Anisotropic scatter patterns and anomalousbirefringence of obliquely deposited cerium oxidefilms

Ian Hodgkinson, Sarah Cloughley, Qi Hong Wu, and Samer Kassam

Cerium oxide films formed by electron-beam evaporation onto oblique substrates are shown to scatterlight strongly into spatially anisotropic distributions and to exhibit large normal-incidence birefringenceDn 5 ns 2 np. The apparatus for direct recording of a useful projection of the scatter distributions isdescribed. Characteristic differences in scatter patterns recorded for cerium oxide, relative to those fromtilted columnar titania and zirconia films, are believed to be associated with unusual microstructuresrecorded for cerium oxide films by scanning electron microscopy. With increasing angle of deposition,the microstructure of cerium oxide was observed to change from densely packed columns to partiallyisolated needlelike columns at angles that do not obey the tangent rule. In particular, deposition at 55°yielded columns nearly perpendicular to the substrate, yet the normal-incidence birefringence was large.The retardation of the films was recorded as a function of angle of incidence for propagation in thedeposition plane. A turning point near 0° incidence for the 55° film confirmed that one principal axis isperpendicular to the substrate. Significant bunching of columns into rows running perpendicular to thedeposition plane was recorded by scanning electron microscopy and may account for both the scatter andthe birefringence. © 1996 Optical Society of America

1. Introduction

Many thin-film materials are known to produce bire-fringent films by oblique deposition.1,2 Tilted colum-nar cerium oxide films, which are in this group, are ofparticular interest because of the large spread ofprincipal refractive indices that can be achieved.Thus, in a recent publication, Horowitz and Mendes3report a spread of 0.32 for a cerium oxide film depos-ited at 58.3°.One problem with birefringent coatings, however,

is that large birefringence tends to be accompanied byexcessive haze. The spatial distribution of opticalscatter often is highly anisotropic, even when thefilms are illuminated at normal incidence.4,5During a recent investigation of anisotropic scat-

ter, some tilted columnar titania films were found togive asymmetric forward- and backward-scatter pat-terns that were visible on a white screen to the un-aided eye. Subsequently the use of the white

When this work was performed, the authors were with the De-partment of Physics, University of Otago, P. O. Box 56, Dunedin,New Zealand.Received 1 January 1996.0003-6935y96y285563-06$10.00y0© 1996 Optical Society of America

painted inside surface of a hemispherical shell cen-tered on the sample was found to improve visualiza-tion of the three-dimensional spatial distribution ofscatter.4An important feature of the above method for view-

ing scatter patterns is that the internal surface of thehemispherical shell acts as a Lambertian diffuser,and the pattern that is seen or photographed from adistance is essentially a circular projection onto aplane through the center of the hemisphere. Forlight incident normally upon the sample, the center ofthe circular projection corresponds to the direction ofthe incident beam and the edge of the circle repre-sents scatter at 90°. If the sample scatters uni-formly into space then the circular projection isshaded evenly; if the scatter is anisotropic then theshading is asymmetric.In practice though, most anisotropic films do not

scatter sufficient light or produce spatial patternswith adequate contrast for direct visual observation.For these reasons we have adapted the visualizationmethod to photometric data acquisition, and in theexperimental section ~Section 2! we describe the ap-paratus developed for automatically recording thedata needed to generate a scatter pattern correspond-ing to a projection from a Lambertian hemisphere.

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2. Experimental

A. Anisotropic Scatter

The scanning apparatus developed for the measure-ment of anisotropic scatter distributions is illustratedin Fig. 1. Rotary stage H with a horizontal axissupports as a unit sample S and a normally incidentlaser beam or collimated white-light source L.Fixing the source with respect to the sample mini-mizes spurious anisotropic effects caused by wedge-shaped thickness variations characteristic of single-layer oblique deposition.1Stage H is in turn mounted on a second rotary

stage, V, with a vertical axis. Stepper motors withshaft encoders are used to control the angular posi-tions of the stages, and by the appropriate choice ofrotations the entire hemisphere in front of the samplecan be scanned. In our setup a host computer isprogrammed to produce the specific set of rotationsthat correspond to a 63 3 63 mesh of square pixels inthe projection plane ~Fig. 2!.Film samples are normally deposited onto BK7

substrates of 20 mm diameter by 5 mm thickness.Before measurements of scatter are made, the edge ofeach substrate is blackened to reduce the effects ofmultiple reflections and secondary scatter.Forward-scattered light from the samples is recordedby a photomultiplier in a detection system that isfixed to the optical bench. The acceptance angle ofthe detection system is just less than the angle cor-responding to the central pixel in the 63 3 63 arrayand matched to the angular divergence of the white-light source.An automatically controlled turret of neutral den-

sity filters and a log amplifier are included in thedetection system to yield a suitable dynamic range, inexcess of 106 for the cerium oxide films reported inthis paper. In practice, software controls the logscatter values at which filter changes are to be made

Fig. 1. Apparatus used for scanning the hemisphere in front of ananisotropic optical coating. Sample S and the normally incidentlight source L are turned as a unit about a horizontal axis by therotary stage H. The axis of rotation passes through the intersec-tion point of the incident-light beam with the coating. A secondstage V carries H and rotates it about a vertical axis, passingthrough the same intersection point; PMT is the photomultiplier-based detection unit.

5564 APPLIED OPTICS y Vol. 35, No. 28 y 1 October 1996

and computes the new gain from measurements re-corded at the same angle before and after a filterchange.Total integrated scatter ~TIS! into the hemisphere

in front of the samples is calculated by summation ofthe pixel values, after geometric corrections are madeto allow for the ratio of the area of a pixel and itsprojected area on the surface of the hemisphere.

B. Birefringence

Obliquely deposited dielectric films behave like crys-talline wave plates. Light that is incident normallyupon the film travels at greatest speed when it ispolarized parallel to the deposition plane ~p polariza-tion! and at slowest speed when it is polarized per-pendicular to the same plane ~s polarization!. Thusat normal incidence the phase thickness fs is largerthan fp. In this work ex situ measurements of thephase retardation,

Df 5 fs 2 fp, (1)

were made by the use of a standard extinctionmethod on an optical bench. The normal-incidencebirefringence,

Dn 5 ns 2 np, (2)

was calculated with the equation

Dn 5 lDfy2pd, (3)

where l 5 633 nm is the wavelength of the light usedfor the measurement. Equation ~3! neglects the ef-fects of interference in the coating. The thickness d

Fig. 2. Method used for direct acquisition of data required forconstructing a projection of the three-dimensional distribution ofscattered light. The notional square array is in the plane of thefilm, fixed with respect to the source and film, and is assumed torotate with the source–film unit. The highlighted pixel in thesquare array is the projection of a small area from the surface ofthe hemisphere. For the case shown, the pixel corresponds toscatter at a particular direction in the deposition plane. Scat-tered light associated with the pixel is obtained directly by thedriving of the stepper-controlled rotary stages ~H and V in Fig. 1!to access the required position.

Table 1. Film Parameters

Sample

DepositionAngle

~dydeg!Thickness

~dymm!Retardation

~Dfydeg!Birefringence

~Dn!Scatter~TISy%!

Tangent RuleAngle

~ccalcydeg!

SEMAngle

~cexpydeg!

ce907 0 0.9 6 0.01 2.0 0 0ce906 5 0.9 18 0.04 3.4 3 0ce905 15 0.6 32 0.09 1.7 8 15ce904 25 1.0 66 0.12 3.4 10 20ce903 35 1.0 86 0.15 4.9 19 12ce902 45 0.8 92 0.20 4.0 27 10ce830 55 1.1 106 0.18 9.0 36 ,5

of each film needed for the calculation of Dn wasmeasured with a Talystep stylus instrument.Additional measurements of retardation were

made with a transmission-mode ellipsometer.6 Inthis case, Df was recorded for a range of angles ofoptical incidence in the deposition plane to provideinformation on the location of principal dielectricaxes.

C. Microstructure

Scanning electron microscope observations weremade to reveal the microstructure of the obliquelydeposited cerium oxide films. Substrates were frac-tured in the film deposition plane by a hot-wire tech-nique7 that produces an edge that is both straightand smooth.Column angles were calculated with the tangent

rule,8 which relates deposition angle d to column an-gle ccalc,

ccalc 5 tan21~1⁄2 tan d!, (4)

and compared with experimental values ~cexp! mea-sured from scanning electron microscopy ~SEM! pho-tographs. For the latter the films were overcoatedwith a thin sputtered metal coating and oriented togive a view perpendicular to the plane of the fracture.

3. Results and Discussion

A set of seven cerium oxide films was deposited byelectron-beam evaporation onto 300 °C glass sub-strates at deposition angles of d 5 0° to d 5 55°.Projections of scatter distributions, from which TISvalues were calculated, were recorded for each film.Table 1 summarizes the deposition parameters and

measured values for the set of seven films. A plot ofDn versus d is given in Fig. 3, and typical projectionsof scatter, recorded for cerium oxide films depositedat angles of 0°, 25°, and 55° and illuminated by whitelight at normal incidence, are illustrated in Fig. 4.Figure 4 ~a! shows nearly isotropic scatter for a film

deposited at d 5 0°. Anisotropy, with a forward-scatter preference in the deposition plane on the sideof the evaporation source, was noticeable for d $ 5°.Scatter distributions with a single peak, as shown ford 5 25° @Fig. 4~b!# were recorded for moderate anglesof deposition. At d 5 55° @Fig. 4~c!# a just-resolveddouble peak was recorded. A pronounced double

peak occurred for scatter from a double layer @Fig.4~d!# deposited at d 5 655°.The sense of the maximum scatter from the oblique

film is opposite to that recorded for titania and zir-conia.5 In the case of titania and zirconia, the dis-tribution of scatter is consistent with diffraction fromfeatures correlated with the tilted columns of themicrostructure.9 Thus our measurements on ce-rium oxide suggest that different microstructural fea-tures must be responsible for the anisotropy of thescatter from this material.Films deposited at d 5 0° were found to have a

dense microstructure, whereas films deposited atlarger angles exhibited an unusual bed-of-nails mi-crostructure, as shown in Fig. 5, which illustrates atypical case. Here the film was deposited at 45° andthe microstructural column angle ~cexp 5 10°! is sig-nificantly smaller that the angle predicted by the tan-gent rule, ccalc 5 tan21~1⁄2 tan 45°! ' 27°. Values ofccalc and cexp for the seven films are listed in Table 1.Further SEM studies in which films were viewed

from above showed bunching of the needlelike columnsinto groups of two or three columns or into longer rows,both running perpendicular to the deposition plane.In Fig. 6, for deposition at 55°, the column angle isnearly vertical, yet the birefringence is large.Elementary theory indicates that anisotropic mi-

crostructural features of this type will influence the

Fig. 3. Normal-incidence birefringence, Dn 5 ns 2 np, recordedfor cerium oxide films deposited obliquely onto glass substrates.

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Fig. 4. Projected scatter patterns ~pseudocolor plots! recorded for cerium oxide films deposited obliquely onto glass at angles of ~a! d 50° ~sce907!, ~b! d 5 25° ~sce904!, ~c! d 5 55° ~sce830!, and ~d! for a double deposition with d 5 655° ~sce831!. Each birefringent coatingis in the plane of the projection and for each single layer coating the columns point into the paper and to the left side of the page. Ahorizontal line through the center of the projection corresponds to scatter in the deposition plane. The log values on the vertical axis arereferenced to the strength of the direct light beam that passes entirely through the central pixel, and the edge of the circular projectioncorresponds to scatter at 80°.

properties of the films in two ways that are signifi-cant here. First, they contribute positively to theobserved birefringence. Form birefringence can bedescribed in terms of depolarization factors, bunchingdecreases a depolarization factor, and hence bunch-ing in the direction perpendicular to the depositionplane increases ns relative to np. As well, the lengthof the rows is significant for diffraction of light, and sothe observed scatter pattern is, at least in part, de-termined by diffraction from bunched microstruc-tural features. This was confirmed by noting that

5566 APPLIED OPTICS y Vol. 35, No. 28 y 1 October 1996

overcoating the cerium oxide films with opaquemetalfilms, to eliminate scatter from the bulk of the film,did not change the preferred direction for scatter inreflection.The perpendicular microstructure of cerium oxide

deposited at 55° is unusual and may lead to usefulapplications. The principal axes of a tilted columnarbiaxial film are ~1! along the column direction, ~2! inthe deposition plane perpendicular to the columns,and ~3! perpendicular to the deposition plane. In thecase of a tilted columnar film, the retardation Df~u!

for propagation in the deposition plane changes sig-nificantly and nearly linearly with a change in theangle of incidence u, from u 5 0°. On the other hand,a biaxial filmwith one principal axis perpendicular tothe substrate and the other two axes in the plane ofthe film exhibits smaller sensitivity to u because theretardation Df~u! has a turning point at u 5 0°. Inother words, the deposition plane sections of the in-ner and outer sheets of the refractive-index surfaceare parallel at u 5 0°.Measurements made on cerium oxide films with

the scanning ellipsometer operated in the transmis-sion mode confirm the dependence of Df on u.Figure 7 shows the curves of Df versus u for filmsdeposited at 45° and 55°. The turning point of theDf curve for the 55° film occurs close to u 5 0°,indicating that a principal dielectric axis runs per-pendicular to the substrate.

Fig. 5. Scanning electron micrograph of a cerium oxide film de-posited at 45° and fractured in the deposition plane. The angle ofthe columns is '10°; significantly less than the angle of '27°predicted by the tangent rule.

Fig. 6. SEM shows the needlelike columns of cerium oxide filmsbunching in rows running perpendicular to the deposition plane.This microstructural effect decreases the depolarization factor fors-polarized light traveling perpendicular to the film and henceincreases ns relative to np.

4. Conclusions

Cerium oxide films deposited at 300 °C and obliquelyby electron-beam evaporation in vacuum have un-usual needle-shaped microstructures that influenceboth the anisotropic scatter patterns and the birefrin-gence for normally incident light. Columnar anglesmeasured for cerium oxide films from SEM photo-graphs do not agree with angles calculated with thetangent rule. Cerium oxide films deposited at 55°provide an example of an obliquely deposited coatingthat exhibits form birefringence even though the mi-crostructural columns are nearly perpendicular tothe surface of the substrate. Such a layer has theadvantage of small sensitivity of retardation tochanges in the angle of the incident light. Bunchingof columns into rows perpendicular to the depositionplane was observed andmay be themajor contributorto the birefringence.The values of Dn recorded for the cerium oxide

films are relatively large, approximately twice thebirefringence of titania films.2 However, the TIS isalso abnormally large, and for cerium oxide to be auseful material for applications such as thin-filmwave plates, a strategy for reducing scatter wouldneed to be found. Alternatively, it may be possibleto make use of the large anisotropic scatter, for ex-ample in smart coatings designed to control daylightentering buildings.

This work was performed at the University ofOtago and was supported by the New Zealand Foun-dation for Research, Science and Technology undercontract UOO408.

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coatings,” Opt. Photon. News 5~5!, S9–S10 ~1994!.

Fig. 7. Retardation of cerium oxide films plotted as a function ofangle of incidence u for light propagating in the deposition plane.The turning point near u 5 0° for the film deposited at 55° indicatesthat a principal dielectric axis of this film is perpendicular to thesubstrate. This is consistent with the columnar angle estimatedfrom SEM photographs.

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3. F. Horowitz and S. B. Mendes, “Envelope and waveguide meth-ods: a comparative study of PbF2 and CeO2 birefringent films,”Appl. Opt. 33, 2659–2663 ~1994!.

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