Langmuir 1991, 7, 2219-2229
2219
Application of Multiple-Angle-of-IncidenceEllipsometry to the Study of Thin Fluid Films Adsorbed on Surfaces C.L.Rhykerd, Jr., J. H.Cushman,' and P. F. Low Department of Agronomy, Purdue University, West Lafayette, Indiana 47907 Received July 30, 1990. In Final Form: April 15, 1991
Many natural and technological processes are governed by the properties of thin films of water adsorbed onto mineral surfaces. The present study was undertaken to better understand the development of thin films. Previous ellipsometric measurements of water-film thicknesson silicates at saturated vapor preseure have yielded thicknessesranging from 10 to 1500 A. However, these measurements relied on assumptions about the refractive indices of the film and substrate which were necessitated by the single-angle-ofincidence method used. The present study involved an environmental cell with flexible bellows as arms so that multiple-angle-of-incidence (MAI) measurements could be made. MA1 measurementa were interpreted with electromagnetictheoryand resulted in the simultaneous measurement of the film thickness, refractive index, and extinction coefficient of the film and substrate. They were made on a fused silica surface after it was carefully cleaned and equilibrated with water vapor at seven relative vapor pressures (pip" = 0.85, 0.90, 0.93 0.95, 0.97, 0.98, and 0.995). The resulting film thicknesses (h) ranged from 24 to 90 A, with only 3-4 A surface roughness measured under vacuum, (p p o = 0.0). Hysteresis between the desorption and adsorption branches was negligible. The refractivein ex of the water films in the range 24-50 A agreed well with the bulk value of water, 1.332.
d
Introduction For many years, studies have been conducted at Purdue University on the nature and properties of water and other fluids adsorbed on surfaces.'-20 Adsorbed fluid films are important in many diverse areas such as tribology, catalysis, hydrology, molecular biology, and geotechnical and environmental engineering. An instrument that is ideally suited to measure the thickness of films on single surfaces is the ellipsometer. Although it is most commonly used to determine the thickness of solid films on solid s u r f a c e ~ , 2 ~it- ~has ~ been applied to water films on (1) Anderson, D. M.; Low,P. F. Soil Sci. SOC.Am. J. 1968,22,99. (2) Low,P. F. Adu. Agron. 1961,13, 269. (3) Oster, J. D.; Low,P. F. Soil Sci. SOC.Am.J. 1964, 28, 605. (4) Kay, B.D.; Low,P. F. Clays Clay Miner. 1976,23, 266. (5) Low. P. F. Soil Sci. SOC.Am. J. 1976. 40. 500. (6) Clementz, D. M.; Low, P. F. In Colloid 'and Interface Science; M.. Ed.: Vol. 3. D 485. -Kerker. -_ -. _ ,. . -.,-_., _.._, (7) haw,P. F. Soil Sci. SOC.Am. J. 1979, 43, 651. (8) Oliphant, J. L.;Low,P. F. J. Colloid Sci. 1982,89, 366. (9) Oliphant, J. L.;Low,P. F.J. Colloid Interface Sei. 1983,95,45. (10) Mulla, D. J.; Low,P. F. J. Colloid Interface Sci. 1983, 95, 51. (11) Viani, B. E.; Low,P. F.;Roth, C. B. J.Colloid Interface Sci. 1983, 9 229. -6 -. , -.. (12) Mulla, D. J.; Low,P. F.; Cushman, J. H.; Diestler, D. J. J.Colloid Interface Sci. 1984,100,576. (13) Sun, Y.: Lin, H.: Low.P. F.J. Colloid Interface Sci. 1986,112, 556. (14) He, H.; Cuehman, J. H.; Dieetler, D. J. In Flow and Transport Through Unsaturated Fractured Rock; Evans, D. D., Nicholson, T. J., Eds.; American Geophysics Union: Washington, DC, 1987. (15) Rhykerd, C. L.,Jr.; Schoen, M.; Dieetler, D. J.; Cushman, J. H. Nature 1987,300,461. (16) Schoen, M.; Diestler, D. J.; Cuehman,J. H. J.Chem. Phys. 1987, 87, 5464. (17) Schoen, M.; Cuehman, J. H.; Diestler, D. J.; Rhykerd, C. L.,Jr. J. Chem. Phys. 1988,88,1394. (18) Schoen, M.; Rhykerd, C. L.,Jr.; Cushman, J. H.: Diestler, D. J. Mol. Phys. 1989,66,1171. (19) Schoen, M.; Rhykerd, C. L.,Jr.; Diestler, D. J.; Cushman, J. H. Science 1989,245, 1223. (20) Cushman, J. H.; Diestler, D. J.; Schoen, M. In Frontiers in Applied Math Series; Fitzgibbon and Wheeler, Ede.; S U M , in press. (21) McCrackin, F. L.;Paeeaglie, E.; Stromberg, R. R.; Steinberg, H. L. J. Res. Natl. Bur. Stand, Sect. A 1963,67A, 363. (22) Roorj, N. F.; Sieverdink, R. J. S.;Tromp, R. M. Thin Solid Films 1977, 43, 21i. (23) Rhazanov, A. V.; Svitashev, K. K. Adu. Electron. Phys. 1979,49, 1.
solids.2529 The constant-angle-of-incidencemethod used in these later studies relies on assumed values of the refractive index of the film and substrate and, therefore, provides values for the film thickness which depend on the reliability of those assumptions. Early ellipsometric studies of thin water films led researchersz6Imto conclude that the index of refraction of the water film could not be determined. With a singleangle-of-incidence technique we concur with their observation. One of the functions of this article is to show how the refractive index of a thin film, it's thickness, and all the system's optical parameters can be determined by using multiple angle of incidence ellipsometry. Several properties, such as self-diffusion coefficient, partial specific volume, viscosity, frequency of 0-D stretching, molar absorptivity, apparent specific heat, apparent specific entropy, apparent specific isothermal compressibility, and apparent specific isobaric expansibility of water in clay-water systems have been found to differ from their corresponding bulk v a l ~ e s . ~ JResults ~J~ of computer experiments for simple Lennard-Jones (12, 6) fluids confined between structurally flat surfaces show changes in the fluid's properties with respect to the corresponding bulk These properties change most strongly for very thin films. Therefore, it is reasonable to suspect that water films on the order of 40 A thickness and less may exhibit refractive indices which differ from the corresponding bulk value. Consequently a method which can measure the refractive indices of the film and substrate, along with the film thickness, is desirable.
Historical Perspective There have been a number of investigationsof adsorbed water films using methods other than ellipsometry. The ~~~
~
~
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(24) Azzam, R. M. A.; Bashara, N. M. Ellipaometry and Polarized Light; North-Holland: New-York, 1987. (25) Derjaguin, B. V.; Zorin, 2.M. Zh. Fiz. Khim. 1966,29, 1010. (26) Hall, A. C. J. Phys. Chem. 1970, 74,2742. (27) Ershova, G. F.; Zorin, A. M.; Chureev, N. V. Kolloidn. Zh. 1976, 37. - . , -208. .-. (28) Perevertaev, V. D.; Metaik, M. 5.;Golub, L. M. Kolloidn. Zh. 1979, 41, 159. (29) Pashley, R. M.; Kitchener, J. A. J. Colloid Interface Sci. 1979,71, 491.
0743-7463/91/2407-2219$02.50/0 0 1991 American Chemical Society
2220 Langmuir, Vol. 7, No.10,1991
earliest studies of water films by Derjaguin and Kussakovg0 involved microscopic observation of optical interference lines of variable wavelength. These films were formed by immersion and then thinned by bubble pressure; a hydrogen bubble is trapped on the underside of the surface (mica or glass), and the resulting relative vapor pressure of water is essentially 1.0. The values of the pressure of the vapor were obtained from the curvature and surface tension of the bubble-liquid interface. As the pressure of the bubble was varied from 4900to 137 700 N/m2, the film on the mica thinned from 1900 to 350 A. The film on glass was thinner (1500-250 A) for pressures of 5300-59100 N/m2. Small reductions of relative vapor pressure were produced by adding salt. Concentrations of 10-l to lo4 N provided much thinner films: 700 A at 3900 N/m2 in NaCl. The lowering of relative vapor pressure near saturation was seen to greatly influencethese fiims.31 Schofield32 presented numerical calculations for the thickness of films of pure water on glass and mica which agreed with the measurements of Derjaguin and Kussakov.80 This agreement with experiment was obtained by modeling the film as the diffuse part of an electricaldouble layer. However, the calculations failed to agree with experiment when salt was added to the solutions, even at lo4 N. Adsorption of water on glass at various relative vapor pressures was studied with electrical capacitance measurements by Garbatski and F ~ l m a n . A~ ~condenser controlled the vapor pressure environment and the changes in capacitance led to their determination of film thickness. The reported accurac was several angstroms, but the values (less than 500 ) are smaller than those reported in earlier studies. The film thickness was seen to decrease exponentially as the relative vapor pressure dropped. Films remained detectable at p l p " = 0.50. Derjaguin and Zorin25 published a technique to measure water film thickness to "an accuracy of one Angstrom". They called the method optical micropolarization. The method resulted from Drude's development of Maxwell's equations in the 18008. Although the concepts for ellipsometry had been developed one century early by Drude,M the 1955report by Derjaguin and Zorin is to our knowledge the first ellipsometric study of water films; however, no numerical values are to be found in this report. With the improvementof accuracy of thickness measurements came values which agree in order of magnitude with the interlayer separation of clays found by X-ray methods.Zs*m*29 Data on the thickness of water films on the surfaces of silicatesdiffer greatly. HallZsobserved films 10-70 A thick on fused quartz at room temperature for 0.95 < p / p " < 1.00. Ershova et al.27observed films 40-45 A thick on fused quartz at room temperature when pip" = 1.0. The films observed by the latter investigators were completely destroyed by raising the temperature to 65 "C but at 10 "C they were 90 A thick. This indicates that electrical (double layer) forceswere not responsible for the formation of these films since the electrical contribution to the pressure is relatively insensitive to temperature.35 Perevertaev et al.28 reported heats of wetting for muscovite mica with film thicknesses ranging from 10to 80 A. These
K
(30)Derjaguin,B. V.; Kussakov, M. Acta Phys. Chem. URSS 1999, IO, 25. (31) Derj in, B.V. Trans. Faraday SOC.1940,36, 203. (32) Scho? ield, R.K. Trans. Faraday SOC.1946,42B, 219. (33) Garbataki, Y.;Folman, M. J. Phys. Chem. 1966,60,793. (34) Drude, P. Ann. Phys. Chem. 1889,36, 532 and 865. (35) Der~eguin,B.V.;Chursev, N.V.; Muller, V. M. Surface Forces; Consultants Bureau: New York, 1987.
Rhykerd et al. film thicknesses agreed more closely with those of but the difference of surface, mica vs fused quartz, makes quantitative comparison difficult. Pashley and KitchenerB studied the affect of different cleaning techniques on the thickness of water films on quartz. Methylated, hydrophobic surfaces showed adsorption to a depth of only 10 A at saturation. Heatdehydroxylated quartz showed films 70 A thick at saturation. Surprisingly,hydroxylated quartz cleaned several hours in concentrated nitric acid followed by rapid (20 s) etching in 30% sodium hydroxide solution, or hot, rapidly decomposing ammoniacal hydrogen peroxide solution showed films 1500 A thick at p / p o = 1. At pip" = 0.975 the hydrophylic quartz still had adsorbed films 250 A thick. Derjaguin35 introduced the terms a film and @ film to describe the stable and metastable states for water films which may be found near p i p " = 1. The two states are separated by an unstable region of thicknessescorresponding to dh/dII > 0, where h is the film thickness and ll is the disjoining pressure (solvation force less atmospheric pressure). In general, CY films are stable with h I100 A and @ films are metastable with h 2 200 A. The collapse of a B film to an a film results in the temporary formation of microdroplets. a films cannot "jump" to @ films without going through a region of negative disjoining pressure (II 0, dh/dII > 0) or supersaturated vapor ressure (p/p" > 1.0). Itappearsthattheverythick (1500 )filmobserved by Pashley and Kitchener was a @ film. This is indicated by its collapse after 3 days to thicknesses in the range of l00A. Evidently, the films of Pashley and Kitchener were metastable. Conventional electrical and van der Waals' equations for the interaction between macroscopic bodies contain many approximations and assumptions (e.g. DLVO theory). Pashley and K i t ~ h e n e rand ~ ~ Derjaguin and Churaev36 have concluded that these conventional equations do not adequately describe the relationship between water film thicknesses on silicate surfaces and the relative vapor pressure over these surfaces. This conclusion is consistent with the extensive work on clays by Low and co-workers.lJ3*37 The assumptions of the conventional equations appear to be too extensive for these equations to precisely represent the data for water adsorption. Recent theories%have provided a more useful equation which we will call the Marcelja equation. This equation, originally developed to explain the adsorption of water by lecithin bilayers, results from minimizing the free-energy density. It has been reviewed by Ninha1n,3~and developed further by Schiby and R u ~ k e n s t e i and n ~ ~Ruckenstein and S ~ h i b y .The ~ ~ Marcelja equation takes the form
jP
II = K exp[-h/l]
(1)
For polarizing lecithin bilayers, K is a function of the polarizability of the water and l is a correlation length. For a single surface, K might be a function of the restructuring of the water near the surface and 1 would again be a correlation length in the water. Three of the more important problems relative to eq 1are (1)it is based on continuum theory but is applied on a molecular level, (2) the boundary conditions used in its derivation are poorly defined, and (3) the Landau expansion of the free energy density from which Marcelja and Radic derive their (36) Derjaguin, B.V.;Churaev, N. V. J . Colloid Interface Sci. 1974, 49, 249. (37) Low,P.F. Soil Sci. SOC.Am. J. 1980,44,667. (38) Marcelja, S.;Radic, N. Chem. Phys. Lett. 1976, 42, 129. (39) Ninham, B. W.J. Phys. Chem. 1980,84,1423. (40) Schiby, D.; Ruckenstein, E. Chem. Phys. Lett. 1983,95,435. (41) Ruckenstein, E.;Schiby, D. Chem. Phys. Lett. 1983, 95,439.
Study of Thin Fluid F i l m By MAI Ellipsometry
Langmuir, Vol. 7, No. 10, 1991 2221
equation is valid only for 1 = OD, yet they assume it is valid in the range 1 = 10 A. Hence, the Marcelja equations should be viewed with some skepticism and used only with caution. Churaev and Derjag~in'~ have used the Marcelja equation to interpret data for the adsorption of water onto glass, quartz, and mica. DerjaguinWates that,"the theory of Marcelja and Radic gives a qualitatively correct dependence of II on h, in good agreement with available experimental data". has developed an empirical equation of similar form
(II + PA)/PA= B exp[a/h]
(2)
Figure 1. Geometry of the optical elements of ellipsometer in the PSCA arrangement. Adapted from ref 21.
s
where B and a are empirical constants and h is the interlayer separation between clay platelets. The empirical formulation agrees very well with the data of Viani et al." who determined h from X-ray measurements on a variety of smectites with widely ranging surface charge densities. Both eqs 1and 2 will be discussed in more detail later in this article. 5
Theory of MA1 Ellipsometry Multiple-angle-of-incidence (MAI) ellipsometry" is capable of determining 2n optical parameters by measuring the reflection off a surface at n angles of incidence. If n is large enough, an overdetermined system of equations results. This is, in general, desirable since experimental measurements contain some error which can be reduced by repetition. Historically, fixed angle-of-incidence ellipsometry was used because of the lack of access to computers and the complexity of designing environmental cells with movable arms. The film must be enclosed in a cell to control temperature and relative humidity. The windows to the cell must be held perpendicular to the light beam, and so the problem of how to design a cell with windows perpendicular to the beam may have caused investigatorsto choose the fixed angle of incidence method. In the measurement of solid films on solid substrates, such as silicon dioxide on silicon, problems of environmental control do not arise. Thus MA1 techniques were first pioneered for bare solid surfaces and later for thin solid films. Although the measurement of solid-film thickness advanced,1312~measurement of liquid films remained difficult owing to problems relative to their production, maintenance, and reproduction. At the present time, computational methods associated with ellipsometry include minimization of the difference between calculated and measured phase shifts (8)- and minimization of the difference in the ellipsometric angles, A and $. It is the latter method that is adopted in this study. Minimizing the relative phase shift was tested previously for solid and liquid films in this lab and found to give satisfactoryresults as well.47 The basis for the measurement of the ellipticity coefficient of a surface by ellipsometry and the interpretation of that coefficientin terms of film thickness and refractive (42) Churaev, N. V.;Derjaguin, B. V. J. Colloid Interface Sci. 1986, 108, 542. (43) Clauseen, B. H.; Flower, M. J.Electrochem. SOC.1963,110,983. (44) Reinberg, A. R. Appl. Opt. 1972,11, 1273. (46) Malin, M.; Vedam,K. Surf. Sci. 1976,56, 49. (46) Bu-Abbud, G.H.; Baehara, N. M. Appl. Opt. 1981,20, 3020. (47) Rhykerd, C. L., Jr.; Cushman, J. H.; Low, P. F. In Flow and Tranaport Through Unuaturated Fractured Rock; Evans, D. D., Nicholson, T. J.; Eds.; American Geophysics Union: Washington, DC, 1987. (48)Reitz, J. R.; Milford, F. J.; Christy, R. W. Foundation of Electromagnetic Theory, 3rd ed.;Addison-Wesley: Reading, MA, 1980.
Figure 2. Ellipsometer design including environmental celk mercury vapor lamp (L), green filter (F), collimater (C), iris diaphragm (I), polarizer (P),window (WI), bellows (Bl),sample support and sample (S),bellows (Bz),window (Wz), variable size aperture (A ), compensator (C),analyzer (A), mirror (M), telescope (TP, photomultiplier tube (PMT).
index lies in electromagnetic theory. The relevant facets of this theory in regards to MA1 are presented in the Appendix.
Instrumentation A schematic diagram of the ellipsometer is shown in Figure 1. Here thePSCA (polarizer,surface,compensator, analyzer) arrangement is illustrated. The idealized componenta are L, a monochromatic unpolarized light source, P, a polarizer, S, the surface being studied, C, a quarterwave plate (or compensator), A, a second polarizer called the analyzer, and D, the light detector. A Rudolph Research ellipsometer (Type 43603-2003) is employed in this study (Figure 2). The light source is composed of a clear mercury vapor lamp [GE H100A4/ TI, a collimator, and a green filter. This combination produces monochromatic light with a wavelength of 5461 A. The polarizer and analyzer were Glan-Thompson prisms. The compensator is a quarter-wave plate for the 5461-A line. The polarizer, compensator, and analyzer are held in bases mounted on the rails of the ellipsometer. The polarizer and analyzer are aligned such that their planes of transmission coincide with the plane of incidence (the x-z plane of Figure 1)when the scales read zero. The compensator is aligned such that its fast axis of transmission falls in the plane of incidence when its scale reads zero. A cell (Figure 2) was constructed to control the environment around the samples and still allow changes in the angle of incidence (80) in the range 5 8 O < 00 < 76O. It was made of brass in a hemicylindricalshape and electroplated with stainless steel. The back of the cell held the sample support, which used plastic fittings to mechanically hold the sample vertically. The curved sides of the cell contained two flanged porta which were attached to flexible stainless steel bellows. As 00 changed, the bellows flexed
2222 Langmuir, Vol. 7, No.10,1991
but kept the cell sealed. The bellows were attached to flanges on supports mounted on the ellipsometer's rails. These supports held the cell windows (Oriel Corp. Model 44920, fused silica, 3/8 in. thick, l/Z-in. diameter). Because the window supports were rigidly bolted to the rails, the windows were held perpendicular to the light beam entering and leaving the cell for all angles of incidence. This design avoided any partial polarization of the light which would have resulted from passage of the light through the window at an angle of incidence other than zero. The cell was made vacuum tight by means of O-rings. There were two small ( l / g in. diameter) gas ports in the cell, one mounted in the cell wall and one in its floor. These ports allowed vapor input and output for vapor pressure control. The metal cell was sufficiently strong to maintain its integrity under vacuum. The stainless steel plating eliminated oxidation of the surfaces and made cleaning simpler. The metal construction also guaranteed good heat conduction so that the interior temperature was controllable with an external array of copper heating/ cooling coils. A large water bath was used to control the temperature of the cell. Two pumps (Little Giant Pump Co. 1.1 and 1.7 A) circulated water out of the path to the cell's array of copper heating/cooling coils and back to the bath through insulated lines. By means of Fiberglas insulation, it was possibleto keep the cell's interior temperature within 0.1 O C of that of the bath at all times. The relative vapor pressure, p / p " , of the water vapor in the cell was controlled with solutions of PEG 200 (Union Carbide's Carbowax 200). Herskowitz and GottliebqDhave reported data from which p / p o could be calculated. The vapor was bubbled through a gas dispersion tube immersed in these solutions by a Master Flex pump (Model 7543-60 with a 7017 pump head) at a rate of 168 mL/min. The vessel containing the control solution was immersed in the water bath, and the tubing conducting the vapor from the vessel to the sample cell was insulated with Fiberglas. The vapor which returned to the bath directly from the Master Flex pump was conducted through heat exchange coils to remove any heat produced in the pump head. The temperature in the cell was measured with precision thermistors (Model YSI 44007) and a Hewlett-Packard Multilogger (Model 3467A). The thermistors were installed a t the top of the cell, in the bellows section of the source arm, and in the water bath. A standard mercury thermometer inscribed every 0.01 "C was also installed in the bath.
Sample Preparation and Measurement Technique A Si-Si02 wafer was chosen as a standard to check the method for correctness and precision. It was prepared by oxidizing a blank silicon wafer at high temperature in the presence of steam. The wafer was subsequently sent to the National Bureau of Weights and Measures for thickness measurement. This silicon wafer was prepared for measurement by ultrasonically cleaning it for 10 min in a solution containing 12.5 mL of ethanol, 12.5 mL of acetone, 25 mL of deionized-distilled water, and 2 mL of nonsudsing "micro" soap. Then it was rinsed for 30 min in running distilled water and was stored in deionizeddistilled water. Just prior to measurement, the silicon wafer was blown dry with nitrogen gas. Two samples were chosen for study in the actual experiment, Pyrex glass (Oriel Corp. Model 44180) and (49) Herekowitz, M.; Gottlieb, M. J. Chem. Eng. Data 1985,30, 233.
Rhykerd et al.
fused silica (Oriel Corp. Model 44990). The surfaces of these samples were prepared for measurement by mechanical polishing, chemical cleaning, and rinsing. The polishing was done on a wet Leco Corp. VARI/POL, VP150 felt polishing wheel at 350 rpm. The wheel was wet with a solution of 0.05-pm A1203. After several minutes of polishing with the A1203 solution, the sample was polished for another 5 min adding only distilled water to the wheel. Cleaning of any latent organics was done by immersing the sample in concentrated HNO3 at 80 "C for 4 h. The sample was then rinsed in distilled-deionized water and stored overnight. Surfaces which showed (under vacuum) gel layers or adventitious layers due to polishing were etched with 0.5% ' HF for several minutes and then repolished lightly. There were three steps in aligning the sample for ellipsometric investigation. These steps guaranteed that the measured angle of incidence was the same as the angle at which the light beam struck the sample. Initially the desired angle of incidence was set and the polarizer and analyzer were set to approximately 90". Step 1. The first step in the alignment procedure was the visual selection of the front reflection from the sample. For transparent substrates, both the front and back reflections were visible. They were separated by about 1 mm, depending on the angle of incidence. These two reflections were best viewed through the exit window of the cell with the compensator and analyzer removed from the rails. When viewed in this way, the front reflection was the furthest to the left and was generally the brighter reflection. The sample was positioned by moving the stage to center the left-most reflection in the exit window. Eventually, the small aperture mounted on the compensator physically excluded the unwanted back reflection from the analyzer's view. Step 2. The second step was to center the beam spot in the field of view of the analyzer's telescope. With the analyzer firmly bolted to the rails, the stage was moved to position the front reflection. Step 3. The third step was to position the beam. The compensator with the smallest aperature attached was bolted to the rails. The aperture was placed against the cell's exit window while the compensator was fixed against the analyzer. This arrangement was almost light-tight, and when the entire apparatus was covered with a double layer of acrylic felt, all unwanted light was excluded from the sensitive photomultiplier tube. The telescope was focused on the iris diaphragm by rotating it completely clockwise and then backing it off 3/8 of one turn. The correct focuswas confirmed with the compensator removed from the system, in which case the sides of the iris diaphragm could be seen as a polygon. When the reflection was viewed through the telescope, with the iris open, a dim ring or halo was visible around the central bright spot created by the aperture attached to the compensator. The stage was finely adjusted until this halo collapsed onto the central spot as the iris was closed. When the stage was correctly positioned, the iris was closed until it very slightly reduced the diameter of the central spot. If the ellipsometric angles A and IC/ were needed for multiple angles of incidence, the sample was realigned after each change of angle of incidence, 80. Six steps were required to measure the ellipsometric angles A and IC/. We started with the compensator set at C = 45O in order to be within zone 2 (see the Appendix for definitions and the notation to follow). Also P was set near 10" and A near 130'. Step 1. P and A were rotated to give a rough visual null
Study of Thin Fluid Films By MAI Ellipsometry
Langmuir, Vol. 7, No. 10, 1991 2223
(extinction of light viewed through the telescope). To preset the sensitive PMT, a piece of aluminum foil was placed over the filter temporarily while the mirror in the analyzer was moved from the "VISUAL" to the "PM" position. The photometer's scale was set to XlOOO, and the aluminum foil was removed. If the meter needle was off scale, the foil was replaced and the visual rough minimum improved. Usually small adjustments to the positions of P and A resulted in scale readings of 0-4 X
140
120
1.
Step 2. The photometer was calibrated with the zero dial reading 1.0 X 1when the light was cut off by the foil. With the analyzer set to minimize the meter reading, P was rotated to get the meter value up to 4.0. This value of P was recorded as P, and P is rotated the other way, through the minimal meter reading, until the meter again read 4.0;this value of P was recorded as P-. The polarizer was then set at the average of P+ and P-, which was now labeled as P2. This averaging is the "method of swings" mentioned in the Appendix. It resulted in a 10-fold increase in precision.24 The method of swings was then repeated to record A+ and A-, which were averaged and recorded as A2. Step 3. The aluminum foil was placed over the filter again while the polarizer, analyzer, and compensator were set for the next zone (zone 1)and then the compensator was set to C = -45'. Usually, P I P2 and A I 270 - A2. The polarizer and analyzer were placed at these estimates. The foil was removed and a better minimum was obtained from the photometer. The method of swings was repeated in zone 1. Step 4. The aluminum foil was replaced over the filter and the optics were moved to measure zone 3. The compensator was left a t -45'. Use was made of eqs Alle and A l l f , positioning the polarizer approximately at P3 = 180- Pl and the analyzer at AB= A1 + 90. Subsequently, the method was repeated to obtain a final P3 and AB. Step 5. In zone 4,the compensator was set at C = 45' and eqs Allc and d were used to estimate P4 = 180 - P2 and A4 = A2 + 90. The method was repeated. Step 6. Final averages of Ai and Jli for a given Boi were obtained from eqs A14a and b. These averages were used in the minimization of G in eq A20 to find nl, n2, and h (recall nl and n2 are complex).
-
n 100 0, Q)
U
U
Q
60
-
Results A standard film of silicon oxide on a silicon wafer was measured to test the MA1 method and the environmental cell. The resulting ellipsometric angles obtained with and without environmental control at angles of incidence between 58O and 69' are plotted in Figure 3. These angles were reproducible to f0.02'. Table I presents the thickness, h, the real part of the refractive index, n, and the extinction coefficient, k (imaginary part of the complex index of refraction), as calculated from the data of Figure 3. Also included in the table are reference values taken from the literature. Symbols with the subscript 1represent the Si02 film and symbols with the subscript 2 represent the Si substrate. As can be seen, the environmentally controlled data (curve 2) agree quite well with those from earlier measurements. The method of surface preparation for the Pyrex glass and the fused silicawas investigated by cleaningthe surface as described earlier and then making measurements in the environmental cell under a pressure of 1.0 mmHg as measured by a barometer. The results for Pyrex glass are presented in Figure 4. Note that the observed index of refraction was greater than the bulk value (Table 11)
-
40
5
*
Cdeg.1 Figure 3. Ellipsometer angles A and J. using eqs A14a and A14b for all measured 190, Si-Si02 wafer: (0) with environmental cell; (A)without the cell.
Table I. Thickness and Refractive Index of Standard Sios Film on Silicon Determined by Minimizing Equation A20 for Data in Figure 3 property h, 8, nl
curve 1 439 1.470
ki
0
n2 kz
4.08 0.012 0.118
G
curve 2 432.8 1.457 0 4.05 0.025 0.128"
ref value 430 1.458 0 4.05 0.028
source NBS ref 43 ref 24 ref 24
Weighting factors l/(6A)2 = l/(6+P = 1 assumed.
and so negative values of A were obtained. This indicated polishingcreated an adventitious surface layer on the glass. A similar observation was made by Vedam and Malin,60 although they were unable to determine the thickness and refractive index of their amorphous layers. After the adventitious layer was removed by etching in 3% HF, polishing lightly, and cleaning in concentrated nitric acid, the triangles in Figure 4 were obtained. From the fact that h = 0.0 A (Table 11),the resulting surface appeared almost perfectly clean. However, after the surface was exposed to water vapor overnight and examined under vacuum again, an amorphous layer was observed (Figure 4,circles). This layer did not disappear under vacuum after 24 h. The formation of such an amorphous layer made the glass unsuitable for studying the thickness of films of adsorbed water. A fused silica surface was prepared by polishing and cleaning as described earlier. Subsequent measurements showed that this surface had an amorphous layer less than 3-4 A thick (Table 111). The absence of an adventitious layer and the very smooth surface made it suitable for studying the adsorption of very thin water films. Such (50) Vedam, K.;Malin,
M. Mater. Res. Bull. 1974,9, 1503.
2224 Langmuir,
Rhykerd et al.
Vol. 7, No.10,1991
0.5
6
0.0
4
7
0
n 0,
Q
U
Q)
U
U
U
Q
Q
-0.s
2
-1.0
0
C
C
Figure 4. A and $ for polished Pyrex glass under vacuum ( 0 , compression layer; A, blank; 0, gel layer). Solid lines are fits with data of Table 11.
~~
Table 11. Surface Properties under Vacuum after Cleaning for Pyrex Glass property polish polish + etch polish + etch + wet h
n1 ki
ma k2
G a
40 1.50 0 1.474 0 0.216
Oriel Corp. reports n2
0
-
0 1.474 0 0.064
0.970 0.950 0.930 0.900
0.850
1.461 0 0.106
1.461 0 0.155
smooth surfaces have been shown by Pashlepl to be required for the study of water adsorption. In addition to control of the vapor pressure with PEG 200, the cell temperature was maintained a t 24.0 f 0.1 "C, and the bath temperature at 24.00 f 0.01 "C. Fluctuations in the room temperature certainly had some effect on the cell's temperature, even though care was taken to insulate the cell. The remainder of this section is devoted to the adsorption and desorption isotherms of water on fused silica. Initially the fused silica with a clean, polished surface was mounted in the environmental cell a t p l p " = 0.995. Then the desorption isotherm was measured with the method of swings in all four zones for plp" = 0.995,0.970,0.950, (51)Pashley, R. M.Surf. Sci. 1978,71, 139. (52)Rhykerd, C. L., Jr.; Cushman, J. H.; Low, P. F. Submitted for
publication in J. Colloid Interface Sci.
Table IV. Desorption (-) and Adsorption (+) Isotherm Branches for Fused Silica pJp" or adsorption (+) 0.995 -
Table 111. Surface Properties of Fused Silica under Vacuum after Polishing and Cleaning rep 1 rep 2 property rep 1 rep 2 property 3 4 ma 1.33 1.33 k2 0 0 G a Oriel Corp. reports n2 = 1.4601.
Figure 5. A and $ for desorption of water on fused silica. Vapor pressures for each curve, starting from the top, are 0.995,0.970, 0.950,0.930,0.900, 0.850, 0.0. Solid lines are fits from data in Table IV.
desorption (-)
12 1.44 0 1.476 0 0.128
1.5.
h nl ki
I
0.900
0.930 0.950 0.970 0.980
-
+ + + + +
h, A 90 63 54 39 29 22 27 37 52 59 60
nl 1.335 1.322 1.339 1.329 1.328 1.330 1.326 1.327 1.311 1.324 1.344
kl 0 0 0 0 0 0 0 0 0 0 0
n2 1.457 1.459 1.459 1.458 1.459 1.460 1.459 1.458 1.456 1.456 1.457
k2 G,deg 0 0.122 0 0.042 0 0.018 0 0.023 0 0.016 0 0.018 0 0.019 0 0.022 0 0.031 0 0.018 0 0.034
0.930, 0.900, and 0.850. The resulting A+ curves are plotted in Figure 5. The solid lines in this figurecorrespond to the data of Table IV. Thereafter, the surface was exposed to water vapor at successively higher values of plp" and adsorption isotherms were measured by the same method. The A+ curves for adsorption were similar to those for desorption. Film thicknesses and optical constantsfor adsorption are also presented in Table IV. Curves of h vsp/po for both desorption and adsorption are plotted in Figure 6. It is clear that the curves are coincident up to plp" = 0.98. The point a t 0.995 was not reproducible. The values of h in the present experiment were a little larger than those reported by Hall%and Derjaguin and Zorin,26 but they are considerably smaller than those of Pashley and Kitchener.29 The error bars in Figure 6 were obtained by adding G (eq A20) to the (A,9)data and then solvingfor the film thickness. Thus the error bars account for the sensitivity of the instrument and the "goodness" of fit to eq A20. The calculated values for the refractive index of the
Study of Thin Fluid Films By MAI Ellipsometry
Langmuir, Vol. 7, No. 10, 1991 2225
100
60
n
n
u
U
a
a
40
50
L
L
20
0
I
t
P/PO Figure 6. Calculated film thickness, h, for adsorption (0) and desorption (A)on fused silica using data from Table IV.
water film,nl, and the substrate, n2, are presented in Table IV. Note that the refractive index of the water is calculated to deviate from the bulk value for thicker films, which is contrary to the fact that it must approach the bulk value as the film thickness increases. However, these computations may contain an erroneous assumption. That assumption, which is fundamental to the MA1 technique, is that the same film is measured at each 00. However, a plot of h vs 00 in Figure 7, which is based on single-angleof-incidence ellipsometry (assuming nl = 1.311 and n2 = 1.456 for p / p o = 0.950) shows great fluctuations in h over the angles measured, These fluctuations are observed to be larger at higher values of p / p o . Two possible explanations come to mind. First, dh/d(p/po) increases with increasing p / p o , resulting in a very steep slope at p / p o > 0.97. In this range a slight error in the control of p / p o may result in a large error in h. The second explanation is that adsorption isotherms for different temperatures vary widely at high p / p o . Thus a slight change in temperature inside the chamber results in a change in isoscatter in the data.
Discussion PashleP3 explains the variability of isotherms by assuming a monolayer or so of the silica surface dissolves in the water film giving rise to an involatile solute effect on the vapor pressure. We do not believe this is a viable explanation (that is, at least if the adsorbed water is assumed to behave like bulk water) for the following reason. It is known that the solubility of Si04 in bulk water is about 3 X lo-' M (IleTM). Thus at the limit of solubility, p / p o may be reduced by only 5 X lo+% (to obtain a 5 % decrease in p / p o requires an addition of approximately ~
(53) Pashley, R. M. J . Colloid Znterjace Sci. 1980, 78, 246. (64) Iler, R. K. The Colloid Chemistry of Silica and Silicates; Come11 University Press: Ithaca, NY, 1955.
Angle
65
of
Incidence
[des.]
Figure 7. Water film thickness, h, va angle of incidence for p/po = 0.950 (0) andp/po = 0.900 (A)for adsorption, calculated
using nl and n2 taken from Table IV.
3 M SiO3. Thus if one is to accept Pashley's explanation of the variability of isotherms for different silica surfaces, one must conclude the solubility of Si04 in a water film must exceed that in bulk by a factor of approximately lo". We have tried to explain our results using van der Waals and DLVO theory. But both theories radically underpredict the thickness of the films.66 It is of interest to examine the relationship between the film thicknesses on fused silica and average film thicknesses between adjacent clay particles or layers. For the montmorillonites studied by Viani et al.," h was found to be about 12 A for a swelling pressure, II, of 7 bars ( p / p o = 0.995), which was the highest II (lowest p / p o )of that study. In this case h = X/2, where Xis the distance between superimposed layers that compose the clay crystal. Clearly, the films on fused silica are much thicker over the entire range of relative vapor pressures studied. There are several possible reasons for this difference. These reasons and two models for the relation between film thickness and II (or p / p o ) are the focus of this section. In the clay system, there is an attractive dispersion (van der Waals) force acting between adjacent parallel plates. Such a force alone would decrease the average film thickness in the clay-water system with respect to that in the water-fused silica system. The confining surfaces of clays alter the properties of the intervening water. This alteration may be much less pronounced in the system under investigation because, in this system, we have vapor-liquid and liquid-solid interfaces. Two clay surfaces acting on interlayer water may cooperate in a way different from that of a single surface. If, for example, an interaction in depth between the molecules of a water film and the substrate occurred, then the zones of influence due to that interaction might overlap (55) Rhykerd, C. L., Jr. MS Thesis, Purdue University, 1990.
2226 Langmuir, Vol. 7, No.10, 1991
Rhykerd et al. 200
100
t
n
