the grating line t t were optimized asindependent parameters. The oxide layer on the substrate t s was kept constant during the optimization. b) The calculatedelectric field strength inside and outside the structure is shown for θ = 1 . ◦ and ϕ = 1 . ◦ . For the nitrogen and oxygenfluorescence the electric field strength is integrated and the reabsorption is calculated with the distance y dis the photon has totravel to leave the structure. as well as for the spectra deconvolution σ num . σ N ( θ ) = (cid:32) (cid:112) F ( θ ) F ( θ ) (cid:33) + σ Ω ( θ ) + σ num ( θ ) (3)By inverting the Hessian matrix H kj [41] of the errorfunction, H kj = ∂ χ ( (cid:126)gp ) ∂gp j ∂gp k (4)at the minimum of χ it is possible to determine theconfidence intervals ( H ) − of the model parameters, ifthey are gaussian distributed as assumed.The standard deviation or noise level at the global min-imum parameter set is defined as STD = (cid:113) χ DOF , whereDOF = N − M is the difference between the numberof measurement points N and the number of free modelparameters M and thus the degrees of freedom.The model parameter confidence interval can then becalculated by σ (cid:126)gp = STD (cid:113) diag(( H ) − ) (5)Based on the Gaussian process model of χ ( (cid:126)gp ) wedetermine an estimate of the Hessian matrix by comput-ing all second derivatives of the Gaussian process model of χ at the minimum and can then estimate the errorcovariance matrix ( H ) − and the parameter confidenceinterval. IV. RESULTS AND DISCUSSIONA. Validation of the optical material parameters
From the angle-dependent measurement of reflectionintensities on a layered system, information about layerthicknesses, densities or even their optical constants canbe obtained [42]. Fig. 2 b) shows the experimental datain comparison with the best simulation. The high fre-quency oscillation visible in the XRR curve, is a clearindication for a multi-layer system. Due to the nativeoxide layer of the Si substrate and the removal of thephoto resist, resulting in an oxidized surface on the Si N layer [43], we apply a three layer model for the XRRsimulation (as shown in the inset of Fig. 2 a)). Sincethe calculation of the reflectivity for a 1D layer system isseveral orders of magnitude faster than the FEM based2D GIXRF modeling, statistical analysis methods of theposterior distributions can be used for a large number ofparameters such as layer thickness, roughness and opticalconstants. We applied the Markow Chain Monte Carlomethod (MCMC) [44] to determine the individual param-eter uncertainties and to resolve possible inter parametercorrelation effects [45]. In Fig. 2 a) the posterior distribu-tion determined in this procedure is shown as projectionsof the refractive index n ( Si N ) = 1 − δ + iβ and thick-ness h of the Si N layer. The almost perfect gaussian-like shape of the distributions, which is also present in allother parameters, allows the determination of uncertain-ties directly from the measurements. The relative un-certainties of the experimental data reconstructed witha linear error model ( ax + b ) [41] are with (0 . ± . SiO ( δ = (8 . ± . − , β = (2 . ± . − ) and the Si N ( δ = (12 . ± . − , β =(2 . ± . − ) layers. By comparing the experimen-tally determined optical constants with tabulated Henkedata [46], one can estimate the densities of the respectivematerials and their deviation from the respective bulkdensities. For Si N , a relative density of (0 . ± . SiO a relative density of (0 . ± .
01) was found.This is in line with the already observed material densityreduction discussed in Ref. [21]. The reduced densitiesas well as the experimental optical constants are used forthe GIXRF reconstruction.
B. GIXRF reconstruction results
1. Virtual Experiment
Before we apply the reconstruction model to real ex-perimental data, we apply it to an artificial dataset inorder to test the reconstruction method and to study,whether an increased incident photon energy, capableof exciting also oxygen fluorescence signal, is benefi-cial. In our previous study [21], measurement data at E i = 520 eV was analyzed and an indirect sensitivity tothe surface oxide layer was found even though no fluo-rescence signal originating from it was used for the re-construction. The indirect sensitivity was merely due tothe attenuation behavior of the oxide layer and thus, weexpect an increased sensitivity if also a direct signal orig-inating from it is used. For this purpose, we generateartificial experimental data by calculating model curvesusing the reconstruction model for a given set of parame-ters and the two incident photon energies of E i = 680 eVand E i = 520 eV. To mimic experimental noise, we applya Gaussian disturbance with a width of 3% (see Tab. I).By reconstructing the artificial datasets, we can now ana-lyze the influence of the increased incident photon energyon the reconstruction results and their confidence inter-vals without the influence of any experimental error con-tributions. In Fig. 3 the corresponding artificial GIXRFcurves and reconstruction results are displayed. Theymatch the artificial data well for both photon energiesand characteristic features, e.g. the first local maximaare very well retrieved. From the BO reconstruction, weare able to calculate the confidence intervals of the re-constructed parameters and, as shown in Tab. I, they Si N SiSiO FIG. 2. a) The posterior distributions for relevant parameters δ Si N , β Si N and the Si N thickness h obtained from theMCMC sampling. The red line marks the mean of the distri-bution and the dotted black lines in the histogram indicatesa 3 σ interval. In the top right corner, a sketch of the usedlayer stack is shown.b) Comparison of the experimental data (black stars) and themodel calculation (red line) as obtained by the MCMC. agree well with the initial parameters within the derivedconfidence interval.From a comparison of the determined confidence inter-vals for the two different configurations (ConfigurationA, E i = 520 eV, only the nitrogen signal is modeled andConfiguration B, E i = 680 eV, both nitrogen and oxygensignals are modeled, see Tab. I), the positive influence ofalso considering the oxygen fluorescence signal is obvious.Especially for the height and the groove oxide thickness,the achieved confidence intervals are significantly smallerfor configuration B. Nevertheless, also for configurationA, the angle-dependent nitrogen fluorescence contains allrelevant information about the dimensional properties ofthe nanostructure and even the surface oxide layer, asalready pointed out in our earlier work [21]. TABLE I. The values of the geometrical parameters of thesynthetic data from the GIXRF BO reconstruction with themodel parameter confidence intervals for E i = 520 eV (Con-figuration A, only the nitrogen signal is modeled) and E i =680 eV (Configuration B, both nitrogen and oxygen signalsare modeled). The pitch was set to p = 50 nm. (height h ,width w , sidewall angle swa , oxide layer in the groove t g andoxide layer on the grating line t t ) Parameter Intial Config. Conf. IntervalName Value A B Ratio BA h/ nm 90 89 . . w/ nm 25 24 . . swa/ ◦
88 88 . . t t / nm 3 3 . . t g / nm 5 5 . . (cid:15) N . . (cid:15) O .
2. Real experimental data
Using the same model and methodologies, also the realexperimental data, measured according to configurationB, was modeled. A comparison of the two experimen-tal datasets and the resulting modeled data is shown inFig. 4. The corresponding optimal parameters and con-fidence intervals are summarized in Tab. II. Again, theconfidence intervals of the structure parameters derivedfrom the BO posterior distribution are very similar tothose determined in the virtual experiment.Similarly as already for the virtual experiment, ahigher sensitivity for the line width is observed as com-pared to the height. This is expected to be a result ofthe relatively large line height with respect to the achie-veable information depth in the soft X-ray regime. Thus,the nitrogen fluorescence radiation from the very bottomof the grating line does not contribute significantly tothe overall observed signal. Nevertheless all calculatedconfidence intervals are in the sub-nm regime.It should also be noted that the two modeling errorparameters (cid:15) N and (cid:15) O deviate from unity within a rangeof 10 %. This is the same magnitude one would expectthe relative uncertainty of the employed fluorescence pro-duction cross sections (product of fluorescence yield andphoto ionization cross section) to be in.Systematic errors not taken into account may increasethe final uncertainties. This problem is often calledmodel error and refers to the whole physical model orvirtual experiment that is applied and is not limited tothe finite element model. The next section shows thatthese modeling uncertainties can have a significant im-pact on the reconstruction parameters.
3. Contamination
In addition to oxygen and nitrogen signals in the fluo-rescence spectra, also carbon fluorescence was observed.
TABLE II. The values of the geometrical parameters of thenanostructures from the GIXRF BO reconstruction with themodel parameter confidence intervals (one sigma). The pa-rameters are height h , width w , sidewall angle swa , oxidelayer in the groove t g and oxide layer on the grating line t t . Parameter ReconstructedName Value h/ nm 97 . w/ nm 49 . swa/ ◦ . t t / nm 2 . t g / nm 5 . (cid:15) N . (cid:15) O . artificial model FIG. 3. Comparison of the expected artificial disturbed simu-lated N-K α (green points) or O-K α (blue points) fluorescenceintensities for the different excitation energies and the corre-sponding BO reconstruction. Clearly visible is how the firstpeak in the nitrogen signal shifts with increasing energy tosmaller incident angles. A presence of carbon on the sample surface is likely asthe sample is stored under normal ambient conditions. Alateral scan of the sample (Fig. 5 a)) at a fixed incidentangle θ = 15 ◦ reveals that this carbonaceous contamina-tion is not homogeneously distributed over the patternedarea. In the center of the grating area ( x = − .
15 mm)a strong increase of the carbon signal and a slight in-crease of the oxygen signal can be observed, whereasthe nitrogen signal is practically constant. In an ear-lier benchmark study, the sample under investigation wasmeasured in various scatterometers and electron micro-scopes around the world. A punctual contamination ofthe grating surface by these techniques can therefore notbe excluded. Here, we take advantage of this artificiallycreated contamination layer to demonstrate the sensitiv-ity and the influence of model errors.At each lateral position shown in the figure, we per-formed a GIXRF angular scan (at ϕ = 0 ◦ ) and per-formed the reconstruction including the confidence in-terval calculation without considering any contamina- /° / ° /° a) N-K α b) O-K α c) exp data F l u o r e sc e n c e i n t e n s i t y / i n c i d e n t p h o t o n simulationexp data simulation /° F l u o r e sc e n c e i n t e n s i t y / i n c i d e n t p h o t o n best-fit model /° F l u o r e sc e n c e i n t e n s i t y / i n c i d e n t p h o t o n FIG. 4. Comparison of the measured and simulated fluo-rescence maps for N-K a) and O-K b) based on the recon-structed parameter set. c) Comparison of the experimentalN-K α (green) or O-K α (blue points) fluorescence intensitiesfor ϕ = 0 ◦ to the reconstructions from the Bayesian optimiza-tion (red lines). tion. Fig. 5 b) shows the obtained differences betweenthe reconstructed model parameters at each position tothe reference position at x = 0 mm (position where thedata shown in Fig. 4 was taken). The model parame-ters at − .
15 mm, which is the position with maximalcarbon and oxygen contamination, differ clearly with re-spect to less contaminated areas. The difference is largerthan the calculated confidence intervals from the recon-struction and they are also much larger than the ex-pected lateral inhomogeneities of the sample. In ad-dition, the nearly constant nitrogen fluorescence signalin X-direction clearly indicates a homogeneous overallamount of Si N , which is in contradiction to the largercross-sectional area of the grating determined by the re-construction from the GIXRF model. The reconstructedheights and widths increase by more than 4 nm.This behavior can be explained considering the XSWnear field distribution inside the grooves: The slight in-crease of the oxygen due to the contamination signal canonly be incorporated by increasing the oxide layer thick-nesses. However, an increase of the oxide layer thicknessweakens the penetrating field inside the Si N and thusthe emitted nitrogen fluorescence. To compensate forthis, a larger grating cross section is reconstructed. Onemay think, that the reconstruction algorithm could cir-cumvent this by simply increasing only the groove oxidelayer thickness, which does not affect the nitrogen signalso much. But as shown in part c) of the figure, wherethe angular oxygen fluorescence signal contributions fromthe different parts in the structure model are shown, the r e l a t i v e d e v i a t i o n o f X R F i n t e n s i t i e s a) N-KC-KO-K sample x position / mm s h a p e d e v i a t i o n / n m b) line widthline heightoxide grooveoxide line / f l u o r e sc e n c e i n t e n s i t y / i n c i d e n t p h o t o n
1e 5 c) O-K emission from groovelinesubstrate
FIG. 5. a) Here the C-K α , N-K α and O-K α fluorescenceintensity at θ = 15 ◦ where no XSW needs to be consideredfrom different positions on the sample are compared.b) The reconstruction results for the width, the height, thethickness of the oxide in the groove and the thickness of oxidearound the line for the different position are plotted.c) The various contributions from the oxide from the line, thegroove and the oxide layer of the silicon wafer to the totaloxygen fluorescence are compared. groove oxide has a significantly different angular behav-ior as compared to the oxide on the grating line surface.Especially the features at about 1 ◦ and 2 . ◦ are very dis-tinct. For this reason, the reconstruction algorithm mustincrease both in order to account for the higher oxygensignal in the contaminated area throughout the angularrange.This shows how sensitive the GIXRF method is, butalso how carefully the models have to be developed fora realistic uncertainty estimation. However, even if themodel is not accurate enough, a spacial resolved recon-struction can reveal flaws of the model. C. Comparison with SEM and AFM
For a validation of the dimensional and compositionalparameters as derived from the GIXRF modeling with-out the thick carbon contamination, we have performedAFM measurements on the sample and use also SEM (on
FIG. 6. Comparison of the AFM data with the result ofthe GIXRF reconstruction and a SEM picture from a wit-ness sample. a witness sample). As AFM is an established method tomap the surface topology of nanostructures with sensi-tivities down to the nm regime, we can use an AFM toverify the GIXRF reconstructed total line heights (differ-ence between top surface and groove surface). From theAFM data, we determined a total line height of 98 . V. CONCLUSION
Here, we have demonstrated how the GIXRF basedmethodology for a dimensional and compositional char- acterization of regular nanostructures can be enhancedwith respect to the achieveable sensitivities by incor-porating fluorescence signals of different elements fromwithin the nanostructure. In addition, the incorporationof supporting experiments as e.g. XRR for optical con-stant verification and machine learning techniques suchas Bayesian optimization decrease the necessary compu-tational effort of the FEM based reconstruction. The BOallows for an intelligent and fast scanning of the param-eter space as compared to other optimizer approaches.Initial steps towards determining a reliable uncertaintybudget for the reconstructed parameter set were takenby deriving confidence intervals for the parameters fromthe Gaussian process model. We have shown, how theincorporation of the oxygen signal shifts the achievablesensitivities well into the sub-nm regime. The obtainedGIXRF reconstruction results agree very well with re-sults from SEM and AFM indicating the validity of themethodology.In addition, we have shown that the methodology isalso somewhat sensitive towards unexpected effects onthe nanostructure using the example of the carbon con-tamination. Especially the element sensitivity of X-rayfluorescence but also the behavior of the reconstructionresults indicate if unexpected effects are present on thenanostructure.By developing more sophisticated techniques to quan-tify the corresponding model error influences to the finalparameter uncertainties this can be a promising tech-nique for nanostructure characterization. In fact, bycombining it with techniques such as soft X-ray GISAXSone may even enhance the obtainable sensitivities andeven learn about important quality parameters e.g. lineroughnesses [16].
VI. ACKNOWLEDGEMENTS
This project has received funding from the Elec-tronic Component Systems for European LeadershipJoint Undertaking under grant agreement No 826589 —MADEin4. This Joint Undertaking receives support fromthe European Union’s Horizon 2020 research and innova-tion programme and Netherlands, France, Belgium, Ger-many, Czech Republic, Austria, Hungary, Israel.JCMwave acknowledges support by the Central Inno-vation Programm of the Federal Ministry for EconomicAffairs and Energy on a basis of a decision by the GermanBundestag (project QUPUS, grant no. ZF4450901RR7).The authors would like to thank J¨urgen Probst for pro-ducing the samples. [1] S. Natarajan, M. Agostinelli, S. Akbar, M. Bost,A. Bowonder, V. Chikarmane, S. Chouksey, A. Dasgupta,K. Fischer, Q. Fu, T. Ghani, M. Giles, R. G. S. Govin-daraju, W. Han, D. Hanken, E. Haralson, M. Haran, M. Heckscher, R. Heussner, P. Jain, R. James, R. Jhaveri,I. Jin, H. Kam, E. Karl, C. Kenyon, M. Liu, Y. Luo,R. Mehandru, S. Morarka, L. Neiberg, P. Packan, A. Pali-wal, C. Parker, P. Patel, R. Patel, C. Pelto, L. Pipes,
P. Plekhanov, M. Prince, S. Rajamani, J. Sandford,B. Sell, S. Sivakumar, P. Smith, B. Song, K. Tone,T. Troeger, J. Wiedemer, M. Yang, K. Zhang, A14nm logic technology featuring 2nd-generation finfet,air-gapped interconnects, self-aligned double patterningand a 0.0588 µ m sram cell size, Electron Devices Meet-ing (IEDM), 2014 IEEE International (2014) 3.7.1 –3.7.3.[2] I. L. Markov, Limits on fundamental limits to computa-tion, Nature 512 (2014) 147–154.[3] G. E. Moore, Cramming more components onto inte-grated circuits, reprinted from electronics, volume 38,number 8, april 19, 1965, pp.114 ff., IEEE Solid-StateCircuits Society Newsletter 11 (2006) 33–35.[4] N. G. Orji, M. Badaroglu, B. M. Barnes, C. Beitia, B. D.Bunday, U. Celano, R. J. Kline, M. Neisser, Y. Obeng,A. E. Vladar, Metrology for the next generation of semi-conductor devices, Nature Electronics 1 (2018) 532–547.[5] K. Takamasu, H. Okitou, S. Takahashi, M. Konno, O. In-oue, H. Kawada, Sub-nanometer line width and lineprofile measurement for CD-SEM calibration by usingSTEM, p. 797108.[6] R. Erni, M. D. Rossell, C. Kisielowski, U. Dahmen,Atomic-Resolution Imaging with a Sub-50-pm ElectronProbe, Physical Review Letters 102 (2009) 096101.[7] V. A. Ukraintsev, C. Baum, G. Zhang, C. L. Hall, Therole of AFM in semiconductor technology development:the 65 nm technology node and beyond, p. 127.[8] A. Franquet, B. Douhard, D. Melkonyan, P. Favia,T. Conard, W. Vandervorst, Self focusing SIMS: Probingthin film composition in very confined volumes, AppliedSurface Science 365 (2016) 143–152.[9] W. Vandervorst, A. Schulze, A. K. Kambham, J. Mody,M. Gilbert, P. Eyben, Dopant/carrier profiling for 3d-structures: Dopant/carrier profiling for 3d-structures 11(2014) 121–129.[10] H. Mertens, R. Ritzenthaler, V. Pena, G. Santoro, K. Ke-nis, A. Schulze, E. D. Litta, S. A. Chew, K. Devriendt,r. Chiarella, S. Demuynck, D. Yakimets, D. Jang,A. Spessot, G. Eneman, A. Dangol, P. Lagrain, H. Ben-der, S. Sun, M. Korolik, D. Kioussis, M. Kim, K.-H.Bu, S. C. Chen, M. Cogorno, J. Devrajan, J. Machillot,N. Yoshida, N. Kim, K. Barla, D. Mocuta, N. Horiguchi,Vertically stacked gate-all-around Si nanowire transis-tors: Key Process Optimizations and Ring OscillatorDemonstration, in: 2017 IEEE International ElectronDevices Meeting (IEDM), IEEE, San Francisco, CA,USA, 2017, pp. 37.4.1–37.4.4.[11] R. Silver, T. Germer, R. Attota, B. M. Barnes, B. Bun-day, J. Allgair, E. Marx, J. Jun, Fundamental limits ofoptical critical dimension metrology: a simulation study,San Jose, CA, p. 65180U.[12] D. F. Sunday, S. List, J. S. Chawla, R. J. Kline, Deter-mining the shape and periodicity of nanostructures usingsmall-angle x-ray scattering, Journal of Applied Crystal-lography 48 (2015) 1355–1363.[13] J. R. Levine, J. B. Cohen, Y. W. Chung, P. Georgopou-los, Grazing-incidence small-angle X-ray scattering: newtool for studying thin film growth, J. Appl. Cryst. 22(1989) 528–532.[14] G. Renaud, R. Lazzari, F. Leroy, Probing surface and in-terface morphology with Grazing Incidence Small AngleX-Ray Scattering, Surf. Sci. 64 (2009) 255–380.[15] V. Soltwisch, A. Fern´andez Herrero, M. Pfl¨uger, A. Haase, J. Probst, C. Laubis, M. Krumrey, F. Scholze,Reconstructing detailed line profiles of lamellar gratingsfrom GISAXS patterns with a Maxwell solver, Journalof Applied Crystallography 50 (2017) 1524–1532.[16] A. F. Herrero, M. Pfl¨uger, J. Probst, F. Scholze,V. Soltwisch, Applicability of the debye-waller dampingfactor for the determination of the line-edge roughness oflamellar gratings, Opt. Express 27 (2019) 32490–32507.[17] M. Pfl¨uger, R. J. Kline, A. Fern´andez Herrero,M. Hammerschmidt, V. Soltwisch, M. Krumrey, Ex-tracting dimensional parameters of gratings producedwith self-aligned multiple patterning using grazing-incidence small-angle x-ray scattering, Journal of Mi-cro/Nanolithography, MEMS, and MOEMS 19 (2020) 1.[18] D. de Boer, A. Leenaers, W. van den Hoogenhof,Glancing-incidence x-ray analysis of thin-layered mate-rials: A review, X-Ray Spectrom. 24(3) (1995) 91–102.[19] M. J. Bedzyk, G. M. Bommarito, J. S. Schildkraut, X-ray standing waves at a reflecting mirror surface, Phys.Rev. Lett. 62 (1989) 1376–1379.[20] J. A. Golovchenko, J. R. Patel, D. R. Kaplan, P. L.Cowan, M. J. Bedzyk, Solution to the surface registrationproblem using x-ray standing waves, Phys. Rev. Lett. 49(1982) 560–563.[21] V. Soltwisch, P. H¨onicke, Y. Kayser, J. Eilbracht,J. Probst, F. Scholze, B. Beckhoff, Element sensitivereconstruction of nanostructured surfaces with finite-elements and grazing incidence soft x-ray fluorescence,Nanoscale 10 (2018) 6177–6185.[22] K. V. Nikolaev, V. Soltwisch, P. H¨onicke, F. Scholze,J. de la Rie, S. N. Yakunin, I. A. Makhotkin, R. W. E.van de Kruijs, F. Bijkerk, A semi-analytical approachfor the characterization of ordered 3d nano structures us-ing grazing-incidence x-ray fluorescence, Journal of Syn-chrotron Radiation 27 (2020) 386–395.[23] P. H¨onicke, A. Andrle, Y. Kayser, K. Nikolaev, J. Probst,F. Scholze, V. Soltwisch, T. Weimann, B. Beckhoff, Graz-ing incidence-x-ray fluorescence for a dimensional andcompositional characterization of well-ordered 2d and 3dnanostructures, Nanotechnology 31 (2020) 505709.[24] B. Shahriari, K. Swersky, Z. Wang, R. P. Adams,N. De Freitas, Taking the human out of the loop: A re-view of Bayesian optimization, Proceedings of the IEEE104 (2016) 148–175.[25] P.-I. Schneider, X. Garcia Santiago, V. Soltwisch,M. Hammerschmidt, S. Burger, C. Rockstuhl, Bench-marking five global optimization approaches for nano-optical shape optimization and parameter reconstruction,ACS Photonics 6 (2019) 2726–2733.[26] D.-X. Zhang, Y.-X. Zheng, Q.-Y. Cai, W. Lin, K.-N.Wu, P.-H. Mao, R.-J. Zhang, H.-b. Zhao, L.-Y. Chen,Thickness-dependence of optical constants for Ta2O5 ul-trathin films, Applied Physics A 108 (2012) 975–979.[27] B. Beckhoff, A. Gottwald, R. Klein, M. Krumrey,R. M¨uller, M. Richter, F. Scholze, R. Thornagel, G. Ulm,A quarter-century of metrology using synchrotron radi-ation by PTB in berlin, Physica Status Solidi (B) 246(2009) 1415–1434.[28] F. Senf, U. Flechsig, F. Eggenstein, W. Gudat, R. Klein,H. Rabus, G. Ulm, A plane-grating monochromatorbeamline for the ptb undulators at BESSY II, J. Syn-chrotron Rad. 5 (1998) 780–782.[29] J. Lubeck, B. Beckhoff, R. Fliegauf, I. Holfelder,P. H¨onicke, M. M¨uller, B. Pollakowski, F. Reinhardt, J. Weser, A novel instrument for quantitative nanoan-alytics involving complementary x-ray methodologies,Rev. Sci. Instrum. 84 (2013) 045106.[30] P. H¨onicke, B. Detlefs, E. Nolot, Y. Kayser, U. M¨uhle,B. Pollakowski, B. Beckhoff, Reference-free grazing inci-dence x-ray fluorescence and reflectometry as a method-ology for independent validation of x-ray reflectometryon ultrathin layer stacks and a depth-dependent charac-terization, J. Vac. Sci. Technol., A 37 (2019) 041502.[31] B. Beckhoff, Reference-free x-ray spectrometry based onmetrology using synchrotron radiation, J. Anal. At. Spec-trom. 23 (2008) 845 – 853.[32] F. Scholze, M. Procop, Modelling the response functionof energy dispersive x-ray spectrometers with silicon de-tectors, X-Ray Spectrom. 38(4) (2009) 312–321.[33] A. Andrle, P. H¨onicke, J. Vinson, R. Quintanilha,Q. Saadeh, S. Heidenreich, F. Scholze, V. Soltwisch,The anisotropy in the optical constants of quartz crys-tals for soft X-rays, arXiv:2010.09436 [cond-mat,physics:physics] (2020). ArXiv: 2010.09436.[34] F. Siewert, B. L¨ochel, J. Buchheim, F. Eggenstein,A. Firsov, G. Gwalt, O. Kutz, S. Lemke, B. Nelles,I. Rudolph, F. Sch¨afers, T. Seliger, F. Senf, A. Sokolov,C. Waberski, J. Wolf, T. Zeschke, I. Zizak, R. Follath,T. Arnold, F. Frost, F. Pietag, A. Erko, Gratings forsynchrotron and FEL beamlines: a project for the man-ufacture of ultra-precise gratings at Helmholtz ZentrumBerlin, Journal of Synchrotron Radiation 25 (2018) 91–99.[35] T. Schoonjans, A. Brunetti, B. Golosio, M. S. del Rio,V. Sol´e, C. Ferrero, L. Vincze, The xraylib library forx-ray–matter interactions. recent developments, Spec-trochim. Acta B 66 (2011) 776 – 784.[36] P. H¨onicke, M. Kolbe, M. Krumrey, R. Unterumsberger,B. Beckhoff, Experimental determination of the oxygenk-shell fluorescence yield using thin sio2 and al2o3 foils,Spectrochim. Acta B 124 (2016) 94–98.[37] X. Garcia-Santiago, P. I. Schneider, C. Rockstuhl,S. Burger, Shape design of a reflecting surface using Bayesian Optimization, Journal of Physics: ConferenceSeries 963 (2018).[38] A. Andrle, P. H¨onicke, P.-I. Schneider, Y. Kayser,M. Hammerschmidt, S. Burger, F. Scholze, B. Beckhoff,V. Soltwisch, Grazing incidence x-ray fluorescence basedcharacterization of nanostructures for element sensitiveprofile reconstruction, Proc. SPIE - Modeling Aspects inOptical Metrology VII 11057 (2019) 110570M.[39] P.-I. Schneider, M. Hammerschmidt, L. Zschiedrich,S. Burger, Using Gaussian process regression for effi-cient parameter reconstruction, Proc. SPIE 10959 (2019)1095911.[40] JCMwave GmbH, Paramter reference, 2020. https://docs.jcmwave.com/JCMsuite/html/ParameterReference/index.html?version=4.0.3https://docs.jcmwave.com/JCMsuite/html/ParameterReference/index.html?version=4.0.3