Anal, Chem.
64
systems are also necessary that will provide the chromatographer with all of the capabilities of SFC (e.g., automated pressure and gradient programming). Finally, an analogous SFC/FT-IR interface to the one described in this paper for packed microbore columns should be built for capillary SFC in view of the improved resolution that can be obtained by using wall-coated open tubular columns. A system based on this principle is currently being constructed in our Iaboratory and results will be reported at a later date.
ACKNOWLEDGMENT We wish to thank Analect Instruments and Brownlee Laboratories for the loan of the spectrometer and pump, respectively, used in this work. Registry No. 2-Methyl-1,4-naphthaquinone, 58-27-5;anthraquinone, 84-65-1; anthrone, 90-44-8; acenaphthenequinone, 82-86-0; phenanthrenequinone, 84-11-7.
LITERATURE CITED Hirschfeld, T. L. Anal. Chem. 1980, 52, 197A. Klzer, K. L.; Mantz, A. W.; Bonar, L. C. Am. Lab. (Fairfieid, Conn.) 1975, 7, 85. Vldrine, D. W.; Mattson, D. R. Appl. Spectrosc. 1978, 32, 502. Shafer, K. H.; Griffiths, P. R. Anal. Chem. 1983, 55, 1939. Oleslk, S. V.; French, S . B.; Novotny, M. Chromatographia 1984, 18,
489.
64-68 Jinno, K.; Fujimoto, C. HRC CC, J . High Resoiut. Chromatogr. Chromatogr. Commun. 1981, 4,532. Jinno, K.; Fujimoto, C.; Hirata, Y. Appl. Spectrosc. 1982, 36, 67. Jinno, K.; Fujlmoto, C.; Ishii, D. J . Chromatogr. 1982, 239,625. Fujimoto, C.; Hirata, Y.; Jenno, K. J . Chromatogr. 1985, 332, 47. Kuehl, D.; Griffiths, P. R. J . Chromatogr. Sci. 1979, 17, 471. Conroy, C. M.; Grifflths, P. R.; Duff, P. J.; Azarraga, L. V. Anal. Chem. 1984, 56, 2636. Shafer, K. H.; Pentoney, S . L.; Griffiths, P. R. HRC CC, J . High Reso/ut. Chromatogr . Chromatogr . Commun . 1984, 7, 707. Conroy, C. M.; Griffiths, P. R.; Jinno, K. Anal. Chem. 1985, 57, 822. Griffiths, P. R.; Fuller, M. P. "Advances in Infrared and Raman Spectroscopy"; Clark, R. B., Hester, R. E., Eds.; Heyden: London, 1979;p 63. Vldrlne, D. W. J . Chromatogr. Sci. 1979, 17, 477. Shafer, K. H.; Hayes, T. L.; Brasch, J. W.; Jakobsen, R. J. Anal. Chem. 1984, 56, 237. Smlth, S.L.; Garlock, S . E.; Adams, G. E. Appl. Spectrosc. 1983, 37,
192. Johnson, C. C.; Jordan, J. W.; Skeiton, R. J.; Taylor, L. T. Pittsburgh Conference on Analytical Chemistry and Applied Spectroscopy, New Orleans, LA, 1985;paper 538.
RECEIVED for review May 16,1985. Accepted August 20,1985. Partial support of this work by the Universitywide Energy Research Group of the University of California and by the U.S. Environmental Protection Agency under Cooperative Agreement CR812258-01 is gratefully acknowledged. S.L.P. wishes to thank the Shell Foundation for a Shell Analytical Fellowship while this work was being performed.
Fourier Transform Infrared Ellipsometry of Thin Polymer Films Robert T. Graf, Jack L. Koenig, and Hatsuo Ishida* Department of Macromolecular Science, Case Western Reserve University, Cleveland, Ohio 44106
Reflectlon spectra contalnlng phase as well as lntenslty Informatlon were collected on a FT-IR spectrometer, uslng two linear polarlrers. The sample conslsted of a poly(vlny1 acetate) (PVAc) fllm on a copper substrate. By the use of well-known principles of elllpsometry, the differential phase retardation (A) and differential amplltude ($) were calculated from these measurements. Given an Independent measurement such as the frequency of the peak maxlma of the carbonyl band of the PVAc, the thlckness and optical constants of the fllm were calculated from the elllpsometrlc measurements. A surface profller determined the fllm thlckness to be 40 nm, whlle I R ellipsometry produced a value of 55 nm. The PVAc optical constant spectra determined by I R elllpsometry compared favorably with reference spectra.
Infrared spectrometry has been increasingly used for surface studies in recent years. Improvements in IR detectors, the use of modulation techniques in the IR, and the inherent, high signal-to-noise ratio of FT-IR have all contributed to this trend. Furthermore, the wide variety of sampling techniques that exist for infrared spectrometry (e.g., diffuse reflectance, photoacoustic, reflection-absorption, etc.) has permitted surface studies on very difficult systems under ambient conditions. Traditional surface techniques such as ESCA, Auger electron spectroscopy, and SIMS, although extremely sensitive, require a high vacuum. The experimental flexibility of IR spectrometry and its huge literature base make it a competitive surface technique despite the sensitivity advantage of the other
surface spectrometries. The current sensitivity of IR surface spectrometry is such that for strongly absorbing molecules on metallic substrates monolayer studies can be considered routine (1). Ellipsometry has long been used in the UV-vis region of the spectrum for probing the thickness and optical properties of surface layers and films. Sensitivities on the order of angstroms are routinely achieved with visible light laser ellipsometry (2). For the rapid determination of the thickness of thin oxide and other layers on metals and dielectrics, UVvis ellipsometry is the technique of choice. Because of the great sensitivities achieved with UV-vis ellipsometry, much less work has been done on applying ellipsometry to other spectral regions. Nonetheless, some researchers have done ellipsometric measurements in the IR region. Dignam et al. have described an IR spectrometric ellipsometer with background noise approaching 2 X AU (3). Their use of IR ellipsometry allowed them to obtain the infrared dispersion properties of surface species as well as the absorption properties. For surface species that exhibit optical anisotropy, Dignam (4) has shown how to extract the IR absorption and dispersion properties normal and perpendicular to the surface. The wealth of information that an infrared spectrum contains makes such surface orientation measurements very desirable. Allen and Sunderland ( 5 ) used the 10.6-hm line from a COP laser to study the oxide thickness on aluminum substrates in the range of 20-200 nm. They chose infrared ellipsometry because of the limitations of visible light ellipsometry for layer thicknesses approaching 200 nm and because IR ellipsometry
0003-2700/86/0358-0064$01.50/00 1985 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 58, NO. 1, JANUARY 1986
is not as sensitive t o surface roughness of the oxide layer as is UV-vis ellipsometry. The optical constants of thin silver and gold films were measured by Bashara et al. (6) at selected infrared frequencies using infrared ellipsometry. The measurement of the optical constants of metals in the infrared region is of considerable interest, and ellipsometry has important advantages over reflection photometry for such determinations, Schaefer has used infrared ellipsometry to investigate ion implanted layers in silicon wafers (7). Both the surface concentration and the dose of the dopants were measured by infrared ellipsometry. Two different methods have been used to perform ellipsometric measurements in the infrared region. One approach uses an infrared laser to measure primarily the thickness of a surface layer, and possibly the optical constants at the given frequency. A typical instrument of this type could operate by either optical null or dynamic photometry. Another approach combines ellipsometry with infrared photometry to obtain ellipsometric spectra of the surface species. Within the realm of spectrometric IR ellipsometry both dispersive (3,8)and Fourier transform (9,10) type spectrometers have been used. These instruments operate in a photometric mode either statically or dynamically. There are several reasons for doing infrared spectrometric ellipsometry with an FT-IR spectrometer: first, to measure the thickness of thin films on surfaces in the range of 10-1OOO nm and, second, to measure the optical constants n and k of the surface film. In any grazing angle reflection experiment the refractive index, n ( ~ and ) , the absorption index, k(ij), both contribute significantly to the measured spectrum. Thus one must extract both the absorption and dispersion properties of the sample to properly interpret the measured spectrum. Third, in a reflection experiment only R, and R, (see definition below) can be measured by normal photometry. With ellipsometry one can also measure A, the differential phase change, and thus obtain phase as well as intensity information. Finally, the high signal-to-noise ratio and wavelength accuracy of FT-IR should be advantageous for ellipsometric purposes as shown by Dignam (11) and Roseler (9, IO). The theory of ellipsometry has been extensively covered in several excellent texts and papers (12-15); however a quick review of the measurable quantities is desirable. For reflection ellipsometry the fundamental quantities are the differential phase retardation, A, and the differential amplitude, $. These quantities are related to R, and R, by the following equations: r p / r s= t a n # exp(iA) (1)
For reflection from a single interface rp and r, represent the Fresnel reflection coefficients and R, and R, represent the reflectance. The subscripts p and s refer to radiation polarized either parallel or perpendicular to the plane of incidence, respectively. The quantities r, and r, can be either positive or negative and real or complex, while the quantities R, and R, are always real, positive, and range between 0 and 1. The quantities IC, and A are always real and range between 0" and 90' and 0" and 360",respectively. In ellipsometry one measures IC, and A, while in reflection photometry one measures R, and R,. Many ellipsometers operate by achieving an optical null. The polarizer, analyzer, and compensator azimuth readings a t optical null are used to calculate $ and A. In a dynamic photometric ellipsometer one of the optical components is modulated (often the polarizer is rotated) and the reflectance R is measured as a function of the modulation. The quantities $ and A can then be calculated from the modulated reflectance data. In a static photometric ellipsometer the reflectance R is measured at
65
Figure 1. Schematic diagram of the reflection ellipsometry experiment. P1 and P2 are linear polarizers; M1, M2 and M4 are flat mirrors: M3 is a spherical mirror; and S is the sample. The azimuth angles of the polarizers are given by a,as one looks into the beam direction. The x axis is horizontal; the y axis is vertical; and the vector z represents the passing axis of a polarizer.
several different azimuth settings of the polarizers and compensator, and IC, and A are calculated from the measured reflectance values. Inspection of 1 and 2 reveals that only three independent quantities can be measured at any one angle. Once A, A, R,, and R, have been determined for a sample at a given angle of incidence, no more information can be extracted either by ellipsometry or photometry (4).
EXPERIMENTAL SECTION Our experimental setup for measuring the ellipsometric variables follows closely the work and suggestions of Dignam (16-19) and Roseler (9, IO). Only two linear polarizers are necessary. These polarizers are placed immediately before and after the reflection attachment. The initial polarizer is set with its passing axis at 45'. The second polarizer or analyzer is set with its passing axis at O", 90°,45', and -45' at which position R,, R,, R45,and R-45 are measured, respectively. The following equations then allow the calculation of $ and A from the four spectra
R , / R , = tan2 # R-45/R45
1 - sin (2#) cos (A) = 1 sin (211.1cos (A)
+
(3)
(4)
Figure 1shows a schematic diagram of our reflection configuration. Because this reflection attachment does not measure absolute reflectance, ratios of the measured spectra are used to calculate the ellipsometric quantities and A. The linear, wire-grid polarizers from Molectron Corp. are rated 99% efficient (20). The precision and accuracy of setting the azimuth angles is estimated to be i0.5'. The reflection attachment is from Harrick Scientific, and the precision and accuracy of the incident angle is again estimated to be 10.5'. The angular spread of the spectrometer beam was measured at i6.5' or 13" of total arc. Once the quantities $ and A have been determined the thickness and optical constants of the surface layers can be calculated. If one uses only a bare substrate with no surface layers present, then n and k of the substrate can be calculated directly from # and A using simple exact equations (13). For film-covered systems the optical equations cannot be inverted; therefore we used a nonlinear least-squaresapproach to solving the equations. Since the thickness, cl, does not vary with frequency and n varies only slightly in nonabsorbing regions of the spectrum, it is possible to calculate d and n in regions where k = 0 using only two independent quantities such as # and A. Once d has been determined in a nonabsorbing region, n and k can be determined for the rest of the spectrum. Thin films of poly(viny1 acetate) (PVAc) were deposited on copper substrates by casting from a THF solution. Prior to the deposition of the polymer film the copper substrates were polished with chromium oxide on a polishing wheel, washed in an ultrasonic bath with acetone, washed in an ultrasonic bath with 1% HCl in HzO,and washed in an ultrasonic bath with HzO. The thickness of the PVAc filmon the copper substrate was determined by using a surface profiler from Tencor Instruments. The surface profile
66
ANALYTICAL CHEMISTRY, VOL. 58,
NO. 1, JANUARY 1986 Calculated vs. observed f o r ZnSe p r i s m R-4S/R45
'ip/Rs f o r Z 6 e p r l s m
60'
0.50-
3.80
C . 40 I
1
0.20:
0.lOj
I ---A ,
0.00
3800
3400
3000
2600
2200 1800 WRVENUMBERS
0
1400
0
1000
.
600.
Figure 2. RJR, calibration spectrum for ZnSe prism for two different incident angles. Prism was mounted in the reflection attachment between the linear polarizers.
0
3800
RESULTS The effect of the reflection optics on the measured reflectance was calibrated with a zinc selenide prism. When mounted in the reflection attachment of Figure 1, this prism permitted the collection of single pass internal reflection spectra a t an angle of 45'. With the first polarizer at an azimuth of 45O, and the analyzer set at 0' and 90°, the reflectance ratio of p-to-s polarized radiation was determined. For total internal reflectance this ratio is 1.0 for all angles above the critical angle. Figure 2 shows the p/s ratio for incident angles of 60" and 75O. The spectra of Figure 2 represent the total p/s throughput of the instrument and the reflection optics and will be used to calibrate all subsequent p/s spectra. The analyzer was then set a t -45O and 45O, and the reflectance ratio of R-45/R45was measured at angles of 60' and 7 5 O . These ratios can also be calculated from the theoretical values of $ and A of ZnSe (using eq 4). For this calculation the refractive index of ZnSe was assumed to be 2.4 across the entire mid-IR region. The effect of beam convergence was accounted for by integrating over the incident angle arc. The calculated and observed results for the R-45/R45reflectance ratio are shown in Figure 3. The calculated ratios are the horizontal lines in Figure 3. The closeness of the calculated and observed spectra indicates that the spectrometer and reflection optics have little effect on the R-45/R45ratios. Experimental results are shown in Figures 4 and 5 from a thin film of PVAc on copper and the bare copper substrate. The R,/R, ratio of the film-covered copper is given in Figure 4 and the R-45/R45ratio is given in Figure 5. The angle of incidence was 75O. The three strongest bands occur a t 1747,
3000
2600 2200 1800 WRVENUMBERS
1000
1400
Figure 3. Comparison of calculated and observed R-,IR,, spectra of ZnSe prism at two different incident angles. 1.00
of the step between the film-covered copper surface and a region where the film had been removed was recorded. All spectrometric measurements were made on a Digilab FTS-20E Fourier transform spectrometer equipped with a narrow band-pass mercury-cadmium-telluride (MCT) detector and a dry nitrogen purge. Spectra were recorded at a resolution of 4 cm-l and a mirror velocity of 1.2 cm/s. A minimum of 100 scans were coadded for each spectrum. All programs for the calculation of $, A, d, n, and k were written in Fortran 77 on a Digital Equipment Corp. VAX/VMS 11-780 computer system. The calculation of n and d from $ and A in nonabsorbing regions, and n(3) and k(?) from d, $, and A in absorbing regions was done by using an algorithm reported by Heavens (21). This algorithm gives exact results for reflectance and transmittance within the limits of classical electromagnetic theory and linear optics. Nonlinear least-squaresrefinement was done by using a Levenberg-Marquardt finite differences algorithm (22) and program (23).
3400
B = 7 9
0.60
1
G . 40
i
calibration
7
Rp/Rs 1
61
I
4
0.20
0.00 I
I
3800
3400
3000
I
2600 2200 1800 Waverumbers
, 1400
I
1000
I 500.
Figure 4. Experimental reflection spectra of PVAc on copper and bare copper. Spectra are ratios of R , and R , spectra at an incident angle of 7 5 O . 50.0
R-45/R45 at 75"
40.0-
R 8
Bare cu PVRc on Cu
30.0-
20.0-
10.0-
0.00 3800
I
I
I
I
I
I
I
3400
3000
2600
2200
1800
1400
1000
6 I.
WRVENUMBERS
Figure 5. Experimental refiectlon spectra of PVAc on copper and bare copper. Spectra are ratios of R,, and R , spectra at an incident angle of 7 5 O .
1375, and 1260 cm-I in the R,/R, spectrum, while these bands have maxima at 1755, 1382, and 1272 cm-l in the R-45/R46 spectrum. The relative intensities of these bands are also different in these two sets of spectra. Comparison of the film-covered copper and bare copper spectra in Figures 4 and 5 reveals a major difference for the R-45/R45spectra but only a subtle difference for the R,/R, spectra in nonabsorbing regions. The spectra in Figures 4 and 5 were used to derive $ and A spectra via eq 3 and 4. The $ and A spectra for the
ANALYTICAL CHEMISTRY, VOL. 58, NO. 1, JANUARY 1986 2.00
,.EO]
1.20
n
1
niol
h
h
1.60-
nlvl
A
1.20-
V
I O
-__
2 . 0 0 . 7
I\
87
0.80
4
I
A
7 0.404
0.404
0.00
I
I
0.00 2000
1
URVENUMBERS
Figure 8. Range of optical constants for PVAc on Cu derived for various trhl thicknesses: (A) 45 nm, (B) 50 nm, (C) 60 nm, (D) 70 nm, (E)80 nm.
1800
1600 1400 WRVENUMBERS
1200
1000
Flgure 8. Comparison of PVAc optical constants derived from (A) transmission measurements of thin films using Kramers-Kronlg integration and from (B) reflection ellipsometry measurements of PVAc on Cu.
range. A second set of optical constants were determined from the transmission spectrum of a thin film of PVAc. The method used for the transmission data was based on KramersKronig analysis (24). These two sets of optical constants for PVAc are compared in Figure 8. The three largest bands of the Kramers-Kronig k(v) spectra have peak positions at 1738, 1373, and 1242 cm-l and peak heights of 0.723, 0.259, and 0.848, respectively. The same bands for the k ( 9 ) spectrum derived by ellipsometry have positions of 1738,1373,and 1244 cm-l and heights of 0.464, 0.178, and 0.482, respectively. The thickness of the same PVAc/Cu sample was also determined by using a surface profiler. A section of the film was removed with THF and the differential step height between the film-covered and bare copper was measured. By this method the PVAc film thickness on the copper substrate was determined to be 40 nm. 1730
1732
1734
1736
1738
1740
1742
1744
WAVENUMBERS
Flgure 7. Plot of the frequency of the peak maxima of the k(B)spectra of Figure 6 vs. the trial thickness.
bare copper substrate were used to directly calculate optical constants for that substrate. No allowance for the formation of Cu,O was made for this calculation. The $ and A spectra of the film-covered sample were then used to refine n and d values in the 3800-2000-~m-~ region. Figure 6 shows the optical constants of the carbonyl stretching mode in the 1800-16M)-~m-~ region derived for the thin film of PVAc on copper by assuming different values for the thickness. Thickness values ranging from 40 to 80 nm were ) k(o) from the measured $ and A used to generate n ( ~and spectra. The k ( s ) band shape in Figure 6 is distorted when the thickness is low, and the peak maximum decreases as the thickness decreases. A plot of the positions of the peak maxima from the k @ ) spectra of Figure 6 vs. the corresponding thickness values is shown in Figure 7. The peak positions range from a low of about 1730 cm-l at 40 nm to a high of around 1744 cm-' at 80 nm. This plot can be used as a calibration curve for the thickness and optical constants if the peak maximum of the carbonyl band of PVAc is independently known. From a simple transmission spectrum of a thin film of PVAc, the absorption peak maximum was determined to be 1738 cm-l. Therefore the thickness of the thin film was estimated from Figure 7 to be 55 nm. With 55 nm as the film thickness, the optical constants of PVAc were derived from J, and A over a broad frequency
DISCUSSION The spectra in Figures 2 and 3 can be used to correct for the effects of the reflection optics. Referring to Figure 1 it can be seen that a total of four mirrors and the sample lie between the polarizer and analyzer. The ideal situation would have only the sample between the polarizer and analyzer. The effect of the mirrors can be corrected for by using the spectra in Figure 2 and 3 for calibration. The measured R,/R, spectrum of a sample is divided by the R,/R, calibration spectrum of Figure 2. The R-45/R45calibration spectra in Figure 3 are very close to the calculated values. Measured R+ JR6 spectra can be corrected by dividing by the calibration in Figure 3. A unique thickness and set of optical constants could not be determined directly from the ellipsometric measurements alone because of insufficient accuracy in the experimental measurements of Figures 4 and 5. Therefore, an additional independent measurement was necessary to select the best set of optical parameters from Figures 6 and 7. Certainly, the precision and accuracy of the polarizer azimuths in our experiments is relatively crude by normal ellipsometric standards. However, the reproducibility that was achieved with such components indicates that sample-related errors may also be important. The effect of oxide formation was not included in the ellipsometry calculations. The oxide layer for a freshly prepared copper surface would be small (
