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Analysis of Multiple-Angle Ellipsometry of Uniaxial Ultrathin Organic Films at the Air-Water Interface and Determination of the Refractive Indices of Behenic Acid Monolayers M. Paudler, J. Ruths, and H.Riegler* Institut fur Physikalische Chemie, Welder- Weg 11, Universitat Mainz, 0-6500Mainz, Germany Received April 23, 1991. In Final Form: August 23, 1991 Multiple-angleellipsometryof uniaxial ultrathin films is discussed analytically and by computer analysis. The various relations between angle of incidence, layer thickness, and refractive indices are presented. It is shown that multiple-angle ellipsometry conveys sets of experimental data well suited for computer analysis with high redundancy by exposing systematic experimental errors. The ellipsometric data allow no unique characterization of ultrathin, uniaxial, nonabsorbing films and it is demonstrated that the derived layer thickness depends strongly on assumptions of the layer anisotropy. For typical experimental results the allowed range of combinations of the refractive index values as a function of an assumed layer thickness is presented. Calculations show that certain combinations of refractive indices will result in an ellipsometric angle &A= 0 for all angles of incidence. Some of these combinations are physically realistic and might in fact be experimentally accessible. The potential of ellipsometric experiments to characterize ultrathin films is demonstrated by combining the method with data known from X-ray diffraction. Thus we have determined the refractive indices for a behenic acid monolayer in the S and CS phase, respectively, to nxS = 1.47, n2S = 1.54 and nxCS= 1.48, nPCS= 1.56. These values are deduced from the measured ellipsometric angles, a Lorentz-Lorenz approximation for the refractive indices, and structural data known from X-ray measurements.
Introduction Ellipsometry is a fast, nondestructive, and convenient optical method for in situ thin-film Although it is best suited for comparatively thick films (>lo00 A) it has also been employed successfully to investigate ultrathin organic films like Langmuir-Blodgett multilayers on solid substrates (LB films) or even Langmuir monolayers on aqueous sub phase^.^-^ For thicker films (>lo0 A) two parameters, the two ellipsometric angles, A and \k, can be assessed, whereas for ultrathin films only one parameter, A, is measurable.2 This renders the unambiguous ellipsometric characterization of ultrathin, nonabsorbing films impossible, because one ellipsometric measurement parameter is affected by two independent film properties: the geometrical thickness and the refractive index. This complication holds the more for LB films and Langmuir monolayers. Their refractive index is anisotropic due to their inherent high molecular ordering.8-l1 Langmuir monolayers are optically uniaxial or biaxial, if the molecules have an overall uniform tilt or a highly ordered molecular packing with low symmetry. However, usually the diameter of the ellipsometric mea-
surement spot (- 1mm diameter) largely exceeds the size of domains of uniform tilt or bond orientation (-20 pm diameter).12J3 A uniaxial interpretation of ellipsometric experiments with the optical axis normal to the surface is therefore often sufficient.ll This orientation of the optical axis reflects the inherent symmetry of the molecular packing with the molecules on the average oriented normal to the surface or with a tilt angle distribution which is rotation symmetrical to the surface normal. It has been shown that for fatty acids and phospholipids the difference between the ordinary and extraordinary refractice index is not very high (less than lo%).+" Nevertheless, the impact of even this little pronounced anisotropy on the interpretation of ellipsometric data can be quite substantial and must therefore be considered, as will be shown below. Various refinements of the ellipsometric method have been explored to alleviate the ambiguity of the interpretation of simple ellipsometric experiments and to reduce the number of variable parameters (one measurable parameter, A, versus three parameters to be determined: the ordinary and the extraordinary refractice index and the thickness). Experiments a t different wavelengths had been pro(1) Azzam, R. M; Bashara, N. M. Ellipsometry and Polarized Light; posed to obtain sufficient data.14 However, it turned out North Holland: New York, Paperback edition 1987. that a unique characterization of uniaxial thin films by (2) McCrackin,F . L.;Passaglia, E.; Stromberg, R. R.; Steinberg, H. L. multiple wavelength ellipsometry is only possible if both J. Res. Natl. Bur. Stand., Sect. A 1963, 67A (4), 363. (3) Kim,M. W.;Sauer,B.B.;Yu,H.;Yazdanian,M.;Zografi,G.Lang- the substrate and the incident medium are highly dismuir 1990, 6, 236. persive.l5 (4) Engelsen, D. D.; Koning, B. D. J. Chem. Soc., Faraday Trans. 1 Multiple-angle ellipsometry also proved not to convey 1974. 70., ~1603. -. - - (5)Rasing, T.; Hsiung, H.; Shen, Y. R.; Kim, M. W. Phys. Reu. A: Gen. additional information.16-18 Nevertheless, this modifica-
Phys. 1988, 37 (7), 2732. ( 6 ) Kawaguchi, M.; Tohyama, M.; Mutoh, Y.; Takahashi, A. Langmuir 1988, 4, 407. (7) Kawaguchi, M.; Tohyama, M.; Takahashi, A. Langmuir 1988,4, A1 1
(8) De Smet, D. J. J. Opt. SOC.A m . 1974, 64 (5), 631. (9) Ducharme, D.;Max, J.; Salesse, C.; Leblanc, R. M. J. Phys. Chem. 1990, 94, 1925. (10) Engelsen, D. D. Surf. Sci. 1976, 56, 272. A m . 1971, 61 (ll), 1460. (11) Engelsen, D. D. J. Opt. SOC.
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(12) Mohwald, H. Thin Solid Films 1988, 159, 1. (13) Garoff, S. Thin Solid Films 1987, 152, 49. (14) Ayoub, G. T.; Bashara, N. M. J. Opt. SOC.Am. 1978,68 (7), 978. Am. (15) Antippa, A. F.;Leblanc, R. M.; Ducharme, D. J. Opt. SOC. 1986, 3 (ll),1794. (16) Johnson, J. A.; Bashara, N. M. J. Opt. SOC.Am. 1971,61, ( 4 )457. (17) Ibrahim, M.M.;Bashara, N. M. J. O p t . SOC.Am. 1971, 61 (12), 1622.
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Langmuir, Vol. 8, No.1, 1992 185
Multiple-Angle Ellipsometry of Ultrathin Films tion is beneficial for the optimum fitting of the experimental data and for minimizing errors, especially by reducing systematic errors. simulation^^^ and model calculationsg have also been used to support ellipsometry in film characterization. This procedure has always the drawback of possibly incorporating too many a priori model assumptions to obtain secure data. The easiest way out of this dilemma is clearly to not rely solely on ellipsometry but acquire sufficient independent data from a complementary method. Excellently suited for this purpose are X-ray data, which have become available in recent times even for Langmuir monolayers on the water subphase.20 From these X-ray diffraction studies the geometrical thickness of the films can be derived, thus reducing the parameters for a complete layer characterization. In the following paragraphs we will first dispose by analytical methods and by computer analysis in some detail the relations between the various parameters of uniaxial, ultrathin, and nonabsorbing films. This will clarify parameter interdependencies and show some interesting theoretical features. Then, in a series of experiments we will determine the refractive indices of behenic acid monolayers on water by combining our ellipsometric measurements with data known from X-ray diffraction.20 Refractive indices and the anisotropy of ultrathin organic films are optical constants relevant for their application in integrated optics and waveguiding. They also reflect the molecular ordering and packing of the film and thus give insight into the film structure. Ellipsometry measures averaged optical and geometrical properties from areas of several pm2to mm2depending on the selected measurement spot size. These data are complementary to data obtained by X-ray reflection and diffraction. Xray reflection probes the thickness and roughness of layer areas averaged over comparatively large areas of several cm2,whereas X-ray diffraction investigates only the molecular packing of ordered parts of the film. The ellipsometric measurement investigates macroscopic properties of selected film spots. The data obtained include defects and disordered parts of the film and thus reflects local macroscopic properties of the films.
Experimental Section Behenic acid (docosanoic acid) was obtained from Sigma (99+% purity) and used without further purification. The monolayers were spread from a chloroform stock solution on a water subphase (millipore water) without additional ions. The homemade, all-Teflon coated trough was covered with acrylic glass for dust protection. A Wilhelmy system was used for measuring the surface pressure. The trough temperature was regulated by a thermostat. The subphase temperature was controlled additionally by a separate temperature sensor in the subphase. The isobars were run slowly (
