Application of Immersion Reflectometry to the Study of Interference Layers W. P. Ellis, L. D. Allen, and A. D. Mulford The reflectance of a thin film changes upon immersion in a transparent dielectric liquid. By use of spec- trophotometry, the changes in reflectance at the wavelengths where maximum or minimum reflectance occurs have been characterized for a variety of optical combinations including both transparent and ab- sorbing films and substrates. The complications and ambiguities of interpretation for each system and the effects of multilayer structure have been examined. Reversal of the direction of observation is dis- cussed as one means to distinguish between absorption and inhomogeneity in the film. 1. Introduction Immersion methods have been a standard technique for several years in chemical microscopy to measure refractive indices of crystals,' and have been extended for example to the ellipsometric study of thin films. 2 Several approaches are in current use to measure optical constants of thin films. 3 A related method of examin- ing the optical characteristics of smooth interference layers is immersion spectrophotometry 4 in which reflec- tance is measured as a function of wavelength with the specimen immersed in a sequence of transparent pure organic media of varied refractive indices. The changes in the interference pattern, i.e., in the wave- length and magnitude of the reflectance at an interfer- ence maximum or minimum, that occur upon immer- sion depend upon the refractive index, transparency, and homogeneity of the film. The purpose of this article is to discuss the changes in reflectance that occur upon immersion and to relate them to the optical properties of the film. The more commonly encountered types of thin film optical sys- tems have been examined. The difficulties of interpre- tation and the sensitivity, or lack of it, of the immersion method to optical structure within those systems are considered. The basis of the immersion spectrophotometric method is the dependence of the amplitude ratio of reflected light, I, at the medium-film interface upon the The authors are with the Los Alamos Scientific Laboratory, University of California, Los Alamos, New Mexico 87544. Received 16 April 1969. refractive index of the immersion medium, 1o. For the special case of a uniform, transparent film of index ni, shown in Fig. 1, F, is real and is given by the Fresnel ratio Pi = ( - no)/1(Q + no) and F2 = (n2 - 1)/(n2 + ni). For purposes of this discussion, only far-field normal-incidence specular plane waves are considered so that the amplitude of component 1 after reflection is a = , and the amplitude of component 2 after reflection and repassing the medium-film interface is 2. In general, d, is the amplitude of the ith component im- mediately after passing the medium-film boundary in the reflection direction. At minimum reflectance the sum of the complex wave vectors including multiple reflections is a minimum. For transparent, homogeneous, uniform films, the phase difference between al and d 2 is (2K + 1)7r, where K = 0, 1, 2..., at wavelengths of minimum reflectance, Xk. At normal incidence the thickness X = k [2K + 1 - (02 - 01)/r]/ 4 n,1 where the discontinuous phase shift upon reflection for Pi is 0 = 0,7r and for F2 is 02. In the following discussions, 6i; is the geometrical phase differ- ence between the ith and jth rays, which for components 1 and 2 shown in Fig. 1 at normal incidence is 612 = 47rniX/X. At no = 71, the Fresnel ratio Pi = (11 - ) (ni + no) goes to zero and hence interference for reflected light also goes to zero. In our experimental arrange- ment, described in Ref. 4, optical density, i.e., logo(I o/ I), is measured. The difference in optical density, Amax, between a reflectance minimum and a reflectance maximum for a transparent film is Amax = 2 logio[(l + r/r 2 )/(l - ri/r2)] - 2 logio[(l + rlr2)/(l - rr 2 )], November 1969 / Vol. 8, No. 11 / APPLIED OPTICS 2177
Transcript
Application of Immersion Reflectometryto the Study of Interference Layers
W. P. Ellis, L. D. Allen, and A. D. Mulford
The reflectance of a thin film changes upon immersion in a transparent dielectric liquid. By use of spec-trophotometry, the changes in reflectance at the wavelengths where maximum or minimum reflectanceoccurs have been characterized for a variety of optical combinations including both transparent and ab-sorbing films and substrates. The complications and ambiguities of interpretation for each system andthe effects of multilayer structure have been examined. Reversal of the direction of observation is dis-cussed as one means to distinguish between absorption and inhomogeneity in the film.
1. IntroductionImmersion methods have been a standard technique
for several years in chemical microscopy to measurerefractive indices of crystals,' and have been extendedfor example to the ellipsometric study of thin films.2
Several approaches are in current use to measure opticalconstants of thin films.3 A related method of examin-ing the optical characteristics of smooth interferencelayers is immersion spectrophotometry4 in which reflec-tance is measured as a function of wavelength with thespecimen immersed in a sequence of transparent pureorganic media of varied refractive indices. Thechanges in the interference pattern, i.e., in the wave-length and magnitude of the reflectance at an interfer-ence maximum or minimum, that occur upon immer-sion depend upon the refractive index, transparency,and homogeneity of the film.
The purpose of this article is to discuss the changes inreflectance that occur upon immersion and to relatethem to the optical properties of the film. The morecommonly encountered types of thin film optical sys-tems have been examined. The difficulties of interpre-tation and the sensitivity, or lack of it, of the immersionmethod to optical structure within those systems areconsidered.
The basis of the immersion spectrophotometricmethod is the dependence of the amplitude ratio ofreflected light, I, at the medium-film interface upon the
The authors are with the Los Alamos Scientific Laboratory,University of California, Los Alamos, New Mexico 87544.
Received 16 April 1969.
refractive index of the immersion medium, 1o. For thespecial case of a uniform, transparent film of index ni,shown in Fig. 1, F, is real and is given by the Fresnelratio Pi = ( - no)/1(Q + no) and F2 = (n2 - 1)/(n2 +
ni). For purposes of this discussion, only far-fieldnormal-incidence specular plane waves are considered sothat the amplitude of component 1 after reflection is a= , and the amplitude of component 2 after reflectionand repassing the medium-film interface is 2. Ingeneral, d, is the amplitude of the ith component im-mediately after passing the medium-film boundary inthe reflection direction. At minimum reflectance thesum of the complex wave vectors
including multiple reflections is a minimum. Fortransparent, homogeneous, uniform films, the phasedifference between al and d2 is (2K + 1)7r, where K =0, 1, 2..., at wavelengths of minimum reflectance, Xk.At normal incidence the thickness X = k [2K + 1- (02 - 01)/r]/4n,1 where the discontinuous phase shiftupon reflection for Pi is 0 = 0,7r and for F2 is 02. In thefollowing discussions, 6i; is the geometrical phase differ-ence between the ith and jth rays, which for components1 and 2 shown in Fig. 1 at normal incidence is 612 =
47rniX/X. At no = 71, the Fresnel ratio Pi = (11 - )(ni + no) goes to zero and hence interference for reflectedlight also goes to zero. In our experimental arrange-ment, described in Ref. 4, optical density, i.e., logo(I o/I), is measured. The difference in optical density,Amax, between a reflectance minimum and a reflectancemaximum for a transparent film is
n2Fig. 1. Ideally flat interferenice filmY of u1niforlm1 thiCkniess X andrefractive index 771, immersed in a mediumr of i(lex 'Jo, and on a
suhst rate of index .72-
B~~~~~~~~~~~~~~~~~7 > ANN ff I-
X(K -2) X k(K - )
WAVELENGTH
Fig. 2. Change of optical density with qo0, hypothetical perfectlyuniform transparent film. Background subtracted out. Xk does
not change with -qo.
which also goes to zero at r, = 0, i.e., at n0 = 71. Thewavelength dependence of reflectance, measured asoptical density, is shown schematically in Fig. 2.
For transparent films, ?I is a real number so that 01 =0 for no < n1, and 0 = r for 0 > 71; as shown in Fig. 2,there is no smooth wavelength shift with no. TheXk's when corrected for dispersion are in the inverseratio of [2K + 1 - (02 - )/7r]. At no = ni, interfer-ence disappears, i.e., Amax = 0, and for no > n, the reflec-tance minima and maxima simply reverse. The plotOf Amax Vs no follows the curve shown in Fig. 3. Underthe most ideal conditions we have encountered to date,ThF4 films on single crystalline ThO2 ,6 a precision of4-0.001 in the measured value of ni was found.
A comparison of this method with the Abeles angularreflectance technique has been performed.6 For an-nealed films of MgF2 freshly deposited on annealedvitria, it was found that the two methods are in verygood agreement.
However, few films are both homogeneous and trans-parent, and for them the preceding discussion has to be
modified. With multilayered films, reflections occur atmore than just two interfaces. With absorbing films,F, is complex so that 0 = 01(Xo) and does not equal 0 or7r. In both cases, i.e., inhomogeneous and absorbing,Amax never equals zero, and Xk changes with no. In thefollowing sections, specific examples are given for thesetwo cases and a reversal method is given for distin-guishing between them.
II. Results and Discussion
A. Transparent, Homogeneous FilmsThe ideal results are described in Sec. I. With
transparent, homogeneous films, Xk is invariant with noand the plot of Smax vs no passes smoothly through zeroat no = ni with no discontinuity. Examples of suchmaterial are freshly deposited films of MgF2
6 and fluorideproduct films produced on U0 2
4 and ThO26 by the
hydrofluorination reaction. Typical values of Xk vs noare given in Table I. In these cited cases, the relativeinvariance of Xk with changing no demonstrates that to afirst approximation these films can be treated as bothhomogeneous and transparent. The slight change ofXk upon immersion with MgF2 , and the shift in Xk at no
-ni with UF4 films on U0 2 and ThF4 on ThO2 demon-strate that the assumption of homogeneity and trans-parency, although good, is not strictly valid. Anodicoxide on Ta7 is another example where the assumption isof limited validity. Thus, for these films one or both oftwo possibilities may be operative: either the films areslightly absorbing, or slightly inhomogeneous. Thesepossibilities are discussed in Secs. II. B and II. C.
Absorption in the substrate affects the interferencewavelengths and intensities, but the plots of Xk or Ama.Vs n are functionally the same as for transparent sub-strates, as indicated in Table I for MgF2 vapor-depos-
1.5 .
1.0 //
0.5
/1.391 0.003
0 0 __
-0.5-
-1.0-
1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7
10(MEDIUM)
Fig. 3. Interference peak height, Ama., vs ijo, annealed film ofMg-F2 0.27 u thick on Pyrex 7740 (see Ref. 6).
a Approximate -q at XD given in table above. For each immersion series, -, was corrected for dispersion to third decimal place. Foradditional discussion on MgF2 films, see Ref. 6.
ited on Ta. LiF films on Ta are similar to MgF2 in thisrespect.
B. Absorbing, Homogeneous FilmsWith absorbing interference films, Xk depends upon
no. From Fresnel's ratio P = (* - n7o)/(nql* + 7o),where nl* = 7n + iki, PI is complex and the discontinu-ous phase shift 01 is given by tan01 = 2k,!o/(n712 + ki 2 -
no2). As no increases, so does 01 and in accordance withthe interference equation, X - Xk [2K + 1 - (02 -01)/
ir]/ 4 ni, the wavelength Xk decreases for the customaryorientation shown in Fig. 4. This equation, althoughexact for uniform transparent layers, is not strictly validfor absorbing films because absorption of multiple reflec-tions has been neglected. Also, it is noted that rl neverequals zero; at o = ni, P = ikj/(2no + ik1) and thephase shift 01 < 7r/2 .
Such effects have been observed for anodic oxide onU,8 Si vapor-deposited onto both electropolished Ta andquartz, and U02 vapor-desposited onto quartz as indi-cated in Table II. In principle, both ni and k can beobtained from the wavelength shifts and interferenceintensities. As yet we have not treated our data in thisfashion, but the possibility is intriguing and seems tomerit examination.
Although Xk decreases with increasing o for an ab-sorbing film, this dependence alone is an insufficient testto unambiguously detect absorption in the film. Withtransparent multilayers, Xk also shifts with immersionand in some instances may decrease as o is increased.
C. Transparent BilayersIf instead of being perfectly uniform, a transparent
film is formed by two layers as in Fig. 5, then three in-terfaces have to be considered. The amplitude sum,
z
to be complete, has to include multiple reflections and isbest performed on a computer.' An approximation toillustrate the effects of immersion consists of includingonly di, &, and d3. For the case shown in Fig. 5(a) of avery thin layer of index nil' > n7 and nl < n2, the vectorsum di + 2 + 3 at minimum reflectance in air is indi-cated in Fig. 6. For this case, 613 is not (2K + 1)7r, andas a result Xk is not inversely proportional to (2K + 1).Also, if the medium is acetone, for example, di is dimin-
b
C
e
Fig. 4. Immersion cell, customary orientation: a, opaquevane; b, thin quartz cover plate; c, immersion medium; d, brassholder, flame blackened, notched at top to control bubble forma-
tion; e, specimen, wedge-shaped, with film up.
Table II. Absorbing Films, Interference Wavelengths (A) vs noa
Fig. 5. Transparent bilayer. Very thin layer of index ni'at (a) the medium-film interface, and (b) the film-substrate
interface.
IMAG
I
Il
a_ 2°2
-,3
-___-__ -REAL
0
Fig. 6. Vector sum di for components 1, 2, 3 of Fig. 5(a), '0 <'1, 771' > 71, 71 < n2- Shown for air immersion at minimum reflec-tance, i.e., at Nk for K = 0. For second-order films, 13 is
2 rgreater than above sketched 13, for third-order 4 7r greater, etc.
III. The effect of a very thin layer of refractive indexw' n at the film-substrate interface, Fig. 5(b), is notnoticeable except at no very close to nm, and in a custom-
I l I l I l I
0.5
0 - - - - - - - - - -
77
0
WAVELENGTH
Fig. 7. Change of optical density with no,, transparent bilayer ofFigs. 5(a) and 6. no < -qi.
ished from its value in air with the result that Xk in-creases (see Sec. II. D, Fig. 11). Also, because of inter-nal reflection within the film, interference in generaldoes not go to zero. but rather through a minimum asshown in Fig. 7. Apparent, but not true, absorptionoccurs in the ir. Such effects have been observed withthin overcoats of LaF3 , (LaF3)> (MgF2), as shownin Fig. 8. The effects were described previously inRef. 6 in connection with the observed ageing char-acteristics of MgF2 films.
In a similar fashion, the other possibilities of Fig. 5have been treated and the results are presented in Table
4
0:
z-J
as
z
L
wI-
z:z
70
Fig. 8. MgF2 - 0.4 ,. thick on soft glass, overcoated with - 22A* of LaF3 as per Fig. 5(a). (a) Amo vs o, note interference goesthrough a min at 0 - ai, but does not disappear. (b) k (K = 2)vs '10. (*As measured with deposition monitor, may be under-
Table Ill. Bilayered Transparent Films, Shift of Xk
with Increasing no
Case 1. Very thin layer at q1l > 77i Xk increases with allmedium-film inter- mediaface, Fig. 5(a). rql' < al Xk decreases with all
media
Case 2. Very thin layer at '1l' > al Xk decreases but only atfilm-substrate inter- 70 - 71
face, Fig. 5(b). is' < -qi Tk increases but only at
'10 1
/
(a) (b)
Fig. 9. Immersion orientations: (a) customary, and (b) re-versed. For (b) a special holder is used.
ary immersion series could be missed entirely. Accord-ing to calculations of this type, the dependence of Xkupon no for fluoride films on UO2 0and ThO2 (see Table I)indicates a very thin layer -20 A thick of slightly lowerrefractive index at the film-substrate interface. WithThO2 the question of homogeneity is especially pertinentto us because the optically derived kinetics indicate anincubation period for the HF(g) + ThO2 reactionwhich, according to these later considerations, cannot beexplained in terms of optical structure within the film. 10With regard to the reactive formation of UF4 on U02,the effect of absorption in the substrate has an order ofmagnitude greater effect on the optically derivedkinetics than inhomogeneity, 1 and from the immersiondata with Xk increasing only at n7o - ni, we conclude thatinhomogeneity may be a larger factor than slight ab-sorption in the film. In assessing the optically derivedkinetic data for such gas-solid reactions, the relativemagnitudes of these optical effects have to be con-sidered.
With a very thin layer of lower index at the medium-film interface, Xk decreases with increasing no, and theplot of Ama, vs no is similar to the one obtained with trueabsorption. The question then is raised of whether it ispossible to distinguish unambiguously between absorp-tion and inhomogeneity with the reflectance immersion
method. For the general case the answer has to be no.In particular, if there is inhomogeneity in addition toabsorption a satisfactory description may be impossible.In isolated cases, the major effect may be identified.For example, if Xk increases with immersion the majoreffect is not absorption. Under other certain specifiedconditions a distinction between absorption and nonuni-formity may be obtained as described below.
D. ReversalOne procedure to distinguish between inherent ab-
sorption and multilayering for a single film is to measureXk in both the customary and reversed orientations asshown in Fig. 9. Care is taken in both instances tomeasure only the light reflected from the surface withthe film and to be near normal incidence.
To demonstrate the effect of reversal for transparentmultilayers, consider the case shown in Fig. 5(a) for ni'> n1, No = 1, X1 < n2 and perform the vector sum of Fig. 6.The interfaces and indexing are given in Fig. 10. Theamplitude sum U, + 62 + U3 and di' + d2' + d3' areshown in Fig. 11; again as in Fig. 6 multiple reflectionsare not included. The effect of diminishing l and a'by increasing no is the same in both the customary andreversed orientations. In both cases, at minimum re-flectance 613 and 613" decrease as di and V3' decrease, withthe result that Xk increases. Experimentally this effecthas been confirmed for very thin layers of LaF3 (7 1.56) on MgF2 (X7 - 1.385) as shown in Fig. 12. For allfour cases of a transparent bilayer given in Table III,reversal does not change the dependence of Xk upon no.
For absorbing films, the effect of reversal is differentfrom the bilayer case: reversal shifts Xk' and causes itto increase with increasing n0. The explanation of thiseffect follows from the Fresnel ratios and the vectorsum,
Ei
7;
17,
(a) (b)
Fig. 10. Transparent bilayer, labeling of components:tomary orientation, and (b) reversed.
(a) cus-
November 1969 / Vol. 8, No. 11 / APPLI ED OPTICS 2181
I MAG
, 133_ _,-----
a__ -r --- KEAL
(a)
IMAG
3 - -AL
- -.L- FA
a21
IMAG
a ,. -- 83 .
02 L 5 REAL
2 a
Mb
served that immersion spectrophotometry is a sensitivetest for multilayering and absorption, and further if thesubstrate is transparent a simple reversal can be used todiscriminate between the two.
Clearly there are limitations to the method. By thevery nature of the approach, the specimen is exposed toair and to pure organic solvents. Reactive, highly
IMAG
03 D
'2
(d)(c)
REAL
Fig. 11. Vector sums 2& and 2di' at min reflectance for Fig. 10:(a)(b) customary and (c)(d) reversed orientation; (a) and (c), inair, (b) and (d), in 1 < < 77i. Reference real positive axis for(a,c) is l, for (c,d) a,'. Axes chosen such that 13 and i13" increase
in counter clockwise direction.
In Fig. 13 the ratios F = (l* - o)/(n1l* + 0), i =
(2 - 1*)/(2 + n1*), 1' = (1* - 2)/(l* + 2), and 2'= (o - nl*)/(nqo + nml*) so that = -r 2 ' and 2 = - 1'.The interference equations for normal incidence and
* = n7 + i are:
(customary) X - Xk[2K + 1 - (02 - )/ir /4,1.
(reversed) X X k'[2K + 1 - (02' - 0i')/i]/ 4 ni.
4
I-Lzw-JW4
0Z
IL
La.I.
Z
(1)
But since F1 = - 2 ' and 2 = -F', then 02' = 0, + rand 0°' = 02 + r so that:
(customary) X - X7k[2K + 1 - (02 - 0)/7r]/4ni,
(reversed) X X k'[2K + 1 + (02 - 0i)/ir/41,.(2)
The phase shifts operate in opposite directions. FromEq. (2), Xk = Xk only at 02 = 0 + r, i.e., at o = 2, butin general Xk' id X. Furthermore, for l > o and o <772, Xk > Xk', Xk decreases with increasing o (see Sec.II. C), but ,)' increases. These effects are observed forabsorbing U0 2 films vapor-deposited onto quartz asshown in Fig. 12.
Thus a simple reflectance test to distinguish betweenabsorption and multilayering is to reverse the specimenand to measure Xk/ in various media. There are obvi-ous limitations to this approach such as (1) the sub-strate has to be transparent enough to allow a measure-ment of Xk', which unfortunately eliminates metal sub-strates, and (2) with both inhomogeneity and absorp-tion present in the same film only the major effect isdetermined. However, for films deposited on trans-parent substrates, the approach holds promise of afford-ing another means of characterization.
ConclusionA variety of optical interference layers have been
examined with immersion spectrophotometry and dis-cussed. In the study of these film systems we have ob-
77
Fig. 12. Interference wavelength vs 70, both customary andreversed orientations. gF 2 film - 0.35 a thick coated withthin layer of LaF3, K = 1. For U0 2 , K = 2 and film - 0.33 u
thick.
I 2
0 V
11.
Fig. 13. Absorbing film of index '11* on a transparent substrate ofindex '12: (a) customary and (b) reversed orientations.
porous or rough layers, or those that show birefringentmicrostructure, cannot be examined in this fashion, andthe films should be at least second- or third-order inoptical thickness. Also, some systems such as anodicoxide layers on Al are inherently unsuited to an accu-rate and thorough immersion study because of the highreflectance ratio 2, or, e.g., with Si films because 77l is somuch greater than the available no. These restrictionsstill leave a large number of materials amenable to thisanalysis, and with reactive films in principle both X, andXk' can be measured with the specimen still in ultrahighvacuum so that, without exposure to air, the reversaltest can be used.
In our studies we have found that reflected light isconsiderably more sensitive than transmitted light toimmersion effects, although in principle both measure-ments should show related behavior. Perhaps more at-tention should be given to transmission studies sincethey are among the ways of obtaining both nql and ki, butto date because of the diminished sensitivity we haveexamined only a few films by immersion-transmissionmeans. Also, as yet we have not examined inho-mogeneous, two component films purposely preparedwith known smooth index gradients. Undoubtedly tosome extent this structure is present in all films, and it isanticipated that the immersion method may be of valuein assigning the sign and relative magnitude of an un-known index gradient. As another extension of the im-mersion concept, a measure of nonspecularly reflectedlight in a fashion similar to the one reported by HaroldBennett'2 with the specimen immersed may helplocalize microgranularity within a film. In combina-
tion with such techniques, the immersion method whereapplicable holds promise of being useful in the char-acterization of optical thin films.
This work was performed under the auspices of theU.S. Atomic Energy Commission.
W. P. Ellis is on research leave at the University ofVirginia, Department of Materials Science, Charlottes-ville, Virginia 22904 during the 1968-9 academic year.
References1. E. M. Chamot and C. W. Mason, Handbook of Chemical
Microscopy (John Wiley & Sons, Inc., New York, 1958), Vol.1.
2. Robert R. Stromberg, Elio Passaglia, and Daniel J. Tutas,in Ellipsometry in the Measurement of Surfaces and Thin Films,E. Passaglia, R. R. Stromberg, and J. Kruger, Eds. (NationalBureau of Standards Misc. Publ. 256, Washington, D.C.,1964), p. 281.
3. 0. S. Heavens, Physics of Thin Films, G. Hass and R. E.Thun, Eds. (Academic Press, Inc., New York, 1964), Vol. 2,p. 193.
4. W. P. Ellis, J. Opt. Soc. Amer. 53, 613 (1963).5. W. P. Ellis and R. M. Lindstrom, Opt. Acta 11, 287 (1964).6. A. D. Mulford, L. D. Allen, and W. P. Ellis, J. Opt. Soc.
Amer. 57, 763 (1967).7. W. P. Ellis, J. Phys. (Paris) 25, 21 (1964).8. W. P. Ellis and E. D. Megarity, J. Opt. Soc. Amer. 54, 225
(1964).9. W. F. Koehler, J. Opt. Soc. Amer. 45, 934 (1955); J. M.
Bennett and M. J. Mooty, Appl. Opt. 5, 41 (1966).10. R. M. Lindstrom and W. P. Ellis, J. Chem. Phys. 43, 994
(1965).11. W. P. Ellis, J. Chem. Phys. 39, 1172 (1963).12. H. E. Bennett, J. Opt. Soc. Amer. 56, 1423A (1966).
November
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