SURFACE AND INTERFACE ANALYSISSurf. Interface Anal. 29, 341–345 (2000)

SHORT COMMUNICATION

Use of ellipsometry and gravimetry to developcalibration standards for measuring silicone coatweight and thickness with x-ray fluorescencespectroscopy

B. Parbhoo,1 S. Izrael,1 J. M. Salamanca2 and J. L. Keddie2*1 Interface Expertise Centre, Dow Corning Ltd, Cardiff Road, Barry, South Glamorgan CF63 2YL, UK2 Department of Physics, University of Surrey, Guildford, Surrey GU2 7XH, UK

There are important technological and scientific needs for accurate and precise measurements of the weightand thickness of silicone coatings, which are used in wide-ranging applications. X-ray fluorescence (XRF)spectroscopy offers one means of achieving such measurements. Here we show that, as predicted fromtheory, the intensity of the XRF intensity is linearly proportional to the thickness and weight of a relativelythin silicone coating on a poly(carbonate) substrate. This linear relationship is demonstrated using bothgravimetry and spectroscopic ellipsometry to provide two independent measurements of coating thickness,resulting in a robust method for the calibration of the XRF intensity. Copyright 2000 John Wiley & Sons,Ltd.

KEYWORDS: silicone; coatings; ellipsometry; thickness; x-ray fluorescence spectroscopy

INTRODUCTION

Polymer coatings and thin films are used in many indus-trial applications, including decorative paints, protectivecoatings, adhesives, semiconductor processing and elec-tronics packaging, to name only a few.1 In specializedapplications, such as in health and personal care prod-ucts, electronics, release coatings and pressure-sensitiveadhesives, coatings of polysiloxanes (commonly knownas silicones) are employed with thickness values rang-ing from a few nanometres to several micrometres. Asjust one specific example, silicone coatings that are justa few nanometres thick provide good biocompatibility2 tomedical devices, such as stents3 and catheters.4

Depending on the application, the substrate and thecoating process, the thickness generally varies from100 nm to 4µm, roughly corresponding to coat weightsof 0.1–4.0 g m�2 (as the density of silicone5 is¾0.97 g cm�3). In all of the applications mentioned above,the thickness or coat weight of the coatings has a directimpact on their performance and, of course, on their costcompetitiveness. As one example, in release coatings6

the amount of silicone applied to the surface of a papersubstrate will affect the coverage of the cellulose fibres,which, in turn, directly affects the release performanceof the silicone coating. If the coating is too thick, thenmaterial is wasted and it is less cost effective. Moreover,scientific studies of the mechanisms of release also needto consider the thickness of the silicone release coating,

* Correspondence to: J. L. Keddie, Department of Physics, Univer-sity of Surrey, Guildford, Surrey GU2 7XH, UK.E-mail: j.keddie@surrey.ac.uk

because the peel energy is related to it.7 There are thusclear commercial and scientific needs for accurate andprecise thickness measurements of silicone coatings. Theanalytical techniques used should additionally be fast,applicable to a variety of substrates and non-invasive.

A number of techniques currently exist that are capa-ble of determining the thickness of silicone coatings tovarying degrees of accuracy. These include Fourier trans-form infrared spectroscopy (FTIR), neutron activationanalysis (NAA), gas chromatographic functionality analy-sis (GCF), Rutherford backscattering spectrometry (RBS),atomic force microscopy, profilometry, microgravimetry,ellipsometry and x-ray fluorescence (XRF) spectroscopy.Here we report our use of the final three techniques, whichare attractive for reasons that will be outlined.

X-RAY FLUORESCENCE SPECTROSCOPY

X-ray fluorescence (XRF) spectroscopy is widely used8 – 10

to measure silicone coat weights ranging from 0.5 to1.5 g m�2. The technique uses a primary beam of x-rays that impinges onto a sample and ejects electronsof a given energy from the core electron shells of thetarget atoms. Electrons from higher energy levels fill thegaps, thus generating secondary x-ray photons that arecharacteristic of the element. In the case of elementalsilicon, Si K̨ radiation, which results from the decayof an electron from an L-shell to a K-shell, is emitted.The emitted radiation is detected to provide quantitativeinformation.11,12 X-ray fluorescence spectroscopy offersrapid and reliable elemental analysis for concentrationranges from parts per million to high percentage levels.

Copyright 2000 John Wiley & Sons, Ltd. Received 1 February 2000Revised 21 February 2000; Accepted 25 February 2000

342 B. PARBHOOET AL.

For a specimen of known and homogeneous composi-tion, the thickness of a layer,h, can be related to the XRFintensity from that layer,Ih, via a constantk

Ih/I1 D 1� e�kh .1/

where I1 is the fluorescent intensity of a sample ofthe same composition but with an effectively infinitethickness, andk is the product of material density (�) andthe mass absorption coefficient (�), which in turn dependson the angle of incidence of the primary radiation and onthe take-off angle of the fluorescent radiation.

In the case of thin samples, such thatkh < 0.1, Eqn (1)can be approximated as

Ih/I1 ³ kh .2/

which can be rewritten as

h ³ .Ih/I1//�� .3/

For a given material,� and � are constants, and soEqn (3) provides a means to relate fluorescence intensityto coating thickness. For the silicone of interest here,� is ¾0.97 g cm�3,5 and � is ¾59.7 cm2 g�1. In thethickness range of principal interest here (up to 4µm),kh is estimated to be�0.023, which thereby meets therequirements for the approximation in Eqn (2) (kh < 0.1).In fact, the value ofkh will not be close to 0.1 until thecoating thickness approaches 17µm.

Accurate determination of coating thickness via Eqn (3)requires accurate values ofI1, � and �. These areoften difficult to determine. Alternatively, if thickness isobtained by a complementary technique such as ellipsom-etry or microgravimetry in a series of calibration samples,then the fluorescence intensity can be related to film thick-ness, provided that there is a clear linear relationshipbetween the two. In this communication, we show thatsuch an approach can be used to calibrate the thicknessmeasurements of silicone coatings using data obtainedfrom XRF spectroscopy. Although gravimetry is less pre-cise than ellipsometry, it is still of importance to use, inorder to have an independent and direct measurement ofcoat weight and thickness, which provides a check on thevalues obtained via ellipsometry.

SPECTROSCOPIC ELLIPSOMETRY

Ellipsometry is an optical technique that provides a well-established means of determining film thickness, amongother unknown quantities, via the change in the state ofthe polarization of light that is reflected from a sam-ple. Its principles have been fully explained elsewhere.13

The application of ellipsometry to the analysis of poly-mer surfaces and interfaces14 has been reviewed recently.The accuracy and precision of ellipsometry have beenexamined for various materials by comparisons withother analyses using neutron reflectivity,15 quartz-crystalmicrobalance gravimetry16 and atomic force microscopy.17

Ellipsometry determines two parameters, and ,which are related to changes in the amplitude and rel-ative phase, respectively, of the s- and p-componentsof the polarized light.13 The two ellipsometry param-eters are defined in terms of the ratio of the Fresnel

reflection coefficients (Rp and Rs, corresponding to thetwo planes):Rp/Rs D tan exp.i/. In turn, the Fresnelcoefficients13,14,18 are functions of the optical constants ofthe materials, the film thicknesses and the interface rough-nesses that constitute the refractive index profile. In a fewsimple cases, an ellipsometry spectrum can be invertedto obtain directly the film thickness and optical constants.In situations with several unknown parameters, measure-ments are obtained by comparison of the experimentaldata to simulations based on an appropriate model. Var-ious computational procedures, outlined elsewhere,19 canbe used to obtain a best-fit model for the data.

EXPERIMENTAL

Sample design and selection

A primary objective of this work is to use three techniqueson a single set of samples. Whereas XRF and micro-gravimetry are somewhat flexible, ellipsometry sets cer-tain restrictions on the samples. For greatest reliability, thesubstrates should have a smooth, planar surface. The backsurface of a transparent substrate should be non-reflective.An isotropic substrate simplifies the analysis. The sensitiv-ity of the technique to surface coatings increases with anincreasing difference in refractive index between the coat-ing and the substrate. To meet the various requirements,we use poly(carbonate) substrates that have a smooth topsurface and a roughened back surface. At a wavelengthof 500 nm, our preliminary measurements found that therefractive index of poly(carbonate) (1.60) is significantlygreater than that of the silicone coating (1.42). A coronadischarge treatment of the poly(carbonate) surface (usingan energy density of 5.7 kJ m�2) imparted greater adhe-sion of the silicone. Poly(carbonate) substrate containedsome silicon-based additive and resulted in a constantXRF background signal adding to the XRF fluorescenceof the silicone coating.

Sample preparation

Silicone coatings were deposited onto polycarbonate sub-strates by spin deposition. A silicone system capable of pro-ducing isotropic coatings by spin deposition was thereforerequired. Dimethylhydroxysilyl-terminated polydimethylsiloxane (HO(CH3/2SiO� [.CH3/2SiO]n � .CH3/2SiOH,with n having an average value of 4000) was dissolvedin 1,1,1,3,3,3-hexamethyldisiloxane in a blender to pre-pare a 10 wt.% solution. This solution was mixed witha crosslinker/organotin catalyst system in a 50 : 1 weightratio. The crosslinker was methyltriacetoxysilane. Allchemicals used were produced by Dow Corning. The finalformulation was deposited onto round poly(carbonate) sub-strates (35 mm diameter) via spin-coating at 8000 rpm.Substrates for ellipsometry were 0.5 mm thick, ensuringthat they remained planar after the coating deposition andduring analysis. Substrates for gravimetry analysis were0.1 mm thick, providing a low mass and decreasing therelative error in measurements. The solution was dilutedwith additional solvent to deposit thinner films. The sil-icone was cured at room temperature for 24 h. Coatingsof 15 different thicknesses were prepared for ellipsometryand XRF analysis.

Surf. Interface Anal. 29, 341–345 (2000) Copyright 2000 John Wiley & Sons, Ltd.

CALIBRATION STANDARDS FOR SILICONE COAT THICKNESS 343

Analytical techniques

An analytical balance (Model I200D, Sartorius, Epsom,UK) that is capable of reading to the nearest 10�5 g wasused for gravimetry. Four measurements of each samplewere made beforeand after the coating deposition. Thick-ness values were obtained5 from the mass measurementsby assuming a uniform silicone density of 0.97 g cm�3.

X-ray fluorescence spectroscopy was performed undera helium atmosphere using the automated procedure of acommercial instrument (Lab-X 3000, Oxford Instruments,Abingdon, UK); Si K̨ radiation was detected. Variable-angle spectroscopic ellipsometry was performed usingan instrument with a rotating analyser configuration20

(VASETM, J. A. Woollam Co., Inc., Lincoln, NE, USA).Data were simulated via the equations that define theFresnel coefficients, as given elsewhere.13,19 A Leven-berg–Marquardt algorithm21 was used in the data analysisto minimize the error between the simulated and exper-imental data. The algorithm found the thickness valuecorresponding to the minimum value of mean-squarederror (MSE), which is defined22 as

MSED 1

2N�MN∑iD1

[( simi � exp

i

� ,i

)2

C(simi �exp

i

�,i

)2].4/

whereN is the number of (,) pairs,M is the numberof variable parameters used in the model,� is the standarddeviation on the experimental data points and the super-scripts ‘sim’ and ‘exp’ refer to simulated and experimentaldata, respectively.

RESULTS AND DISCUSSION

The optical constants of the substrate were determinedindependently by ellipsometric analysis of the bare poly(carbonate) surface. The real part of the refractive index,n, as a function of the wavelength of light,�, wasdescribed using the Cauchy equation

n.�/ D AC B

�2.5/

where � is expressed in micrometres and A (unitless)and B (µm2) are constants. (Note that higher order termsare neglected here.) For the poly(carbonate) substrates,A was determined to be 1.559 and B is 0.0101 µm2.By analysis of the entire series of samples, the best-fitCauchy parameters for the silicone were determined tobe A D 1.400 and BD 0.0044. This analysis inherentlyassumes that the density and chemical composition of thecoatings do not vary significantly with varying thickness.Past experience and investigation support this assumption.Thus, during the best-fit analysis of the data, only thecoating thickness was used as a fitting parameter.

The reproducibility of ellipsometry measurements onthe same sample was very good. The uncertainty on a sin-gle measurement of a coating of the order of 600 nm thickis š1.0 nm. Four measurements at different positions butin the same region of the sample varied by¾7 nm, whichreflects some non-uniformity in film thickness. The repro-ducibility of XRF intensity readings is excellent. Four

independent XRF measurements on each of four samplesof varying thickness obtained very good reproducibilitywith a standard deviation of<54 counts s�1 in each ofthe samples. This corresponds to<1.0% relative error.

Microgravimetry measurements had greater uncertaintyas a result of the low weight of the coating relative to thesubstrate, especially in the thinnest coatings. The standarddeviation of the mass measurements is typicallyš140 µgor less. Although the absolute value of this deviation issmall in absolute terms, it corresponds to relative errorsof >100% in the thinnest coatings. Despite this poorprecision, microgravimetry is accurate provided that thebalance has been correctly calibrated, and so it is still agood complementary technique. Moreover, it is a directtechnique to check the values obtained via ellipsometry,which is an indirect technique.

Figure 1 shows typical ellipsometry spectra, and,obtained at three angles of incidence and with wavelengthsbetween 350 and 750 nm from a silicone coating onthe poly(carbonate) substrate. Simulated spectra, whichuse the Cauchy parameters (as given previously) in aslab model (air/coating/substrate), are also shown. Thesimulated spectra are the best-fit to the experimental dataas obtained via the iteration of film thickness. Thereis good agreement between the two types of spectra,indicated by an MSE value of 3.8.

Ellipsometry analysis revealed that the film thicknessvaried laterally across a coating. The spin-coating tech-nique is prone to depositing films that vary in thicknessradially. In these samples, according to ellipsometry anal-ysis, the centre region (within about a 0.5 cm diameter)tended to be different in thickness in comparison to therest of the coating, typically by¾5% or less. Both XRFand gravimetry analysis probe the entire coating area to

Figure 1. Ellipsometry spectra obtained from a silicone coatingon poly(carbonate) at three angles of incidence: (ž) 55°; (M) 60°;(�) 65°. The best-fit to the data (shown as the solid lines) isbased on a coating thickness of 647.5 nm.

Copyright 2000 John Wiley & Sons, Ltd. Surf. Interface Anal. 29, 341–345 (2000)

344 B. PARBHOOET AL.

yield an average thickness. Ellipsometry, on the otherhand, averages over the area of the light beam’s ‘footprint,’ which is¾8 mm2 in this case.

In some cases, the quality of the fit to the ellipsom-etry data, as indicated by the MSE, could be improvedby incorporating thickness non-uniformity22 into the orig-inal slab model. In this case, the simulation takes intoaccount variations in film thickness across the area ofthe probing light beam by considering the partial polar-ization that results from probing films of varying thick-ness. The non-uniformity typically corresponded to a 5%local deviation from the average film thickness. When asignificant improvement was found, this non-uniformitymodel was used. The two models (i.e. with and withoutnon-uniformity) resulted in comparable values of coat-ing thickness. As an example, the assumption of a non-uniform film for a 600 nm thick coating increased thevalue of the best-fit thickness by¾2 nm.

If Eqn (3) holds, the thicknessh (expressed in nanome-tres and obtained by either ellipsometry or microgravime-try) can be related to the fluorescence intensity (Ih) by anequation of the form

h D mIh C b .6/

wherem andb are the best-fit constants. Figure 2 showsthe correlation between the intensity from XRF spec-troscopy and the thickness as determined by gravimetry.As indicated by the error bars, thickness is determinedwith low precision using gravimetry. Nevertheless, a lin-ear relationship can be observed within the error of the

Figure 2. Film thickness determined by gravimetry () and byvariable-angle spectroscopic ellipsometry (ž) in comparison tothe Si K˛ XRF intensity (given as counts s�1) for a series ofsilicone coatings on poly(carbonate) substrates. The error bars(representing two standard deviations) on the thickness valuesare shown (although they are the same size as the symbolsfor the ellipsometry data). The dashed line is the best-fit linearrelationship for the gravimetric data; the solid line is the fit tothe ellipsometry data.

Table 1. Constantsobtained fr om the best-fit analysisof thecorrelation betweenXRF intensity and thickness

Value from ellipsometry Value from gravimetryConstant (standard deviation) (standard deviation)

m (nmÐs count�1) 0.0904 (0.0014) 0.0936 (0.0041)b (nm) �97.10 (14.06) �66.31 (23.13)

measurements.Table1 lists thevaluesobtainedfor m andb from the best-fit to the data in Fig. 2 along with theiruncertainty,asdeterminedfrom thestandarddeviationonthe fit to the data.

Figure 2 additionally shows the correlation betweenthe thicknessof the coatingsdeterminedby ellipsometryand the XRF intensity. As with the gravimetric data,there is a clear linear relationship.The uncertaintyonthicknessvaluesin thecaseof ellipsometryis significantlylower. The best-fit constantsdeterminedfrom the datain Fig. 2 are listed in Table 1. Within the limits ofuncertainty,the valuesof m andb determinedby the twotechniques(gravimetry and ellipsometry) are the same.Thetwo techniquesarethusconsistentwith eachotherandprovidean independentcheckon the correlationbetweenthicknessand XRF intensity. Owing to its much greaterprecisionandsimplicity of use,however,ellipsometryisthe more preferableof the two techniquesfor thicknessmeasurement.

The linearity betweencoating thicknessh and Ih, aspredictedin Eqn (3), holdsover the rangeof thicknessesexamined.More importantly, Eqn (6) (with appropriatevalues of the constantsas in Table 1) can be used toprovide a calibration to obtain the coating thickness(inthe range between0 and 2000 nm) from analysis byXRF spectroscopy.Various usersof XRF spectroscopyaroundthe world havedevisedstandardsand techniquesfor calibration. However, to the best of our knowledgethereare no publishedreportsof a thoroughcalibrationusingtwo independentandcomplementarytechniques,aspresentedhere.

CONCLUSIONS

Variable-anglespectroscopicellipsometryandmicrogravi-metry are in close agreementin the measurementofsilicone coating thicknesson poly(carbonate)substrates.Ellipsometry is much more precisethan gravimetry,butthe latter provides a direct measurementthat servesasan independentcheckon ellipsometry.Over the thicknessrangestudied(0–2000 nm) thereis a good linear corre-lation betweenthicknessvaluesandXRF intensity.X-rayfluorescencespectroscopy,whencalibratedusinga seriesof standardsas shownhere,is thereforean accurateandprecisewayto measuresiliconecoatweightandthickness.

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Copyright 2000 John Wiley & Sons, Ltd. Surf. Interface Anal. 29, 341–345 (2000)