Surface Film Thickness Determinationby Reflectance MeasurementsD. T. Larson, L. A. Lott, and D. L. Cash

The thicknesses of U0 2 films from 100 A to 1800 A on uranium substrates were determined from reflec-tance measurements in the visible region. The reflectance measurements on the U-UO2 system wereanalyzed by two different methods to determine film thicknesses. In the first method, film thicknesseswere determined by comparing theoretical reflectance calculations with the experimental reflectancemeasurements. In the second method, film thicknesses were determined by obtaining the best match ofthe clorimetric properties (wavelength, excitation purity, and luminous reflectance) of the sample withthe colorimetric properties of a predetermined film thickness calibration curve.

Introduction

In manufacturing processes involving chemicallyreactive metals, the condition of the metal surface isoften critical at certain stages of the process. Forexample, surface films produced by the atmosphericoxidation or contamination by lubricants or chemi-cals can cause difficulties in subsequent welding orbrazing operations or can in themselves be unaccept-able for the ultimate application of the component.Thus, a quantitative technique would be useful forcertifying the condition of a metal surface.

One way of accomplishing this is by obtaining thereflectance spectrum (fraction of incident light re-flected by the surface as a function of wavelength),as the spectral reflectance of a metal is affectedstrongly by the presence of surface films. This paperdescribes two methods of determining the surfacelayer thickness from the reflectance spectrum in thevisible wavelength region.

Thickness Determination Methods

Method of Comparing Theoretical and ExperimentalReflectance Values

In this approach, theoretical reflectance calcula-tions are utilized to determine film thickness bycomparison with experimental normal incidence re-flectance data.

For the simplified case of normal incidence, the re-flection coefficient of a single absorbing film on anabsorbing substrate is. given by", 2

= Irl exp(ib) = [ 12 + r23 exp( - i)]/[1 + 12i23 exp( -i)

The authors are with Dow Chemical U.S.A., Rocky Flats Divi-sion, Golden, Colorado 80401.

Received 22 September 1972.

with the reflectance, R, given by R = IJr2 . Here P12and P23 are the Fresnel reflection coefficients for theair-film and film-substrate interfaces, respectively:

r12 = 2- nl)/(h 2 + n1) and r23 = (03 - f 2)/(n3 + h2).

The quantity A is given by A = 4ir 2 d/X.In these expressions:

X = the vacuum wavelength of the light;d = the film thickness;ni = the refractive index of the surrounding medium (n = 1);fl2 = n2 - k2i, the complex refractive index of the film;.l3 = n3 - k3i, the complex refractive index of the substrate; andi = (-1)1/2.

The film thickness is determined by finding thefilm thickness, d, which minimizes the least squaresexpression

(Rexp - RXdcalc,)2

Here Rexp is the experimental reflectance at a spe-cific wavelength, and RXdcaic is the theoretical re-flectance at a specific wavelength and thickness. Itshould be noted that it is necessary to know the opti-cal constants of the film and substrate to use thismethod. In this work, these were found for the ma-terial studied by ellipsometric measurements.

Color Analysis MethodChanges in color are observed with the growth of a

film on a metal surface. The colors are caused byinterference between light reflected at the air-filmand film-metal interfaces and have been used to ob-serve film formation on metals.3 This phenomenonsuggests that the experimental reflectance spectra besubjected to a color analysis to obtain a calibrationcurve of color parameters vs film thickness. Thiscalibration curve can then be used to determinethickness from the color parameters of unknownsamples.

June 1973 / Vol. 12, No. 6 / APPLIED OPTICS 1271

The properties selected to define the colors of thesamples in this study are luminous reflectance,wavelength, and excitation purity. The propertieswere determined for type C illumination, which rep-resents average daylight.4

The method used to calculate these color proper-ties from the reflectance spectrum was to calculatethe tristimulus values using the selected ordinatemethod. 5 The tristimulus values are given by

X = P X p, A dX I PxdA,

Y X 3Ppd?/ fYxPdA,

Here X, y'x, and 2xare the tristimulus values of thespectrum adopted by the International Commissionon Illumination; Pie is the spectral distribution of theruminating light source; px is the reflectance with Xrepresenting the wavelength. The tristimulus valueY is the luminous reflectance. Chromaticity coordi-nates x and y are related to the tristimulus values byx =X/(X+ Y+Z)andy = Y/(X+ Y+Z). Thusby using the chromaticity diagram, the excitationpurity (saturation) and wavelength (hue) are deter-mined.

By calculating the color parameters for sampleswith known film thicknesses varying over the thick-ness range of interest, calibration curves are pre-pared. The surface film thickness of an unknownsample is then obtained from its reflectance data byfirst calculating the three color properties. Then thebest match to the calibration curves is determinedby finding the film thickness, d, which minimizes theerror given by

E = (XP - ydcal)2 + (pexp - pdal) 2

and satisfies the criterion that the wavelength regionof the calibration curve at that film thickness agreeswith the wavelength determined for the sample ofunknown thickness.

In this expression,

YexP = luminous reflectance determined from experimental reflec-tance data,

ydcal = luminous reflectance obtained from calibration curve atspecific film thickness,

pexP = excitation purity determined from experimental reflectancedata, and

pdcal = excitation purity obrained from calibration curve atspecific film thickness.

Experimental Methods

The U-UO2 system was studied to demonstratethe thickness determination methods. Polished ura-nium metal coupons were slowly oxidized by heating

them in air at approximately 100'C. The oxide filmformed under these conditions was verified by x-raydiffraction analysis to be U0 2. As the samples oxi-dized, concurrent ellipsometric measurements andreflectance measurements in the wavelength range425 m/i to 650 mg were taken.

The reflectance measurements were made with asystem consisting of a bifurcated fiber optics, reflec-tance probe and a visible-near infrared spectropho-tometer.6 The measurements were made relative toan evaporated aluminum front surface mirror stan-dard.

Film thicknesses used for comparison purposesand to prepare the calibration curve were deter-mined using ellipsometry. The wavelength of lightused was 546.1 mg, and the angle of incidence was70.000. The ellipsometric measurements were usedto calculate film thicknesses directly using the meth-od of McCrackin and Colson.7 To make these cal-culations, the refractive indices of the film and sub-

OR

Lij

KR

KLij

Wi

/800 I I I I I I I I

/700-

/600 . */500 0 *

/400 . 00

/300 .

00*

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900 800_700 -

600-0

500_

40'0

300_

200 -

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0 1 1 , 1 , 1 -

200 600 /000 /400ELL/PSOMETRIC TCKNESS (R)

/800

Fig. 1. Film thickness determined by comparison of experimen-tal reflectance with theoretical reflectance calculations vs ellipso-

metric thickness.

1272 APPLIED OPTICS / Vol. 12, No. 6 / June 1973

strate must be known. The refractive index of ura-nium at 546.1 mg was previously determined 8 to be2.79-4.04i. This value is for a clean uranium surfacein which the oxide film was removed by argon ionbombardment. The refractive index of the U0 2 film(2.2-0.44i) was determined by standard ellipsometrictechniques from experimental ellipsometric measure-ments taken periodically as the uranium sample oxi-dized. 7

Results

Comparison of Theoretical and ExperimentalReflectance Values

The indices of refraction of the substrate and filmdetermined ellipsometrically at 546.1 mAt were usedover the entire wavelength region from 425 mg to 650mgt. Since there is little variation of the optical con-stants of U0 2 over this small wavelength range,9 theuse of the optical constants at 546.1 mgu for the re-flectance calculations would have little effect on theresults.

The reflectance data were analyzed over the thick-ness range 0-1800 A in 10-A increments. These re-sults compared with the absolute (ellipsometric)thicknesses are shown in Fig. 1. The results are in

wave/ensA/

570-6/0rmr . 1450 -500n0.6

0.5-C

k 0.4 1* .

C~~~~~

L0.3 _ to. \

i0.2 I°4

close agreement with the absolute thicknesses exceptin the regions around 300 A and 1300 A. This is at-tributed to the fact that the reflectance curves forfilms in these two thickness regions are very similar,and thus it is difficult to deduce the correct thick-ness from the reflectance curve.

Color Analysis Method

With the oxidation conditions used, uranium wasfound to oxidize by the following color sequence:silver, yellow, red brown, violet, blue, second ordersilver, second order yellow, and gray. The wave-length, excitation purity, and luminous reflectanceas a function of the thickness determined ellipsome-trically are shown in Fig. 2. The data are for the ox-idation of three samples. The chromaticity wave-lengths as a function of thickness are represented byfour regions. The two regions at 570-610 m and450-500 m/i are for yellow-orange and blue colors,respectively. The region indicated by a 1 in the fig-ure includes the wavelengths rotated on the chroma-ticity diagram from 610 myt through the complemen-tary wavelengths to 450 mAi. This is the transitionzone where the color of the sample changes from theyellow-orange region to blue. The region shown by

800 /0007//CKNESS (R)

/800

Fig. 2. Wavelength, excitation purity, and luminous reflectance as a function of ellipsometric thicknessfor U-UO 2 system. The wavelengths are represented by four regions. Region indicated by 1: domi-nant wavelengths 610-780 m; complementary wavelengths 4 9 3 c-5 6 7 c m and dominant wavelengths

380-450 m. Region indicated by 2 is for dominant wavelengths from 500 m to 570 mg.

June 1973 / Vol. 12, No. 6 / APPLIED OPTICS 1273

/000 900 -

800-

7 700-

3 600.kIZ 500-

400-300

200

/000 /...,.,.,.,.,.I.,.

400 800 /200 /600ELL/PSOMETR/C THICKNESS )

Fig. 3. Film thickness determined by color analysis method vsellipsometric thickness.

a 2 in Fig. 2 is for the wavelengths from 500 m to570 mgi, and it is the transition region where thesample changes from blue to the yellow-orangerange.

As stated before, the colorimetric properties as afunction of thickness provide a method to determinefilm thickness from a sample's reflectance measure-ments. Once a calibration curve of the colorimetricproperties as a function of thickness is obtained, thefilm thickness can be determined from its reflectancespectrum. The experimentally determined wave-length, excitation purity, and luminous reflectance ofthe specimen are matched with the calibration curveto determine film thickness. The reflectance datawere analyzed in this manner using calibrationpoints from 0 A to 1800 A in 10-A increments. Theresults compared with the absolute (ellipsometric)thicknesses are shown in Fig. 3.

The discrepancies in film thicknesses occur in thesame thickness regions as the previous thickness de-terminations that utilized theoretical reflectance cal-culations. As mentioned, this ambiguity arises dueto the similarity of the reflectance curves of the firstand second order yellow. By examining the calibra-tion curves (Fig. 2), it is noted that calorimetric databetween film thicknesses of approximately 250 A and350 A are similar to calorimetric data between filmthicknesses of 1100 A to 1500 A. Thus, in these re-gions thickness determinations from reflectancemeasurements in the wavelength range 425-650 mptare ambiguous.

This ambiguity can be removed by extending thereflectance measurements to the near infrared. Fig-ure 4 shows the reflectance spectra of uranium withfilm thicknesses of 284 A and 1274 A. The reflec-tance curves are very similar between 425 m,4 and650 mgi with a marked difference in the near in-frared.

Conclusions

Spectral reflectance measurements were used todetermine surface film thicknesses by two differentmethods. In the first method, film thicknesses aredetermined by comparing theoretical reflectancecalculations with experimental reflectance measure-ments. The second method utilizes the phenomenonof interference colors caused by thin films on a metalsurface. The reflectance measurements are used todetermine the calorimetric properties (wavelength,excitation purity, and luminous reflectance). Bycomparing the colorimetric measurements of a sam-ple with a predetermined calibration curve of thecolorimetric properties as a function of thickness, thethickness of the sample can be determined. In bothmethods, confusion can result from the similarity ofthe visible reflectance spectrum between first andsecond order colors. This ambiguity can be resolvedby taking reflectance measurements in the near in-frared.

To use these methods, the type of film-metal sur-face system must be known. The first method re-quires a knowledge of the refractive indices of themetal substrate and film, while in the second meth-od it is necessary to make independent thicknessmeasurements to prepare the calorimetric calibrationcurves. The second method offers the advantagethat the calibration curves for the metal-film systemare prepared using similar preparation and environ-mental conditions to those the metal will experience.Thus, if the theoretical reflectance equation for thin

1274 APPLIED OPTICS / Vol. 12, No. 6 / June 1973

I I1 I I1 I TT

400 600 800 /000 /00 /400 /600WAVELENGTH (mg)

Fig. 4. Reflectance spectra for U0 2 films on uranium substrates.

actual metal-film system,

The authors wish to express their appreciation toG. D. Lassahn for developing the equations and pre-paring the, computer program for the theoretical re-flectance calculations. This work was performedunder the auspices of the U.S. Atomic Energy Com-mission contract AT(29-1)-1106.

References

1. 0. S. Heavens, Optical Properties of Thin Solid Films (Dover,New York, 1965).

2. E. P. Lavin, Specular Reflection (American Elsevier, NewYork, 1971).

3. U. R. Evans, The Corrosion and Oxidation of Metals (EdwardArnold, London 1961), pp. 20, 54, 85, and 787.

4. See for example,OSA Committee on Colorimetry, The Scienceof Color (Washington, D.C., 1963), Chaps. 7 and 8.

5. OSA Committee on Colorimetry, The Science of Color, (Wash-ington, D.C,, 1963), p. 270.

6. L. A. Lott and D. L. Cash, Appl. Opt. 12, 837 (1973).7. F. L. McCrackin and J. P. Colson in Ellipsometry in the Mea-

surement of Surfaces and Thin Films, E. Passaglia, R. R.Stromberg, and J. Kruger, Eds., NBS Misc. Publ. 256 (U.S.Govt. Printing Office, Washington, D.C., 1964), p. 61.

8. D. T. Larson, J. Vac. Sci. Technol. 8, 80 (1971).9. P. Camagni, A. Manara, and E. Landais, Surface Sci. 10, 332

(1968).

June 1973 / Vol. 12, No. 6 / APPLIED OPTICS 1275

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films fails to describe themethod two will still work.

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