Détermination par spectrophotométrie par immersion des constantes optiques de films interférentiels d'oxyde anodique sur support en tantale

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Détermination par spectrophotométrie par immersion des constantes optiques de films interférentiels d’oxyde

anodique sur support en tantale

Walton P. Ellis

To cite this version:

Walton P. Ellis. Détermination par spectrophotométrie par immersion des constantes optiques de

films interférentiels d’oxyde anodique sur support en tantale. Journal de Physique, 1964, 25 (1-2),

pp.21-24. �10.1051/jphys:01964002501-202100�. �jpa-00205742�

21.

DÉTERMINATION PAR SPECTROPHOTOMÉTRIE

PAR IMMERSION DES CONSTANTES OPTIQUES

DE FILMS INTERFÉRENTIELS D’OXYDE ANODIQUE ^SUR SUPPORT EN TANTALE

By ^{WALTON P.} ELLIS,

Résumé.

L’immersion d’un film interférentiel in situ dans un liquide ^modifie _ses propriétés optiques par la diminution de l’amplitude du vecteur d onde réfléchi à l’interface milieu-couche.

Avec des couches interférentielles obtenues par oxydation anodique ^d’un support ^{de tantale,}

l’immersion dans des liquides d’indice de réfraction progressivement croissant diminue le con-

traste des interférence d’une manière régulière. ^{On a} obtenu, par ^une analyse des maximums d’interférences déterminés par ^une méthode spectrophotométrique, l’indice de réfraction d’un

oxyde ^{de tantale} anodique pour différents ordres d’interférence dans le domaine spectral

4 000

6 100 Å.

Abstract.

Immersion of an in situ interférence film into a liquid ^{alters the} optics by ^dimi- nishing ^the amplitude ^{of the wave} vector reflected at the medium film interface. With inter- ference layers of anodic oxide on tantalum, immersion into liquids ^of progressively higher ^refrac-

tive indices decreases the degree of interference in a regular fashion. From an analysis ^{of the} spectrophotometrically determined interférence peak heights, the refractive index of anodically

formed tantalum oxide was obtained for différent orders of interférence in the wavelength range 4 000

6 100 Å.

PHYSIQUE 25, 1964,

.

Introduction.

Immersion of a solid inter- ference film into a liquid diminishes the amplitude

of the wave-vector reflected- at the medium-film interface. In ^a study ^{of this} effect, ^Mallemann

and Suhner [1] ^{obtained the} optical ^{constants of}

thin films by analyzing ^the change in reflection of

elliptically polarized light upon immersion. Simi-

larly, by observing ^the change in the interference

peak height ^with immersion, ^the optical ^constants

of an interference film can be obtained spectro- photometrically. ^{In a} previous report [2] ^the principles of. immersion spectrophotometry ^were

outlined. In this approach, ^the interference peak heights ^are measured with the specimen ^immersed

in various pure liquids. ^As the refractive index of the fluid approaches ^{that of the} film, interference is diminished and the peak height goes ^{to zero at} the index of refraction of the layer. This method

was used to determine the refractive index of inter- ference films of UF 4(s) ^on UO 2(s) ^{and of anodic}

oxide films on uranium metal. For the present report, the method was modified and extended to the study ^of anodic interference oxide films on

tantalum metal. With anodized ^{Ta where the} refractive index of the oxide is much larger ^than

that of the immersion media, ^direct extrapolation

of the peak heights ^{to zero} interference results in considerable uncertainty. Instead, ^{a more} precise approach ^{was to determine} graphically ^{the set of} parameters ^which gave the correct peak heights ^for

all media.

Materials and apparatus.

The tantalum speci-

mens were prepared ^{from 99. 98} % pure, ^arc-melted

material. The major impurities ^after melting

were 29 _ppm Nb, 40 ppm W, 24 ppm Si,

29 ppm 0,14 ppm N, 16 ppm C and 25 ppm Al.

The other detected impurities ^{were less than}

10 ppm. The Ta specimens ^were machined into buttons and lapped through ^600A SiC,1/0, 2/0, 3/0 ^and 4/0 emery paper, and finally ^with 1 u

diamond paste ^{on a} silk-velvet cloth. The surface

was electropolished ^{with a} pulsed ^{current at 15 V}

in a stirred mixture of 1 part ^{of 48} % ^{HF to 9} parts of conc. H2SO4 ^{at room} temperature. ^{Films of}

oxide were formed anodically in 0.2 N H2S04

at 4.6 mA/cm2 ^{in a manner described} by Young [3].

The modified optical arrangement ^{of the} Cary

Model 14X spectrophotometer ^{has been described} previously [2]. Background spectra ^{were taken}

for each specimen ⁱⁿ various media after electro-

polishing. Interference peak heights ^{of the ano-}

dized specimens ^{immersed in the same media were}

then measured.

Theory ^{and results.}

^The theory ^{has been pre-}

sented in detail earlier [2] ^{and is} only briefly ^sum-

marized in the following treatment. The notation of Heavens [4] ^is followed. An interference system

is represented by ^a solid substrate of refractive

index YJ2, a thin film of index _n1 and ^an immersion medium of index _"fJo. The wave vector reflected at the medium-film interface is denoted by r1 and the

wave vector reflected at the film-substrate inter- face is _r2. Both _r, and _r2 depend upon ^the refrac- tive indices of the -system. ^{For a} transparent

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:01964002501-202100

22

film and normally ^incident light, ^the magnitude of r 1 is

With an instrument such as the Cary ^{Model 14X}

that -measures optical density ^versus wavelength,

the interference peak height, Amax, ^is given by

This expression ^holds exactly ^{for a} transparent

film. With this equation ^{it is seen that Amax}

⁰

if ₇₁

0. But from eq. (1), ri

0 if _{n1 = n0.}

Thus, ^{if Amax is} plotted ^versus n0, the extrapolation

to Amax

⁰ gives no

n 1 directly.

FIG. 1.

Optical density ^vs. wavelength ^{for an anodic}

oxide film on tantalum metal. The third-order inter- ference wavelength ^is 5 783 ± 15 A.

Figure ^{1 is a} tracing ^{of a} typical interference

curve of an in situ film ^of anodically ^{oxidized tan-}

talum immersed in acetone. The third-order peak height ^{is 0.88 + 0.01} optical density ^units.

Agreement ^between background ^{and the minima}

of the curve for the anodized specimen ^is approxi- mately 0.01 units. Figure ^{2 is a} plot ^{of Amax}

versus no for the same specimen ^{immersed in a}

series of liquids. ^An extrapolation ^{from the most} highly refractive medium («-bromonaphtalene) ^is

seen to be somewhat arbitrary within ± ^{0.1 unit.}

In this instance where _n1 is so much greater ^than the _rlo of the conveniently managed media, ^this

method of analysis ^{is not exact} enough.

In equations 1 ^and 2, the unknowns _{are r2} and _n1.

For a given ^immersion medium, a curve can be drawn relating n1 ^to r2 for a given ^{Amax. The}

intersection of these curves for different refractive media gives the values of r2 ^and n1 which satisfy

the conditions for all liquids. Figure ^{3 is a} plot of r2 ^vs. n1 calculated from the set of data shown

FIG. 2.

Peak height ^vs. n0 for the third-order (K

2) peak ^{shown in} figure ^1.

FIG. 3.

Plot of r2 ^vs. 7]i to give ^correct åmax for different refractive media : 1 : air ; ^{2 :} acetone ; ^{3 :} n-heptane ;

4 : toluene ; ^{5 :} ac-chloronaphtalene ; ^{6 :} a-bromonaph-

thalene.

in figure 2. The intersection is, at n1 = 2.218 with a spread ^{of 0.015.} By ^this method, n1 of

anodically formed tantalum oxide was determined

as a function of wavelength for different orders of interference. Figure ⁴ summarizes the results.

The plot of n1 ^versus wavelength ^{is seen to be a}

smooth curve with a standard deviation of the fit’

of 0. 016.

These values differ greatly from those reported by ^{Waber et al.} [5] ^for macro-crystalline Ta2O5,

and the agreement ^with previously reported ^values

FIG. 4.

Refractive index vs. interference wavelength.

For second-order films K = 1, ^for third-order K

2, ^etc.

Standard deviation of the fit is 0.016.

of anodic oxide layers ^on tantalum is only ^fair [3, 6, 7, 8, 9].

The value at 5 900 A of 2.205 ± .016 is in

good agreement ^with 2. 20 + ^0.02 reported by Young [3] ^{for the same} wavelength from the Becke immer’sion of a detached flake of anodic tantalum oxide prepared under similar conditions. Unfor-

tunately, this is the only wavelength ^{for which he} reports ^a value obtained by ^{the Becke} method, ^and

at shorter wavelengths agreement is within only

5’ %. ^{At 4 358 A the value of} n1 of the present

work is 2.35 + ^{0.02 in} comparison ^with 2.281 ± . ^{001 which} Masing, ^{Orme and} Young [6]

reported ^for anodic oxide prepared ^{in the same}

bath at 2 mA jcm2. ^Their analysis ^{was the Abel6s}

method of plotting ^the reflectivity ^{in air versus} angle ^{of incidence of two or more} films of critical

wavelengths.

The data represented by figure ^{4 were taken with} unpolarized light ^{and with no} angle ^{of incidence}

correction _{in eq.} (1). ^{As a} check, ^{several measu-}

rements were taken with p-light ^{with an} angle ^of

incidence correction. The values are within one

standard deviation ^of the ^{curve in} figure ^{4 :}

and

Also, anodic oxide films prepared in aqueous 3 %

tartaric acid adjusted ^with NH40H ^{to a} pH

5.5,

gave values of 1)1 in agreement ^with figure ^4.

Apparently ^{there are no available voids in the}

film which become filled when the specimen ^is immersed, since if there ^were such pores, the inter-

ference wavelength would increase with immer- sion. Instead, ^{the 3rd-order} wavelength ^decreases approximately 1/2 % ⁱⁿ going ^{from air to chloro-} naphtalene ^{at 5 500} A, ^{which indicates that the}

film absorbs slightly ^{with an} extinction coefficient of approximately 0.005. The interference wave-

length ^{does not} change ^at all within the limits of

error of the determination at 4 000 A, which indi- cates that at this wavelength the film is transpa-

rent. Evacuating ^the spectrum ^{to 10-5 torr with} gentle heating prior ^to flooding ^with liquid- ^does

not alter either the interference wavelengthlor ^Amax...

neither does boiling ⁱⁿ liquid, ^nor shaking ^ultra- sonically ^nor soaking ^{a week at room} temperature.

Figure ^{5 is a} plot of interference peak height ⁱⁿ

air versus interference wavelength ^{for different}

FIG. 5.

Plot of Amax in ^{air vs.} interference wavelength.

Anodic oxide films on Ta..

orders. The shape ^{of the} curve is explained by

the minimum in reflectance ^at the film-metal inter- face at 5 350 + ¹⁰⁰ A. The observation that Amax is approximately ^{the same} for different orders is in agreement ^{with the} findings ^of Masing ^{et al.} [6]

that to a first approximation ^{the film can be consi-}

dered to be transparent.

Acknowledgments.

^The author wishes to express gratitude ^{to R. J. Bard and R. D. Baker}

for support ^and encouragement, ^{and to Keith} Davidson for supplying ^{the tantalum.}

Discussion

M. HEAVENS. - The spread of values obtained for the film index cannot evidently ^{be accounted for} by ^the assumption of accessibles voids, ^{with variable} accessibility ^{to different} liquids ^{since the} position

of the turning values does not change ^with filling

liquid. ^{However the} possibility of inaccessible

24

voids which may ^{account for the} gradient gra- dient of index observed in some tantalum oxide films.

R6ponse : 1) ^The definition of _r2 is contained in the text ; ^{as defined} there, ^{it is} invarient with immersion.

2) ^{With an} inhomogeneous film the conclusion of plotting ^{Amax versus} YJo is unaffected since the

extrapolation ^{to zero} interference is to YJo

Y/l at the medium film interface. However the plot ^{of r2}

versus YJI is certainly ^affected by inhomogeneities

since _r2 would have to be re-defined.

BIBLIOGRAPHY [1] ^{DE MALLEMANN} (R.) and SUHNER (F.), ^Rev. d’Optique,

1944, 23, 193.

[2] ^ELLIS (W. P.), ^J. Opt. ^Soc. Amer., 1963, 53, ^613.

[3] ^YOUNG (L.), ^Proc. Roy. Soc., A, 1958, 244, 41.

[4] ^HEAVENS (O. S.), Optical Properties ^of Thin Solid

[5] Films, Academic Press Inc., ^New York, 1955, p. 56.

[5] ^WABER (J. T.), ^STURDY (G. E.), ^WISE (E. M.) ^and

TRIPTON (C. R., Jr.), ^J. Electrochem. Soc., 1952, 99,

121.

[6] ^MASING (L.), ^ORME (J. E.) ^{and YOUNG} (L.), J. Electro- chem. Soc., 1961, 108, ^428.

[7] ^VERMILYEA (D. A.), ^Acta Met., 1953, 1, 282.

[8] ^HEAVENS (O. S.) ^{and KELLY} (J. C.), ^Proc. Phys. Soc., 1958, 72, 906.

[9] ^CHARLESBY (A.) and POLLING (J. J.), ^Proc. Roy. Soc., A, 1955, 227, ^434.

DÉTERMINATION EXPÉRIMENTALE DE LA VARIATION DE PHASE 03C8T ^SUBIE

PAR LA LUMIÈRE A LA TRAVERSÉE DES COUCHES MÉTALLIQUES ^MINCES

EN VUE D’APPLICATIONS A L’APODISATION

Par H. FOUSSE et B. ROIZEN-DOSSIER,

Faculté des Sciences de Nancy.

Résumé. - Nous déterminons 03C8T par l’intermédiaire de la fonction de filtrage B(03BD) ^{d’une lame}

de verre carrée métallisée sur l’une de ses moitiés (épaisseur ^{du métal} e, transmission T). ^{La com-} posante imaginaire ^de B(03BD) ^{nous fournit} (T/2) ^sin (03C8T + 203C0e/03BB), ^la composante ^réelle (T/2) ^cos (03C8T + 203C0e/03BB). ^Le montage ^de Hacking que ^nous utilisons nous fournit B(03BD) ^{sous la forme de la}

transformée de Fourier de l’intensité diffractée. Un exemple simple ^{montre que le terme de} phase

~ = 03C8T + 203C0e/03BB ^a relativement peu d’influence ^sur la qualité ^d’un apodiseur.

Abstract.

We determine 03C8T by ^the spatial frequency response function B(03BD) ^{of a} square glass plate metallised on half its width (thickness ^{of the} metal layer : ^e, transmission T). ^The imaginary part of B(03BD) gives ^us (T/2) ^sin (03C8T + 203C0e/03BB), ^{its real} part: (T/2) ^cos (03C8T + 203C0e/03BB). ^{The device}

proposed by Hacking ^{is used for} determining ^the Fourier transform of the diffraction function,

i.e B(03BD). ^We finally ^find that ~

03C8T + 203C0e/03BB has little effect on the quality ^{of an} apodiser.

LE JOURNAL DE PHYSIQUE ^TOME 25, JANVIER-FÉVRIER 1964,

Introduction.

La détermination expérimentale

de la variation de phase §T ^que la travers6e d’une couche metallique mince, d’épaisseur .e, impose ^à

un faisceau de lumi6re monochromatique ^{en inci-}

dence normale, ^est importante a connaitre a divers

egards ; elle constitue une donn6e utile pour la determination de l’indice complexe ^{de la} couche,

mais pour certains utilisateurs des couches, ^{elle est}

d’un int6rOt plus ^{direct encore :} pour nous, par

exemple, qui fabriquons ^des apodiseurs, ^constitués

on le sait, par des lames de ^verre ayant ^{subi une}

metallisation afin d’acquérir ^une transparence ^non

uniforme convenable, la connaissance de la varia- tion de phase §r ^{a la travers6e du metal} importe, puisqu’une distribution non uniforme des phases

sur l’objectif garni ^{de son} apodiseur ^et suppose

eclaire par ^un point a l’infini sur l’axe equivaut ^a

des aberrations qui peuvent contrecarrer dans

l’image 1’effet cherche, Rappelons que cet effet consiste dans I’att6nuation des pieds ^{de la} figure ^de diffraction., ou, par extension, ^dans I’am6lioration de l’une quelconque ^{des autres} caractéristiques ^de

cette figure. ^{Un cas} analogue ^est celui de la micro-

scopie par contraste ^de phase, lorsqu’on ^m6tallise

les lames de phase pour les rendre absorbantes et ameliorer le contraste de l’image finale. ^Cette

metallisation modifie quelque peu les ^caract6-

ristiques ^de phase de la lame et peut appeler ^une

correction.

Or, ^{dans la} litt6rature, les donn6es concernant §r

sont rares pour les couches absorbantes. Nous nous

proposons de d6crire la méthode que nous avons