Effects of phase changes on reflection andtheir wavelength dependence in optical profilometry

Takuma Doi, Kouji Toyoda, and Yoshihisa Tanimura

The method as well as an appropriate instrumentation for measuring phase changes of reflected light isdescribed. The phase changes on samples of Au, Al, Ag, and Cr evaporated films are measured for fivewavelengths ~l! from 442 to 633 nm, with respect to the phase change at the glass–air interface, whereit should be zero. The measured results for the Au film are in fairly good agreement with valuescalculated by use of optical constants from a handbook or the complex refractive index measured by anellipsometer. The phase changes for Al and Ag films are different from calculated values by ;5° or ashift length of 4.4 nm at l 5 633 nm, while those of the Cr film show large shifts as high as 16° or a shiftlength of 9.8 nm at l 5 442 nm. © 1997 Optical Society of America

Key words: Phase change, surface profilometry, phase-shifting interferometer.

1. Introduction

Advances in manufacturing integrated circuits andhigh-quality optical components in the visible andx-ray regions require very precise measurements oftheir surface fine structures and film thickness. Op-tical methods are useful and provide powerful toolsfor such measurements because they are noncontactand nondestructive methods with a high sensitivityand a resolution of less than 1 nm.1,2 In accuratedimensional metrology with an interferometer, theeffect of the phase change of reflected light from thesurface or from the interface between two mediashould be considered. For instance, if the surface ofthe sample is composed of different materials, thephase changes on reflection vary over the surfaceeven if the surface is flat. Because the surface of thesample has a distribution in a complex refractive in-dex, the difference of phase change gives rise to mea-surement errors of several tens of nanometers.3–6

Even though the sample has a constant complex re-fractive index, the wavelength dependence of thephase change must be estimated when white lightinterferometry is used for surface profilometry, suchas multiple-beam fringes of an equal-chromatic-ordersystem.7 So far only the phase changes in reflection

The authors are with the National Research Laboratory of Me-trorology, 1-1-4 Umezono, Tsukuba, Ibaraki 305, Japan.

Received 4 September 1996; revised manuscript received 4 Feb-ruary 1997.

0003-6935y97y287157-05$10.00y0© 1997 Optical Society of America

from semitransparent films have been measured,8and its method requires special instrumentation andsample preparation.

This paper describes the method, instrument, andsample preparation that enable us to measure thephase changes of light reflected from not only semi-transparent films but also bulk materials. Our ex-periments are carried out by using a conventionalmicroscope interferometer, and the effects of phasechanges in surface profilometry can be estimated di-rectly. The phase changes of light reflected fromgold ~Au!, aluminum ~Al!, silver ~Ag!, and chromium~Cr! evaporated films and their wavelength depen-dence are measured with respect to the glass–air in-terface, where the phase change is zero. We choosethese four metals because they are often used to coatoptical components and are thus important in manyapplications. Au is chosen as an almost ideal mate-rial that shows a complex refractive index similar tohandbook data and has been well estimated.5,8 Cr ischosen as an easily contaminated material whosecomplex refractive index easily varies with the con-dition of sample preparation.5,6 The measured re-sults are compared with values calculated fromoptical constants in handbooks.9,10 Furthermore,the implications of the phase change for surface me-trology and applications of the wavelength depen-dence of phase change to evaluation of the surfaceproperties are discussed.

2. Theory of Phase Change

When light is specularly reflected at an interface be-tween two dielectric media having refractive indices

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n0 and n1 as shown in Fig. 1~a!, an amplitude reflec-tance r is expressed using Fresnel’s equation by8

r 5 EryEi 5 2~n1 2 n0!y~n1 1 n0!. (1)

In this equation Ei and Er represent the electric fieldof the incident light and the reflected light, respec-tively. If n0 is smaller than n1, r becomes negativeso that the phase change of reflected light is p. Onthe other hand, if n0 is greater than n1, r becomespositive, and the resulting phase change of reflectedlight is zero. If the incident medium is a dielectric~or air! of refractive index n0 and the emergent me-dium is a measured sample that has a complex re-fractive index ~n1 2 ik1!, the complex amplitudereflectance r at the interface is obtained by substitut-ing ~n1 2 ik1! into n1 of Eq. ~1!. Thus r is given by

r 5 @n02 2 ~n1

2 1 k12! 1 2in0k1#y@~n0 1 n1!

2 1 k12#

5 a 1 ib. (2)

Figure 1~b! shows the relation between the electricvectors of the incident light and the reflected light ina complex plane when the electric vector of the inci-dent light ~Ei! is along the positive real axis. In Fig.1~b! the phase change of reflected light is measured inthe counterclockwise direction from the positive realaxis.

When the light impinges onto a sample surfacefrom air ~n0 5 1!,~n1

2 1 k12! . n0

2. This means thata , 0 and b ^ 0 and that Er must lie in the secondquadrant. Therefore the phase change between theincident and the reflected lights is given by

b 5 p 2 r, (3)

r 5 tan21@2n0k1y~n12 1 k1

2 2 n02!#,

0 % r % py2. (4)

Since the phase change b varies depending on thecomplex refractive index, the difference of phasechanges on the sample surface leads to an error in themeasurement of surface fine structure by optical in-terferometry. It can be considered that the reflec-tion point of the light penetrates from the geometricalsurface to the inside of the substrate by

r9y2 5 l ry4p, (5)

Fig. 1. ~a! Reflection of light at normal incidence on a boundarybetween two media. ~b! Definition of the phase change of light.

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where l is the wavelength of light. The value of rcalculated by Eq. ~4! is often treated as a phasechange.4–6 In this paper b 5 p 2 r is treated as aphase change of reflected light.

3. Sample Preparation for Measuring Phase Changes

Figure 2 shows a cross section of a sample that isfabricated to allow us to measure the phase change onreflection at the glass–Au interface. On a face ofparallel flat glass plate, Au is evaporated in line pat-terns by use of a mask with line and space patterns of100 mm in width. The evaporated Au film with athickness greater than 0.3 mm is thick enough to beregarded as having the same optical properties asthat of a Au substrate. The roughness of the paral-lel flat glass plate is smaller than ly4 in the area of20 3 20 mm. The measured area ~0.65 3 0.65 mm!is so small that the glass plate around one of Au linepatterns can be considered flat.

The phase change of reflected light from the inter-face in Fig. 2 is measured by a microscope interferom-eter. The phase change of reflected light is zero atthe glass–air interface, since the refractive index ofthe incident medium ~glass, n0 5 1.515! is greaterthan that of the reflected medium ~air, n1 5 1!. Ac-cordingly we can measure the phase change at theglass–Au interface with respect to the glass–air in-terface. To reduce error signals that are due to un-desirable reflection from the glass surface andmultiple reflections inside the parallel glass plate,the opposite surface of the parallel glass plate iscoated with an antireflection film with a reflectivitybelow 0.7% for visible light.

4. Instrument for Measuring Phase Changes

Figure 3 shows a schematic diagram of the instru-ment used to measure the phase change of reflectedlight from the sample. The Linnik-type microscopeinterferometer11 is widely used for measuring surfacefine structures. The principle of this interferometeris the same as the Twyman–Green interferometer,which makes interference fringes from the superim-position of two wave fronts reflected by a referenceand a test surface. To observe the fine structure onthe test surface, the observation point in the infini-tesimal area must be magnified by an objective lens.To compensate for the aberration caused by the ob-jective lens, the reference beam is also focused on thereference surface by the identical objective lens.The Linnik-type microscope interferometer has alonger working distance for a given objective lens

Fig. 2. Cross section of the sample used to measure the phasechange of light on reflection from Au film.

compared with microscope interferometers such asthe Michelson and Mirau types. In practice this issuitable for our experiments because the measure-ment beam must be focused onto the back surface ofa parallel flat glass plate with a thickness of 1 mm.

Spatially and temporally incoherent light radiatedfrom the tungsten ~w! lamp source is collimated by acondenser lens. The wavelength of the light is se-lected by the bandpass filter with full width at half-maximum of 10 nm. The collimated beam is dividedinto the reference and measurement beams by abeam splitter, and these beams are focused, respec-tively, on the sample and the reference mirror by amicroscope objective ~103, N.A. 5 0.2!. To adjustthe two optical pass lengths for the reference andmeasurement beams at the same value, the identicalparallel flat glass plate with the sample is used as thereference mirror. The Cr film is evaporated on thereference interface to make a reflectance of 15%.The optical wedge shown in Fig. 3 is inserted to ad-just the optical path length of the reference beam.The light beams reflected at the sample and the ref-erence mirror are mixed through the beam splitterand fed to a charge coupled device ~CCD! detectorarray ~512 3 512 pixels!. The interference image isobserved by the CCD detector array, and the inten-sity of the interference signal is digitized to an 8-bitsignal and stored in the digital frame memory.

The phase changes of light reflected from the sam-ple are measured by a phase-shifting technique.12

We can change the phase difference between the ref-erence and measurement beams in four steps of 0,py2, p, and 3py2 by means of a piezoelectric trans-ducer ~PI Polytec, P267! attached to the referencemirror. If f is the original phase difference betweenthe measurement and reference beams and I1, I2, I3,and I4 are the intensities corresponding to additionalphase shifts of 0, py2, p, and 3py2, respectively, theoriginal phase difference f is given by12

f 5 tan21~I4 2 I2!y~I1 2 I3!. (6)

By distinguishing the signs of the denominator andthe numerator in the arctangent term, f can be cal-culated from 2p to p. To measure the precise f, thereference mirror must be displaced in steps of ly8.

Fig. 3. Schematic diagram of the microscope interferometer usedfor measuring the phase change of reflected light.

The displacement is controlled by the closed loop byuse of the displacement signal measured by a straingauge incorporated into the piezoelectric transducer.The control signal corresponding to the displacementof ly2 is calibrated so that two kinds of interferencepatterns are superposed before and after the inter-ference pattern is shifted by one fringe. A micro-computer controls image acquisition and mirrorscanning simultaneously and automatically calcu-lates phase changes. To estimate the performanceof the instrument, we differentiate Eq. ~5! as follows:

D~r9y2! 5 l~Dry4p! 1 Dl~ry4p!. (7)

Assuming that the spectral width of light used at l 5560 nm is Dl 5 10 nm and that the minimum readingfor the phase change is Dr 5 1° at r 5 60°, theuncertainty of measurement in a shift length is ob-tained as 1.6 nm from Eq. ~7!.

5. Results and Discussion

First we tested the phase changes of light reflected atthe glass–air interface, where it should be zero. Inpractice the values were scattered within 8° for themeasurement distance of 650 mm as shown in Fig. 4.This is due to the surface roughness of the parallelflat glass, and the phase change of 8° is equivalent toa shift length of ;7 nm from Eq. ~5!. The fluctuationof the phase changes is negligibly small in the rangeof ;30 mm. Therefore we conclude that the glass–air interface is a valid reference for measuring thephase changes of the light reflected from the glass–metal interface. Figure 5~a! shows the photographof interference fringes in the area of Au line patterns,which is illuminated by quasi-monochromatic light atl 5 633 nm. Within the field of view in the micro-scope interferometer, adjusting the inclinations of thereference mirror makes the interference fringes per-pendicular to the line patterns. The interferencefringes shift by an amount corresponding to a valuegreater than a quarter of a fringe. It is obvious thatthe phase change of reflection on the glass–metalinterface is b 5 p 2 r instead of r as expressed by Eq.~4!.

By changing the bandpass filter with a center spec-trum of 633, 589, 532, 488, and 442 nm, we measurethe wavelength dependence of phase change. Fig-ure 5~b! shows the results measured along the lineindicated by arrows in Fig. 5~a!. In this figure, r 5p 2 b is shown instead of the phase change ~b! toemphasize the difference of the phase changes amongfive wavelengths. Spikes, like noises, inevitably ap-

Fig. 4. Phase distribution of reflected light on the glass platemeasured by microscope interferometer.

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pear at both edges of the Au line patterns, becausepixels of the CCD arrays detect simultaneously bothreflected lights from the Au and glass lines. There-fore 10% of the line width is rejected from both edgesand the difference between the average of phasechanges of the Au and the glass lines is accepted as themeasurement result. The phase change at theglass–Au interface is the mean value of phase changesfor six Au lines at a specific wavelength. The similarsamples for the Al, Ag, and Cr films were measured inthe same way. In Fig. 6 the measured phase changesfor five wavelengths of light are depicted by symbols ~E,Au; ‚, Al; h, Ag; ƒ, Cr!, and the wavelength dependenceof phase changes for each metal are calculated withoptical constants from handbooks.9,10 The averageand the maximum standard deviations of values mea-sured for each wavelength and sample are 2.5° and 5°,respectively. If the phase changes are converted toshift lengths given by Eq. ~5!, the average and themaximum standard deviations calculated in the abovesame way are 2 and 3.4 nm, respectively. The mea-sured phase changes for the Au film are in fairly good

Fig. 5. ~a! Interference fringe pattern produced by microscopeinterferometer. The shift lengths of the fringes correspond to thephase change of reflected light ~b 5 p 2 r! from Au. ~b! Measuredphase changes of reflected light from Au at wavelengths of 633,589, 532, 488, and 442 nm. r 5 p 2 b is shown instead of thephase change ~b! to emphasize the difference in the phase changeamong five wavelengths.

7160 APPLIED OPTICS y Vol. 36, No. 28 y 1 October 1997

agreement with calculated values and show the ab-sorption edge near 500 nm. The measured and cal-culated values for the Al and Ag films show a similartendency and increase monotonically with wavelengthincreases. However, measured values shift by ;5°from calculated values. For the Cr film, the discrep-ancy between measured and calculated values in-creases from 4° to 16° as the wavelength shortens.

To further examine the differences between theseresults, we also measured the complex refractive indexof evaporated metal films exposed in atmosphere byellipsometry at l 5 633 nm. Direct measurements ofthe complex refractive index at the glass–metal inter-face were very difficult. We list the optical constantsof evaporated metals from data in handbooks9,10 andcompare them with measured values at l 5 633 nm inTable 1. The phase changes calculated by use of theoptical constants listed in Table 1 are also comparedwith values measured by the microscope interferome-ter. It is found that the phase changes calculated byuse of measured optical constants for Au, Al, and Agfilms are in agreement with measured values within2.8°. In contrast, the measured optical constants ofthe Cr film correspond to approximately half of thevalues given by the handbook.10 This leads to thelarge shift of 26.8°. The discrepancy here is likely dueto the Cr oxide at the air–Cr interface. We have notfurther clarified the causes yet.

Since the phase changes on reflection are highlysensitive to the complex refractive index of the sam-ple and depend on wavelength as demonstrated ex-perimentally here, the effect of phase change onsurface profilometry can be detected by a conven-tional microscope interferometer. For example, weconsider measurements of a step height samplewhose base and step are made of Cr and Au, respec-tively. There is little wavelength dependence ofphase changes for the base part ~Cr! between l 5 442nm and l 5 488 nm, while the step part ~Au! providesa difference of 14° as shown in Fig. 6. Thus themeasured step height at l 5 488 nm is 13.3 nm smallerthan the measured one at l 5 442 nm as calculated

Fig. 6. Wavelength dependence of the phase change of light ~p 2r! on reflection from Au, Al, Ag, and Cr. The symbols denote themeasured phase changes. The curves denote the theoretical val-ues calculated from optical constants in the handbooks.

Table 1. Comparison of the Phase Changes Given by Experiment and by Calculations Based on Optical Constants in Handbooks and ThoseMeasured by Ellipsometry

Metal

Phase Change Calculatedfrom ~n, k! in a Handbook

Phase Change Calculatedfrom ~n, k! Measured by

an EllipsometerMeasured

Phase Change

n kp 2 r~deg! n k

p 2 r~deg!

p 2 r~deg!

Au 0.162 3.212 129.6 0.202 3.102 128.1 130.9Al 1.213 6.926 156.0 1.074 5.839 151.8 150.0Ag 0.067 4.047 138.9 0.122 4.225 140.6 143.3Cr 3.530 4.361 156.0 2.081 2.020 135.0 161.8

from Eq. ~5!. By measuring surface profile with dif-ferent wavelengths and subtracting one result fromthe other, we can get the map that shows the relativechanges in phase change ~in other words, optical con-stants! versus wavelength. The map also shows thechange in substance of the surface. The surface pro-filometry with multiple wavelengths allows us to mea-sure changes in substance of the surface and isavailable for specifying the portion of processing dete-rioration, contamination, oxide layer, and so on.

6. Conclusions

We quantitatively measured the phase changes onreflection for Au, Al, Ag, and Cr films with respect tothe phase change at the glass–air interface at fivewavelengths of 442, 488, 532, 589, and 633 nm.

In summary, we demonstrated experimentally thatthe phase changes of light reflected at the metal sur-face is p 2 r from measurements of the interferenceshift between the glass–air and the glass–metal in-terface. The measured phase changes are comparedwith values calculated from complex refractive indi-ces given in handbooks. The phase changes for theAu film agree with values calculated, while a shift of5° is observed with the Al and Ag film. For the Crfilm, there is a large discrepancy between measuredand calculated values. The wavelength dependenceof phase change measured in surface profilometrywith multiple wavelengths is very useful for the eval-uation of surface properties.

We thank T. Kurosawa for fruitful discussions anduseful suggestions. T. Doi is also grateful to T. Vor-burger of the National Institute of Standards andTechnology ~U.S.! for his comments and critical read-ing of the manuscript.

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