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Infrared ellipsometric analysis of organic film-on-substrate samples
Thin Solid Films 313]314 Ž1998. 708]712
Infrared ellipsometric analysis of organic film-on-substrate samples U Arnulf Roseler , Ernst-Heiner Korte ¨
Institut fur ¨ Spektrochemie und angewandte Spektroskopie, Institutsteil Berlin, 12484 Berlin, Germany
Abstract The characterization of a thin organic coating on an organic substrate by spectroscopic infrared ellipsometry is outlined and applied to the fluorinated surface of the polymer wall of a motorcar fuel tank. Q 1998 Elsevier Science S.A. Keywords: Infrared ellipsometry; Optical constants; Organic coatings; Layer thickness
1. Introduction The oscillator strengths of most molecular vibrations are much smaller than those of typical reststrahlen bands. As a consequence, the features of the ellipsometric spectra are comparatively weak in the infrared range and this may become a problem in studies of thin organic layers. After having used spectroscopic infrared ellipsometry w1,2x to characterize layers in semiconductors quantifying their thickness reliably down to a few nanometers w3,4x, we were interested in exploring the analytical potential of this method for organic layers. It turned out that it can be applied even if the thickness is 10y3 or 10y4 times smaller than the wavelength of the analyzing radiation w5x. Among the reasons why more detailed and more reliable information on such thin layers can be gathered by infrared ellipsometry in comparison with conventional techniques are: two spectra are obtained rather than one spectrum; quite a number of experimental inadequacies are compensated for by using ratios of spectra only;
v
v
U
Corresponding author. Fax: q49 30 63923544; e-mail: [email protected] 0040-6090r98r$19.00 Q 1998 Elsevier Science S.A. All rights reserved PII S0040-6090Ž97.00982-6
v
v
the ordinate of these spectra is quantitatively specified; and these results are interpreted quantitatively by comparing to the optical theory.
As an example, the reflection from a surface layer on a substrate can be modelled on the basis of Fresnel’s and Airy’s equations. Comparing the calculated result with the measured one indicates the validity of the assumptions on the layered structure. Even slight inadequacies of the model become obvious due to the width of the infrared spectral range wherein the wavelength varies by more than one order of magnitude. For this article we did not focus on ultrathin organic layers but, rather, on the different challenge of two quite similar polymers one on top of the other. Here we report on the basic steps of evaluation; a further discussion including other techniques is in progress. 2. Sample and data acquisition For economic and technical reasons, fuel tanks of motorcars are increasingly made from polymers rather than from metals. Materials based on, e.g. polyethylene ŽPE. provide the necessary stability at moderate weight, but do not prevent the fuel from penetrating the plastic moiety. For this reason the inner surface
A. Roseler, E.-H. Korte r Thin Solid Films 313]314 (1998) 708]712 ¨
of the tank is treated with fluorine, thus generating a sealant sufficiently thick to be impermeable to the hydrocarbons. With conventional spectroscopic techniques, such as infrared transmission or attenuated total reflection the sample is hardly addressable because it strongly absorbs and the surface is neither planar nor smooth. For this study, we have used an infrared ellipsometer constructed and built in our laboratory. The device is attached to a Bruker IFS 55 Fourier-transform spectrometer. The analyzer in front of the DTGS detector is set to an azimuth of 458 with respect to the plane of reflection and full spectra are recorded with the polarizer at 08 and 908 as well as at 458 and 1358 Žwith a repeatability better than 0.018.. One pair of spectra is accumulated alternately and divided, subsequently the other pair is recorded. This procedure takes slightly more time than collecting all four positions in sequence as has been used before; however, the new approach is more effective at removing absorption bands due to atmospheric H 2 O and CO 2 . The two ratios are readily converted into the ellipsometric parameters C and D. These parameters are defined in terms of the ratio of the complex reflection coefficients r 5 for radiation polarized parallel and r H for radiation polarized perpendicular to the plane of reflection:
D s r 5rr H s tan C exp Ž iD . .
Ž1.
In other words, tan C is the ratio of the reflection amplitudes and D is the difference between the phase shifts for the two components w1x. A second set of spectra is taken after a retarder prism was placed in the optical path behind the sample. This improves the sensitivity of measuring D in intervals where otherwise it is poor, i.e. around 08 and 1808, and resolves the sign ambiguity over the entire period from 08 to 3608 w1x. The state of polarization of the radiation leaving the spectrometer is measured at least once a week and taken into account by a calibration file.
709
Fig. 1. Ellipsometric parameters C and D in the infrared range for a surface-fluorinated polyethylene sample. Index F refers to the fluorinated front surface, index B to the back surface, i.e. the substrate.
leads directly to spectra in the optical constants, i.e. the refractive index n and the absorption index k. These are specific to the material in general and especially in the infrared range, since it comprises all the vibrational structure of the molecules. The evaluation of the back surface spectra results in the optical constants of the substrate presented in Fig. 2. It is noticeable that k does not approach zero between the bands, however, this can be ascribed to the carbon black which is commonly used as filler. Since the fluorinated layer is infrared transparent, the ellipsometric spectra of this surface are determined by the optical constants of the substrate as well as the optical constants of the layer, plus the layer thickness. There is no way to analytically invert the equations for the layer characteristics. Instead, an iterative approach must be applied in which a model of the sample is developed. The spectra to be ex-
3. Evaluation The spectra of the ellipsometric parameters measured at the front Žindex F. and back Žindex B. surfaces of the sample described above are presented in Fig. 1. A first inspection indicates that one set of spectra refers to bulk material Žspectra with horizontal background. while the slope of the other spectra points towards a thin surface layer. The strong features around 1200 cmy1 in both the oblique spectra are due to the C]F stretching vibrations and make clear that these spectra probe the fluorinated layer. For a semi-infinite sample, standard evaluation
Fig. 2. Refractive index n and absorption index k of the substrate as calculated from the ellipsometric spectra shown in Fig. 1.
710
A. Roseler, E.-H. Korte r Thin Solid Films 313]314 (1998) 708]712 ¨
pected are easily calculated for an angle of incidence w 0 and a thickness d1 using Airy’s equation rA s Ž r 01 q r 12 X . r Ž 1 q r 01 r 12 X . 2 with ln X s 4p i ˜ ¨d1 Ž n1 q i k 1 . y n20 sin 2 w 0
Ž2. 1r2
.
Here ˜ ¨ denotes the wavenumber; the reflection coefficients r 01 at the interface between the air Žindex 0. and the layer Žindex 1. and r 12 at the interface between the layer and the substrate Žindex 2. are calculated from Fresnel’s equations. The ratio of the coefficients rA for parallel and perpendicular polarizations is divided into tan C and D as before ŽEq. Ž1... Using the measured optical constants of the substrate ŽFig. 2., the calculated spectra are fitted to the measured ones by adjusting n1 , k 1 and d1. However, fitting with three variables is not always straightforward. Advantageously, the infrared spectra of organic molecules exhibit ranges of negligible absorption, in particular in the section above 2000 cmy1 . In such a case just two quantities are to be determined from two experimental results. Furthermore, the lack of measurable absorption bands within a spectral interval implies that no dispersion occurs and that the refractive index remains at its background level n` . Since the thickness must be independent of the wavelength and at the same time the refractive index is virtually constant, noise can be reduced by averaging and any failure of the basic assumption becomes obvious. We applied Reinberg’s algorithm w6x as outlined below to obtain the results presented in Fig. 3. The refractive index is found to be n` s 1.27 and the thickness of the fluorinated layer to be 340 " 5 nm. Deviations from these values can be attributed to unbalanced absorption bands of the substrate Ždue to low spectral resolution; in such an interval approx. 2800]3000 cmy1 data are omitted in Fig. 3. and of atmospheric components, or to the increase of k when approaching the fingerprint range. The algorithm proposed by Reinberg w6x for nonabsorbing samples, is based on a quadratic equation derived from the ratio D s r 5 Arr H A of the Airy coefficients Eq. Ž2.: Ž D G y C. X 2 q Ž D E y B . X q Ž D Dy A. s 0 with As r 5 01 , B s r 512 q r 5 01 r H 01 r H 12 , C s r 512 r H 01 r H 12 , Ds r H 12 , E s r H 12 q r 5 01 r 512 r H 01 and
Ž3.
Fig. 3. The refractive index n and the geometric thickness d of the fluorinated layer as derived by the Reinberg algorithm.
G s r 5 01 r 512 r H 12 where the reflection coefficients r are defined as above with an additional index stating parallel or perpendicular polarization. The coefficients are calculated using the optical constants of the substrate and air, respectively, and an estimated value of the refractive index of the layer n1. Substituting the experimental results into D , the quadratic equation can be solved for X. On the other hand according to its definition, < X < must equal unity when k 1 is taken to be zero. Therefore n1 is varied until a solution < X < s 1 is obtained. This gives n` and the geometric thickness d1 is deduced from arg X. Basically the sensitivity of Reinberg’s algorithm to uncertainties of the input depends on the properties of the sample, as does the precision of the results for n` and d1. However, we found this procedure to be widely applicable, in particular to samples with an organic substrate, whereas, e.g. for metal substrates different schemes may be preferred w5x. The next step is to model the molecular vibrations of the layer material in the dielectric function ˆ e s n`2 2 q SŽ e 9j q i e 0 j . s Ž n q i k . . The contribution from vibration j is taken into account by
e jX s
2
½ FŽ ˜¨ y ˜¨ . r Ž ˜¨ y ˜¨ . q G ˜¨ 5 e s ½ FG ˜ ¨r Ž ˜ ¨ y˜ ¨ . qG ˜ ¨ 5 Y j
2 0
2
2 0
2 0
2
2
2
2
2
2
j
2
j
Ž4.
and its position ˜ ¨ 0 , strength F and damping G are adjusted to match the experimental results C and D. The final optical constants obtained in the C]F stretching vibration range for the sample under consideration are presented in Fig. 4. In Fig. 5 the spectra of the ellipsometric parame-
A. Roseler, E.-H. Korte r Thin Solid Films 313]314 (1998) 708]712 ¨
711
Fig. 4. The optical constants n and k of the fluorinated polyethylene in the C]F valence vibration range, modelled by an oscillator fit to the ellipsometric data within this range.
ters of the fluorinated layer on top of the substrate from Fig. 1 are plotted together with the simulated ones. The simulation was carried out using: Ži. the optical constants of the substrate, as derived from the ellipsometric measurement at the outer surface; Žii. n` and the thickness of the surface layer, as derived by Reinberg’s algorithm; and Žiii. the contributions to k and n from the fitted oscillators. Anisotropy may be present, however, its orientation is unknown and could vary within the area sampled. Since no indication of its influence was observed, any anisotropy was neglected. The interface between the substrate and the fluorinated layer is believed to be sharp, otherwise the model would not lead to consistent results over such a wide spectral range. Considering the extended ordinate scales of Fig. 5, the agreement provides convincing evidence that the model developed here represents the real sample. 4. Conclusions As a reflection technique, spectroscopic infrared ellipsometry provides non-destructive and contact-free analysis even for non-ideal surfaces. Since the infrared spectra of organic molecules exhibit intervals of negligible absorption, spectroscopic infrared ellipsometry grants non-destructive and contact-free analysis even of technical surfaces which cannot be studied with transmission or attenuated total reflection techniques. Since the infrared spectra of organic molecules comprise intervals of negligible absorption, the Reinberg algorithm provides us with a robust way of determining the refractive index and the geometric thickness. The point-by-point evaluation indicates where inconsistencies come into play and otherwise facilitates efficient averaging. The two results are
Fig. 5. Comparison of experimental and simulated spectra Žthick and thin lines, respectively. of the ellipsometric parameters tan C and D deduced for reflection at the front surface.
indispensable input for a subsequent oscillator fit when the vibrational structure of the molecules is modelled. The surface-fluorinated polymer system is comparatively difficult to analyze since it is a combination of weakly absorbing, chemically related compounds. It was demonstrated that even this can be characterized in detail by spectroscopic infrared ellipsometry. Acknowledgements The authors are indebted to Prof. Dr. Karl Molt, University of Duisburg, for stimulating discussions and Dr. Karoly Brenner, Messer Griesheim GmbH, Duisburg, for the samples. The financial support by the Senatsverwaltung fur ¨ Wissenschaft, Forschung und Kultur des Landes Berlin and by the Bundesministerium fur ¨ Bildung, Wissenschaft, Forschung und Technologie is gratefully acknowledged.
712
A. Roseler, E.-H. Korte r Thin Solid Films 313]314 (1998) 708]712 ¨
References w1x A. Roseler, Infrared Spectroscopic Ellipsometry, Akademie¨ Verlag, Berlin, 1990. w2x A. Roseler, Spektroskopische Infrarot-Ellipsometrie, in: H. ¨ Gunzler et al. ŽEds.., Analytiker Taschenbuch Bd. 14, ¨ Springer-Verlag, Berlin, 1996, p. 89.
w3x M. Weidner, A. Roseler, Phys. Status Solidi A 130 Ž1992. 115. ¨ w4x A. Markwitz, H. Baumann, W. Grill, B. Heinz, A. Roseler, E.F. ¨ Krimmel, K. Bethge, Fresenius J. Anal. Chem. 353 Ž1995. 734. w5x A. Roseler, R. Dietel, E.H. Korte, Mikrochim. Acta wSuppl.x 14 ¨ Ž1997. 657. w6x A.R. Reinberg, Appl. Opt. 11 Ž1972. 1273.
Infrared ellipsometric analysis of organic film-on-substrate samples U Arnulf Roseler , Ernst-Heiner Korte ¨
Institut fur ¨ Spektrochemie und angewandte Spektroskopie, Institutsteil Berlin, 12484 Berlin, Germany
Abstract The characterization of a thin organic coating on an organic substrate by spectroscopic infrared ellipsometry is outlined and applied to the fluorinated surface of the polymer wall of a motorcar fuel tank. Q 1998 Elsevier Science S.A. Keywords: Infrared ellipsometry; Optical constants; Organic coatings; Layer thickness
1. Introduction The oscillator strengths of most molecular vibrations are much smaller than those of typical reststrahlen bands. As a consequence, the features of the ellipsometric spectra are comparatively weak in the infrared range and this may become a problem in studies of thin organic layers. After having used spectroscopic infrared ellipsometry w1,2x to characterize layers in semiconductors quantifying their thickness reliably down to a few nanometers w3,4x, we were interested in exploring the analytical potential of this method for organic layers. It turned out that it can be applied even if the thickness is 10y3 or 10y4 times smaller than the wavelength of the analyzing radiation w5x. Among the reasons why more detailed and more reliable information on such thin layers can be gathered by infrared ellipsometry in comparison with conventional techniques are: two spectra are obtained rather than one spectrum; quite a number of experimental inadequacies are compensated for by using ratios of spectra only;
v
v
U
Corresponding author. Fax: q49 30 63923544; e-mail: [email protected] 0040-6090r98r$19.00 Q 1998 Elsevier Science S.A. All rights reserved PII S0040-6090Ž97.00982-6
v
v
the ordinate of these spectra is quantitatively specified; and these results are interpreted quantitatively by comparing to the optical theory.
As an example, the reflection from a surface layer on a substrate can be modelled on the basis of Fresnel’s and Airy’s equations. Comparing the calculated result with the measured one indicates the validity of the assumptions on the layered structure. Even slight inadequacies of the model become obvious due to the width of the infrared spectral range wherein the wavelength varies by more than one order of magnitude. For this article we did not focus on ultrathin organic layers but, rather, on the different challenge of two quite similar polymers one on top of the other. Here we report on the basic steps of evaluation; a further discussion including other techniques is in progress. 2. Sample and data acquisition For economic and technical reasons, fuel tanks of motorcars are increasingly made from polymers rather than from metals. Materials based on, e.g. polyethylene ŽPE. provide the necessary stability at moderate weight, but do not prevent the fuel from penetrating the plastic moiety. For this reason the inner surface
A. Roseler, E.-H. Korte r Thin Solid Films 313]314 (1998) 708]712 ¨
of the tank is treated with fluorine, thus generating a sealant sufficiently thick to be impermeable to the hydrocarbons. With conventional spectroscopic techniques, such as infrared transmission or attenuated total reflection the sample is hardly addressable because it strongly absorbs and the surface is neither planar nor smooth. For this study, we have used an infrared ellipsometer constructed and built in our laboratory. The device is attached to a Bruker IFS 55 Fourier-transform spectrometer. The analyzer in front of the DTGS detector is set to an azimuth of 458 with respect to the plane of reflection and full spectra are recorded with the polarizer at 08 and 908 as well as at 458 and 1358 Žwith a repeatability better than 0.018.. One pair of spectra is accumulated alternately and divided, subsequently the other pair is recorded. This procedure takes slightly more time than collecting all four positions in sequence as has been used before; however, the new approach is more effective at removing absorption bands due to atmospheric H 2 O and CO 2 . The two ratios are readily converted into the ellipsometric parameters C and D. These parameters are defined in terms of the ratio of the complex reflection coefficients r 5 for radiation polarized parallel and r H for radiation polarized perpendicular to the plane of reflection:
D s r 5rr H s tan C exp Ž iD . .
Ž1.
In other words, tan C is the ratio of the reflection amplitudes and D is the difference between the phase shifts for the two components w1x. A second set of spectra is taken after a retarder prism was placed in the optical path behind the sample. This improves the sensitivity of measuring D in intervals where otherwise it is poor, i.e. around 08 and 1808, and resolves the sign ambiguity over the entire period from 08 to 3608 w1x. The state of polarization of the radiation leaving the spectrometer is measured at least once a week and taken into account by a calibration file.
709
Fig. 1. Ellipsometric parameters C and D in the infrared range for a surface-fluorinated polyethylene sample. Index F refers to the fluorinated front surface, index B to the back surface, i.e. the substrate.
leads directly to spectra in the optical constants, i.e. the refractive index n and the absorption index k. These are specific to the material in general and especially in the infrared range, since it comprises all the vibrational structure of the molecules. The evaluation of the back surface spectra results in the optical constants of the substrate presented in Fig. 2. It is noticeable that k does not approach zero between the bands, however, this can be ascribed to the carbon black which is commonly used as filler. Since the fluorinated layer is infrared transparent, the ellipsometric spectra of this surface are determined by the optical constants of the substrate as well as the optical constants of the layer, plus the layer thickness. There is no way to analytically invert the equations for the layer characteristics. Instead, an iterative approach must be applied in which a model of the sample is developed. The spectra to be ex-
3. Evaluation The spectra of the ellipsometric parameters measured at the front Žindex F. and back Žindex B. surfaces of the sample described above are presented in Fig. 1. A first inspection indicates that one set of spectra refers to bulk material Žspectra with horizontal background. while the slope of the other spectra points towards a thin surface layer. The strong features around 1200 cmy1 in both the oblique spectra are due to the C]F stretching vibrations and make clear that these spectra probe the fluorinated layer. For a semi-infinite sample, standard evaluation
Fig. 2. Refractive index n and absorption index k of the substrate as calculated from the ellipsometric spectra shown in Fig. 1.
710
A. Roseler, E.-H. Korte r Thin Solid Films 313]314 (1998) 708]712 ¨
pected are easily calculated for an angle of incidence w 0 and a thickness d1 using Airy’s equation rA s Ž r 01 q r 12 X . r Ž 1 q r 01 r 12 X . 2 with ln X s 4p i ˜ ¨d1 Ž n1 q i k 1 . y n20 sin 2 w 0
Ž2. 1r2
.
Here ˜ ¨ denotes the wavenumber; the reflection coefficients r 01 at the interface between the air Žindex 0. and the layer Žindex 1. and r 12 at the interface between the layer and the substrate Žindex 2. are calculated from Fresnel’s equations. The ratio of the coefficients rA for parallel and perpendicular polarizations is divided into tan C and D as before ŽEq. Ž1... Using the measured optical constants of the substrate ŽFig. 2., the calculated spectra are fitted to the measured ones by adjusting n1 , k 1 and d1. However, fitting with three variables is not always straightforward. Advantageously, the infrared spectra of organic molecules exhibit ranges of negligible absorption, in particular in the section above 2000 cmy1 . In such a case just two quantities are to be determined from two experimental results. Furthermore, the lack of measurable absorption bands within a spectral interval implies that no dispersion occurs and that the refractive index remains at its background level n` . Since the thickness must be independent of the wavelength and at the same time the refractive index is virtually constant, noise can be reduced by averaging and any failure of the basic assumption becomes obvious. We applied Reinberg’s algorithm w6x as outlined below to obtain the results presented in Fig. 3. The refractive index is found to be n` s 1.27 and the thickness of the fluorinated layer to be 340 " 5 nm. Deviations from these values can be attributed to unbalanced absorption bands of the substrate Ždue to low spectral resolution; in such an interval approx. 2800]3000 cmy1 data are omitted in Fig. 3. and of atmospheric components, or to the increase of k when approaching the fingerprint range. The algorithm proposed by Reinberg w6x for nonabsorbing samples, is based on a quadratic equation derived from the ratio D s r 5 Arr H A of the Airy coefficients Eq. Ž2.: Ž D G y C. X 2 q Ž D E y B . X q Ž D Dy A. s 0 with As r 5 01 , B s r 512 q r 5 01 r H 01 r H 12 , C s r 512 r H 01 r H 12 , Ds r H 12 , E s r H 12 q r 5 01 r 512 r H 01 and
Ž3.
Fig. 3. The refractive index n and the geometric thickness d of the fluorinated layer as derived by the Reinberg algorithm.
G s r 5 01 r 512 r H 12 where the reflection coefficients r are defined as above with an additional index stating parallel or perpendicular polarization. The coefficients are calculated using the optical constants of the substrate and air, respectively, and an estimated value of the refractive index of the layer n1. Substituting the experimental results into D , the quadratic equation can be solved for X. On the other hand according to its definition, < X < must equal unity when k 1 is taken to be zero. Therefore n1 is varied until a solution < X < s 1 is obtained. This gives n` and the geometric thickness d1 is deduced from arg X. Basically the sensitivity of Reinberg’s algorithm to uncertainties of the input depends on the properties of the sample, as does the precision of the results for n` and d1. However, we found this procedure to be widely applicable, in particular to samples with an organic substrate, whereas, e.g. for metal substrates different schemes may be preferred w5x. The next step is to model the molecular vibrations of the layer material in the dielectric function ˆ e s n`2 2 q SŽ e 9j q i e 0 j . s Ž n q i k . . The contribution from vibration j is taken into account by
e jX s
2
½ FŽ ˜¨ y ˜¨ . r Ž ˜¨ y ˜¨ . q G ˜¨ 5 e s ½ FG ˜ ¨r Ž ˜ ¨ y˜ ¨ . qG ˜ ¨ 5 Y j
2 0
2
2 0
2 0
2
2
2
2
2
2
j
2
j
Ž4.
and its position ˜ ¨ 0 , strength F and damping G are adjusted to match the experimental results C and D. The final optical constants obtained in the C]F stretching vibration range for the sample under consideration are presented in Fig. 4. In Fig. 5 the spectra of the ellipsometric parame-
A. Roseler, E.-H. Korte r Thin Solid Films 313]314 (1998) 708]712 ¨
711
Fig. 4. The optical constants n and k of the fluorinated polyethylene in the C]F valence vibration range, modelled by an oscillator fit to the ellipsometric data within this range.
ters of the fluorinated layer on top of the substrate from Fig. 1 are plotted together with the simulated ones. The simulation was carried out using: Ži. the optical constants of the substrate, as derived from the ellipsometric measurement at the outer surface; Žii. n` and the thickness of the surface layer, as derived by Reinberg’s algorithm; and Žiii. the contributions to k and n from the fitted oscillators. Anisotropy may be present, however, its orientation is unknown and could vary within the area sampled. Since no indication of its influence was observed, any anisotropy was neglected. The interface between the substrate and the fluorinated layer is believed to be sharp, otherwise the model would not lead to consistent results over such a wide spectral range. Considering the extended ordinate scales of Fig. 5, the agreement provides convincing evidence that the model developed here represents the real sample. 4. Conclusions As a reflection technique, spectroscopic infrared ellipsometry provides non-destructive and contact-free analysis even for non-ideal surfaces. Since the infrared spectra of organic molecules exhibit intervals of negligible absorption, spectroscopic infrared ellipsometry grants non-destructive and contact-free analysis even of technical surfaces which cannot be studied with transmission or attenuated total reflection techniques. Since the infrared spectra of organic molecules comprise intervals of negligible absorption, the Reinberg algorithm provides us with a robust way of determining the refractive index and the geometric thickness. The point-by-point evaluation indicates where inconsistencies come into play and otherwise facilitates efficient averaging. The two results are
Fig. 5. Comparison of experimental and simulated spectra Žthick and thin lines, respectively. of the ellipsometric parameters tan C and D deduced for reflection at the front surface.
indispensable input for a subsequent oscillator fit when the vibrational structure of the molecules is modelled. The surface-fluorinated polymer system is comparatively difficult to analyze since it is a combination of weakly absorbing, chemically related compounds. It was demonstrated that even this can be characterized in detail by spectroscopic infrared ellipsometry. Acknowledgements The authors are indebted to Prof. Dr. Karl Molt, University of Duisburg, for stimulating discussions and Dr. Karoly Brenner, Messer Griesheim GmbH, Duisburg, for the samples. The financial support by the Senatsverwaltung fur ¨ Wissenschaft, Forschung und Kultur des Landes Berlin and by the Bundesministerium fur ¨ Bildung, Wissenschaft, Forschung und Technologie is gratefully acknowledged.
712
A. Roseler, E.-H. Korte r Thin Solid Films 313]314 (1998) 708]712 ¨
References w1x A. Roseler, Infrared Spectroscopic Ellipsometry, Akademie¨ Verlag, Berlin, 1990. w2x A. Roseler, Spektroskopische Infrarot-Ellipsometrie, in: H. ¨ Gunzler et al. ŽEds.., Analytiker Taschenbuch Bd. 14, ¨ Springer-Verlag, Berlin, 1996, p. 89.
w3x M. Weidner, A. Roseler, Phys. Status Solidi A 130 Ž1992. 115. ¨ w4x A. Markwitz, H. Baumann, W. Grill, B. Heinz, A. Roseler, E.F. ¨ Krimmel, K. Bethge, Fresenius J. Anal. Chem. 353 Ž1995. 734. w5x A. Roseler, R. Dietel, E.H. Korte, Mikrochim. Acta wSuppl.x 14 ¨ Ž1997. 657. w6x A.R. Reinberg, Appl. Opt. 11 Ž1972. 1273.