Nanoporous structure of a GdF3 thin film evaluated by

Nanoporous structure of a GdF3thinfilm evaluated by variable angle spectroscopic ellipsometryJue Wang,1,*Robert Maier,1Paul G.Dewa,1Horst Schreiber,1Robert A.Bellman,2and David Dawson Elli21Corning Tropel Corporation,Fairport,New York144502Corning Incorporated,Corning,New York14831*Corresponding author:wangj3@Received7August2006;revised4December2006;accepted30January2007;posted31January2007(Doc.ID73820);published15May2007As excimer lasers extend to deep-ultraviolet and vacuum-ultraviolet wavelengths at193and157nm,optical coatings experience the challenge of eliminating possible environmental contamination,reducingscattering loss,and increasing laser irradiation durability.Wide bandgap metalfluorides become thematerials of choice for the laser optics applications.To understand the optical properties of nanostructurefluoridefilms,thin GdF3films grown on CaF2(111)substrates were evaluated by variable angle spec-troscopic ellipsometry.An effective medium approximation model was used to determine both thefilmporosity and the surface roughness.Structural evolution of the GdF3film was revealed with improvedellipsometric modeling,suggesting the existence of multilayer structure,a densified bottom layer,middlelayers with increasing porosity,and a rough surface.The nanostructure of thefilm and the surfaceroughness were confirmed by atomic force microscopy.The attraction of the nanostructure to environ-mental contamination was experimentally demonstrated.©2007Optical Society of AmericaOCIS codes:160.4670,310.0310.1.IntroductionAs excimer lasers extend to deep-ultraviolet(DUV) and vacuum-ultraviolet(VUV)wavelengths at193 and157nm,the requirement for low loss optical com-ponents increases drastically.The usage of oxide materials is limited due to their intrinsic absorption.A renewed research interest has arisen for wide bandgapfluoride thinfilms for laser optics applica-tions[1–11].Among the very limited number of materials,GdF3is a potential candidate as a high refractive index layer for wavelengths below200nm. The optical,mechanical,and microstructural prop-erties of GdF3films have been the subject of several reports in the literature[9–13].GdF3films exhibit tensile stress,which is independent of the substrate. However,the growth behavior of GdF3is different on CaF2(111)and SiO2substrates[6,12].The former prefers heteroepitaxially orientatedfilms with the GdF3͑010͒plane parallel to the CaF2(111),whereas thefilm on an amorphous substrate formsfiber tex-tured grains with(101)and͞or(020)crystallites,de-pending on the substrate temperature[11,12].The reported refractive index values vary from1.53to1.69 at193nm in the literature.The results obtained via x-ray diffraction(XRD),transmission electron micros-copy(TEM),and from scattering measurements pro-vide useful information for understanding the physical property of GdF3films.Further coating design and process development require one to directly correlate film microstructure to optical properties.Spectro-scopic ellipsometry is a nondestructive optical tech-nique for determination of the physical thickness and optical constants of a homogeneous thinfilm.At the same time,it is possible to obtain additional struc-tural information from the relationship between op-tical properties andfilm microstructure via proper optical modeling.When considering a nonabsorbing film with an inhomogeneous structure,theoretical analysis of spectral ellipsometric data suggests that the quarter-wave and half-wave points are sensitive to thefilm mean refractive index and the degree of inhomogeneity,respectively[14–17].UV–visible–0003-6935/07/163221-06$15.00/0©2007Optical Society of America1June2007͞Vol.46,No.16͞APPLIED OPTICS3221near-IR spectroscopic ellipsometry has been used to characterize inhomogeneous nonabsorbing TiO2di-electricfilms[18].In this paper,the inhomogeneous nanostructure of the GdF3was evaluated by vari-able angle spectroscopic ellipsometry in the spectral region from the visible down to the DUV,where environmental contamination leads to an absorb-ingfilm.The optical model was verified by atomic force microscope(AFM)analysis of thefilm surface nanostructure.The attraction of the nanostructure to environmental substances was experimentally demonstrated.2.ExperimentalThe GdF3thinfilms were grown on CaF2(111) substrates by molybdenum thermal boat evapora-tion in a commercial cryopumped deposition system (SYRUSpro1110,Leybold Optics).The deposition system was pumped down to a base pressure of less than5ϫ10Ϫ6mbar.A plasma cleaning process was performed before evaporation.During the deposition the substrate temperature was kept at240°C.The deposition rate was controlled by a quartz monitor at 0.1nm͞s.Thefilms were evaluated by variable angle spectroscopic ellipsometry(VUV-300,J.A.Woollam Company).The ellipsometric parameters psi(⌿)and delta(⌬)were obtained by the ellipsometer with a rotating analyzer[20].The sample holder and the detectors were mounted on precision goniometers, which gave an angular resolution ofϳ0.01°.Purged with high-purity nitrogen,the measurement was per-formed in the spectral range from0.9to6.5eV under angles of incidence ranging from55°to60°in steps of2.5°.The measured data werefitted by WVASE32soft-ware(J.A.Woollam Company)using the least-(root-) mean-squared-error(MSE)approach[19].The MSE is the sum of the squares of the differences between each measured and calculated data,divided by the standard deviation of the experimental data point, which is the parameter being minimized during the fitting process,i.e.,MSEϭͱ1͚iϭ1N ͫͩ⌿i ModϪ⌿i Exp␴⌿i Expͪ2ϩͩ⌬i ModϪ⌬i Exp␴⌬i Expͪ2ͬ,(1)where N is the number of(⌿,⌬)pairs,M is the num-ber of variable parameters in the model,and␴are the standard deviations on the experimental data points. The MSE function described in Eq.(1)is normalized by the standard deviations on the experimental data, so noisy points are weighted less heavily.A small MSE implies a better modelfit to the data. Ultraviolet ozone(UVO)cleaning was used to re-move contamination prior to ellipsometral measure-ment[20].In addition,absorptance as a function of UVO cleaning time was determined at193nm by measuring the spectral transmittance from150to 250nm.An AFM operating in tapping mode with an etched silicon probe of5–10nm radius was employed to an-alyze the surface microstructure.The AFM scanning was taken over an area of20␮mϫ20␮m,5␮m ϫ␮m,and1␮mϫ1␮m with256ϫ256data points, respectively.3.Results and DiscussionsEllipsometry is a sensitive measurement technique that uses polarized light to characterize thinfilms, surfaces,and material microstructures.The mea-sured values are expressed as⌿and⌬.These values are related to the ratio of Fresnel reflection coeffi-cients r p and r s for p-polarized and s-polarized light, respectively,␳ϭr pr sϭtan⌿e i⌬.(2)Because the ratio is a complex number,it also con-tains“phase”information(⌬),which makes the mea-surement very sensitive.The combination of variable angle of incidence and spectroscopic measurements allows one to select the most sensitive spectral acqui-sition range and angles of incidence.A proper structural model enables one tofit spec-troscopic ellipsometer data of an unknown sample. Since CaF2and GdF3are wide bandgap materials, the photon energy used for the ellipsometric mea-surement is well below their fundamental bandgaps. In the transparent spectral region,the Cauchy for-mula is used to represent the material dispersions [19].Figure1shows both the experimental data and thefitted results at an angle of incidence of55°by assuming a smooth and homogeneous GdF3layer on the CaF2surface.The measured data are labeledϪm, whereas thefitted data are labeledϪf in Figs.1–3 The layer thickness is87.2nm with a MSE of15.77. The high MSE indicates that there are some offsets between the single layer model and the actual GdF3film.As can be seen in Fig.1,the homogeneous model fits the experimental data only in the low-photon energy region(0.9–2eV)or long-wavelengthregionFig.1.Fitting spectral data of ellipsometric⌬and⌿with a smooth and homogeneous GdF3layer on CaF2.3222APPLIED OPTICS͞Vol.46,No.16͞1June2007͑1378–620nm ͒.However,as the photon energy in-creases,the modeled results begin to depart from the experimental data.The results suggest that high-photon energy or short-wavelength light is more sensitive to film microstructure.Ellipsometric measurements performed in the spectral region of the UV and the DUV enhances the capability of ellipsometry for resolving film nanostructure.In the second approach,a thin top layer was added to the homogeneous layer model to simulate surface roughness.The Bruggemann effective me-dium approximation (EMA)was employed to corre-late physical porosity with the refractive index of the layer [21],p1Ϫn p 21ϩ2n p2ϩ͑1Ϫp ͒n d 2Ϫn p 2n d 2ϩ2n p2ϭ0,(3)where p is the physical porosity and n p is the equiv-alent refractive index of the top layer.n d is the re-fractive index of the relatively dense film.Here it hasbeen assumed that a thin layer with 50%porosity represents the top rough surface,and the porous structure is uniformly distributed on the film surface.Figure 2shows the modeled ellipsometric ⌬and ⌿as a function of photon energy.Improved data fitting is recognized when compared with the first modeling shown in Fig.1.The MSE drops to 8.35in the second model,which is almost 50%lower than the first mod-eling.It is interesting to note that in the low-photon energy region of 0.9–3.7eV,corresponding to 1378–335nm,the fitted ellipsometric ⌿is consistent with the measured data,whereas the difference between modeled and measured ⌬is obvious.The observation indicates that ellipsometric ⌬is more sensitive than ⌿for revealing film structure in nanometer scale.Further improved data fitting was accomplished when the homogeneous layer was replaced by an in-homogeneous layer.Since GdF 3films prefer to grow epitaxially on GaF 2(111),the GdF 3film might have some inhomogeneous structure along the film growth direction z .One may modify the homogeneous EMA model of Eq.(3)to an inhomogeneous case,i.e.,p ͑z ͒1Ϫn p ͑z ͒21ϩ2n p ͑z ͒2ϩ͑1Ϫp ͑z ͒͒n d 2Ϫn p ͑z ͒2n d 2ϩ2n p ͑z ͒2ϭ0,(4)where the only difference is that both the porosity p and the equivalent refractive index n p are a function of z if comparing with Eq.(3).As shown in Fig.3,good fitted region extends to ϳ6eV or 210nm in wave-length by using the inhomogeneous model.The MSE reduces to 0.98.Figure 4shows the material dispersions deter-mined from models A,B,and C for the GdF 3film grown on CaF 2(111).The dispersion of CaF 2is also included for comparison.The refractive indices de-rived from models A and B are based on homogeneous film structure.Because the rough surface has been excluded from the film volume,model B determines the mean refractive indices of the inhomogeneous film.Figure 4also includes the refractive indices of the bottom layer (labeled as Model C-b)and the top layer (labeled as Model C-t)derived from model C.As expected,the refractive indices of the bottom layer are higher than the mean refractive indicesderivedFig.4.Material dispersions determined from models A,B,and C for the GdF 3film grown on CaF 2(111).The dispersion of CaF 2is also included forcomparison.Fig.2.Fitting experimental data with a rough surface but homo-geneous GdF 3layer on CaF 2.Fig.3.Fitting experimental data with a rough surface and an inhomogeneous GdF 3layer on CaF 2.1June 2007͞Vol.46,No.16͞APPLIED OPTICS3223from model B,whereas the refractive indices of the top layer are lower than the mean refractive indices.For DUV-coating development,one is more inter-ested in the film optical parameters at the wave-length of the ArF excimer laser.Table 1summarizes the refractive index at 193nm,surface roughness,and the related MSE obtained from the three models.The modeled surface roughness (SR)corresponds to AFM measured root-mean-square (rms)roughness if a proper approach is employed.As can be seen in Fig.4,the material dispersions obtained from different models show similar wavelength dependence.By se-lecting the dense homogeneous bottom layer disper-sion (Model C-b in Fig.4)as a reference,one may compare the porosity difference derived from the three models according to Eq.(4).The mean porosity derived from model A is 10.3%.Introducing the SR layer leads to the reduction of the mean porosity to 9.3%in model B.A linear relationship between the mean porosity p and the layer thickness z in model C indicates a dense bottom layer (p ϭ0)and a porous top layer (p ϭ15.8%).The best-fitted model suggests that the refractive index of the GdF 3film is a function of layer thickness because of its inhomogeneous structure.As a result,the value of the refractive index of GdF 3film is thick-ness dependent.Figure 5plots the depth distribution of the GdF 3film grown on a CaF 2(111)surface.At the beginning of the GdF 3film formation,a dense thin layer is formed on the CaF 2(111)surface,probably due to its preference for epitaxial growth,leading to a refractive index of 1.738at 193nm.As film thick-ness increases,the growth mechanisms of columnarand polycrystalline microstructure may introduce gaps between the grains.As a consequence,the film density decreases as the layer thickness accumulates.A refractive index of 1.727at 193nm is expected when the film thickness reaches ϳ10nm.At the end of the film growth,corresponding to a physical thick-ness of ϳ81.3nm,the refractive index further drops to 1.620at 193nm.A refractive index of the surface roughness layer is 1.353at 193nm based on Eq.(3).The result suggests that GdF 3film growth mecha-nisms play a critical role in the film structure for-mation.In addition,this may also explain why different refractive indices of GdF 3films are re-ported in the literature,depending on not only de-position conditions but also on film thickness and how the refractive indices were extracted from op-tical measurements.The assumption of the epi-taxial growth mode of GdF 3on CaF 2(111)and the inhomogeneous microstructure have been confirmed by XRD and TEM,respectively.Details will be sum-marized and presented.In fact,the inhomogeneous microstructure of GdF 3films has been observed by various authors.The graded grain size and the cone-shaped column struc-tures of thermal boat deposited GdF 3films have been observed by SEM and TEM cross-sectional morphology [12].In the boundaries of structures,high-population pores and voids separate the boundaries between the grain and the column structures.The inhomogeneous property of GdF 3film grown on a CaF 2substrate also leads to spectral transmittance higher than the bare substrate [12].Figure 6exhibits AFM images over 1␮m ϫ1␮m,5␮m ϫ5␮m,and 20␮m ϫ20␮m scanning sizes with a rms of 1.5,2.3,and 3.1nm,respectively.The grain and the pore sizes range from 300to 350nm.It is not a surprise that the measured rms is correlated to the AFM scanning size,indicating that the GdF 3film has different spatial frequency features.The AFM,which measured rms over a relatively large scanning area 20␮m ϫ20␮m,is consistent with the surface roughness derived from model C as listed in Table 1,because the ellipsometric measurement cov-ers an area of 3mm ϫ6mm,which is much larger than the size of nanometer-scale features of the film.Figure 7shows the grain analysis of the AFM image scanned over 5␮m ϫ5␮m.As can be seen,the per-centage of the grain coverage is close to 50%,suggest-ing the reasonable assumption made in Eq.(3).The refractive index of the surface roughness layer at 193nm is 1.353as shown in Fig.5.The AFM images clearly reveal the nanoporous morphology of GdF 3film growth on a CaF 2(111)sur-face.As can be seen in the 1␮m ϫ1␮m image,there are some gaps between the accumulated dense grains,leading to the formation of porous structure.By in-creasing the AFM scanning size to 5␮m ϫ5␮m and 20␮m ϫ20␮m,the porous network is more obvious on the film growth plane.As predicted by ellipso-metric model C,the inhomogeneity of the GdF 3film is a result of film porosity change during growth.The randomly distributed porous structures withrela-Fig.5.Refractive index depth profile of the GdF 3film grown on CaF 2(111)according to model C.Table parison of the Homogeneous and Inhomogeneous Modeling of the Ellipsometric Data Acquired from the GdF 3FilmGrowth on CaF 2(111)Model A B Cn at 193nm 1.664 1.670 1.738(bottom)1.620(top)p (%)10.39.30(bottom)15.8(top)SR (nm)09.2 3.5d (nm)87.284.781.3MSE15.778.350.983224APPLIED OPTICS ͞Vol.46,No.16͞1June 2007tively high internal surface area may connect to each other to some degree.Since environmental contam-ination starts to absorb at the DUV wavelength [22,23],the porous open structure of the GdF 3films may be decorated by environmental substances,lead-ing to high absorption at the DUV.By removing the contamination,one may expect a reduction of absorp-tion at 193nm.UVO cleaning is an effective solution for decontam-ination of hydrocarbon-related substances [20].The UVO cleaning removes hydrocarbons by photosen-sitized oxidation processes,where the contaminant molecules are excited and dissociated by the absorp-tion of the bright line at 253.7nm from a low-pressure mercury (Hg)lamp.Simultaneously,atomic oxygen O and ozone O 3are produced when oxygen is irradiated by the Hg lamp with strong emissions at 184.9and 253.7nm in the following ways:2O 2→184.9nmO ϩO 3,(5)O 3→253.7nm O ϩO 2.(6)The excited contaminant molecules and the free rad-icals produced by the dissociation react with atomic oxygen generated according to Eqs.(5)and (6)to form simple,volatile molecules,such as CO 2and H 2O.For a dense smooth surface,UVO cleaning is very efficient.For a porous film with an open network,such as the GdF 3film,one would expect that a pro-longed cleaning is required,due to its porous struc-ture.As products of the embedded contaminants under UV irradiation,the volatile molecules have to pass though the porous channel to get out of the film.Figure 8plots the absorptance of the GdF 3film at 193nm as a function of UVO exposure time.As pre-dicted,the decontamination time is ϳ40min.For comparison,typical UVO cleaning time is 10min for Si wafers [20].Figure 9shows the absorptance of the cleaned GdF 3film at 193nm as a function of laboratory ambient exposure.It takes much longer to recontaminate the film.After a few months,the absorptance is still unsaturated.The difference be-tween the fast cleaning and the slow recontaminat-ing may be explained by gas molecule dynamics in the porous network with and without UV irradia-tion.It is worthwhile to note that the measured ellipso-metric data can be well described by model C as shown in Fig.3.On the other hand,the difference between the measured transmittance spectrum and the generated one according to model C is obvious,especially at a high-photon energy region,because the measured ellipsometric parameters described in Eq.(2)are related only to the ratio of Fresnel reflec-tion coefficients of polarized light.⌿and ⌬represent the relative changes of polarized light interaction with measured surfaces,which reduce the impact of scatter when evaluating porous structures in a short wavelength region.The ellipsometric modeling de-scribed here enables one to get quick feedback for making a dense and smooth GdF 3film during processdevelopment.Fig.6.(Color online)AFM images over 1␮m ϫ1␮m,5␮m ϫ5␮m and 20␮m ϫ20␮m scanning size with a rms of 1.5,2.3,and 3.1nm,respectively.Fig.7.(Color online)Grain size analysis of a 5␮m ϫ5␮m AFM image of the GdF 3film.Fig.8.Absorptance of the GdF 3film at 193nm as a function of UVO exposure time.1June 2007͞Vol.46,No.16͞APPLIED OPTICS32254.ConclusionsThe inhomogeneous structure of GdF 3films grown on CaF 2(111)surfaces was revealed by variable angle spectroscopic ellipsometry.Model fitting suggests that the ellipsometric ⌬is more sensitive to the film microstructure than ⌿.Extending the measurements to high photon energies,or short wavelengths,fur-ther enhances the capability of ellipsometry to re-solve structural evolution,as a function of GdF 3film growth on CaF 2(111)substrates.Structural evolu-tion of the GdF 3film was described by an improved ellipsometric modeling,suggesting a dense bottom layer,middle layers with increasing porosity,and a rough surface.As a result of the inhomogeneous porous structure,the refractive index of GdF 3films is related to film thickness.The surface rough and po-rous morphology predicted by the ellipsometric model were confirmed by AFM.The environmental contam-ination was easy to be attracted within the nano-porous film structure as a result of ambient air exposure,leading to long UVO irradiation time to clean 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