Langmuir 2002, 18, 6437-6444
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New Experimental Setup To Use Ellipsometry To Study Liquid-Liquid and Liquid-Solid Interfaces Jan-Willem Benjamins,*,† Bengt Jo¨nsson,‡ Krister Thuresson,† and Tommy Nylander† Department of Physical Chemistry 1 and Department of Biophysical Chemistry, Lund University, P.O. Box 124, S-221 00 Lund, Sweden Received January 30, 2002. In Final Form: May 15, 2002 Different types of optical light guides were constructed and tested to enable convenient multiple angle of incidence ellipsometry, on solid and liquid interfaces in liquid solutions. Two light guides are needed on an ellipsometer, one to guide the incoming light and one to guide the light that is reflected at the test surface, and therefore one light guide was mounted on the laser arm and one on the detector arm of the ellipsometer. With this arrangement the optical windows automatically adjust to always be perpendicular to the direction of the light independent of the angle of incidence. The purpose with these light guides is to facilitate the passage of light through the air/solution interface. A thorough theoretical and experimental analysis of optical errors introduced by such light guides is presented. This discussion includes the effect of multiple reflections between and within the windows of the light guides. On the basis of this analysis a new ellipsometry setup with light guides, consisting of glass tubes with glued end windows, was developed. This setup makes it possible to perform accurate measurements in almost any type of measuring cell at any angle of incidence.
Introduction When light is reflected at a surface, the change in intensity and state of polarization of the reflected beam is determined by the optical properties of the reflecting interface. Such changes can be determined by ellipsometry and are often expressed as the amplitude ratio (Ψ-value) and relative phase shift (∆-value) between the incident and reflected light beam.1 For many years ellipsometry has been an important tool for determining surface properties of the solid-air interface. One example is in the electronics industry where this technique is employed for routine characterization of the silicon wafers used in the production of memory circuits and microprocessors.1 This includes determination of refractive indices and thickness of oxide layers, which can be calculated from the Ψ- and ∆-values.1,2 The measured parameters can also be used to determine the amount of adsorbed material at an interface.3,4 In surface and colloid science, ellipsometry has been utilized to study the adsorption and desorption of surfaceactive substances on solid surfaces in aqueous solutions (cf. refs 4-7). The adsorption at solid surfaces in aqueous solutions can also be studied by other techniques, but the advantage with ellipsometry is that the adsorption process can be followed in situ with a time resolution of a few seconds or better. Thus, both adsorption isotherms (ad* To whom correspondence may be addressed. E-mail:
[email protected]. † Department of Physical Chemistry 1. ‡ Department of Biophysical Chemistry. (1) Azzam, R. M. A.; Bashara, N. M. Ellipsometry and Polarized Light; North-Holland Elsevier Science Publishers: Amsterdam, 1987. (2) McCrackin, F. L.; Passaglia, E.; Stromberg, R. R.; Steinberg, H. L. J. Res. Natl. Bur. Stand., Sect. A 1963, 67A, 363-377. (3) De Feijter, J. A.; Benjamins, J.; Veer, F. A. Biopolymers 1978, 17, 1759-1772. (4) Cuypers, P. A.; Corsel, J. W.; Janssen, M. P.; Kop, J. M. M.; Hermens, W. Th.; Hemker, H. C. J. Biol. Chem. 1983, 258, 2426. (5) Eskilsson, K.; Tiberg, F. Macromolecules 1997, 30, 6323. (6) Tiberg, F.; Jo¨nsson, B.; Tang, J.; Lindman B. Langmuir 1994, 10, 2294. (7) Ho¨o¨k, F.; Kasemo, B.; Nylander, T.; Fant, C.; Sott, K.; Elwing, H. Anal. Chem. 2001, 73, 5796.
sorbed amount vs concentration of the adsorbing solute) as well as adsorption (and desorption) kinetics can be followed. In most of these studies, oxidized silicon wafer surfaces are used as they have good reflectivity and have a well-defined silica layer with a constant thickness. These surfaces can also be relatively easily modified. Two examples are reaction with dimethylsilane to obtain a hydrophobic surface5,8 and deposition of cellulose to mimic the surface properties of cellulose fibers.9 Liquid interfaces, for example, liquid-air and liquidliquid interfaces, are important in many technical applications. Ellipsometry has also been used to study the properties of the liquid-air interface (refs 10-14) and the adsorption of surface-active substances to this interface. Due to experimental difficulties, significantly fewer studies have been published on the liquid-liquid interface (refs 15-19). Ellipsometry measurements at liquid-air and liquid-liquid interfaces require special arrangements, which for instance ensure a well-defined angle of incidence.15,16,19 Another obvious complication at the latter interface is that if no specially designed cuvette is used, the light needs to pass an air-liquid interface before it (8) Elwing, H.; Welin, S.; Askendal, A.; Nilsson, U.; Lundstro¨m, I. J. Colloid Interface Sci. 1987, 119, 203. (9) Bergstro¨m, L.; Stemme, S.; Dahlfors, T.; Arwin, H.; O ¨ dberg, L. Cellulose 1999, 6, 1. (10) Teppner, R.; Bae, S.; Haage, K.; Motschmann, H. Langmuir 1999, 15, 7002. (11) Manning-Benson, S.; Bain, C. D.; Darton, R. C. J. Colloid Interface Sci. 1997, 189, 109. (12) Goates, S. R.; Schodield, D. A.; Bain, C. D. Langmuir 1999, 15, 1400. (13) Hutchison, J.; Klenerman, D.; Manning-Benson, S.; Bain, C. Langmuir 1999, 15, 7530. (14) Walsh, C. B.; Wen, X.; Franses, E. I. J. Colloid Interface Sci. 2001, 233, 295. (15) Nylander, T.; Hamraoui, A.; Paulsson, M. Int. J. Food Sci. Technol. 1999, 34, 573. (16) Bylaite, E.; Nylander, T.; Venskutonis, R.; Jo¨nsson, B. Colloids Surf., B Biointerfaces 2001, 20, 327. (17) Russev, S. C.; Arguirov, T. V.; Gurkov, T. D. Colloids Surf., B 2000, 19, 89. (18) De Hoog, E. H. A.; Lekkerkerker, H. N. W.; Schulz, J.; Findenegg, G. H. J. Phys. Chem. B 1999, 103, 10657. (19) Hutchison, J.; Klenerman, D.; Manning-Benson, S.; Bain, C. Langmuir 1999, 15, 7530.
10.1021/la025588x CCC: $22.00 © 2002 American Chemical Society Published on Web 07/10/2002
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is reflected in the liquid-liquid interface. Thus, since the light has to pass, or is reflected, at two different surfaces, experimental data are dependent on surface properties of both interfaces (liquid-liquid and air-liquid). The same problem is encountered when liquid-solid interfaces are studied (where the solid surface is immersed in a solution). Building a cell where the light passes perpendicular through the entering and exiting windows can circumvent this problem. The same strategy has been used in a first attempt in our lab to investigate the liquid-liquid interface, where a cubic cuvette was used (refs 15 and 16). The disadvantage is that the measurements are restricted to a particular measuring cell. Measurements at different angles of incidence require correction for the refraction of the beam in the cuvette window. The accuracy of the ellipsometric measurements is often affected due to multiple reflections and optical defects, i.e., birefringence, caused or affected by thermal and mechanical stresses in the cuvette windows.18 With the liquid-solid interfaces, this disadvantage is in most cases acceptable because here the optical contrast (difference in refractive indices) between the liquid and the solid is large and conclusions can be drawn from data obtained at only one angle of incidence. The situation is different at liquid-liquid interfaces, where the refractive indices of the two liquids usually are quite similar. In this study we present an new measuring setup for the ellipsometer, where simple light guides that automatically adjust to the angle of incidence are used. A theoretical discussion about the optical errors introduced, on the ellipsometric measurements, by different types of light guides is presented. The effect of multiple reflections between and within the end windows of the light guides is also analyzed. With this arrangement we hope to open the field of multiple angle ellipsometry as a convenient and accurate tool to study liquid-liquid interfaces in any type of measuring cell. As the mechanical force on the end window in a light guide is rather small, we can use very thin windows to reduce birefringence. This makes the setup less sensitive to optical errors induced by thermal and mechanical stresses. The setup is demonstrated by measurements at the air-decane interface, the air-water interface, the decane-water interface, and the well-known silicon/silica surface immersed in an aqueous solution. Experimental Section Materials. Pure decane (99+%, lot no. A013827101) was purchased from Acros Organics (New Jersey, USA) and used without further purification. Water was deionized and passed through a Milli-Q water purification system (Millipore Corporation, Bedford, MA). Methods. An Optrel Multiskop Ellipsometer (Optrel, Berlin, Germany), which has been extensively described elsewhere (ref 20), was modified and used as described below. The instrument consists of two adjustable arms, the laser arm and the detector arm, mounted on a goniometer. These two arms can be positioned at virtually any angle. For the experiments described here the arms rotate in the vertical plane, but rotation in the horizontal plane (and any plane between) is also possible. The laser arm contains the laser (Nd:YAG, λ ) 532 nm), a quarterwave plate, a polarizer, and a compensator, and the detector arm contains an analyzer, and a photodetector; see Figure 1a. In the present study we have used the instrument as a null-ellipsometer, where Ψ- and ∆-values are obtained from the settings of the analyzer and polarizer when the reflected beam is of minimal intensity. To be able to perform measurements on interfaces in a liquid solution, the instrument was modified as illustrated in Figure 1b. Light guides, mounted on the laser and detector arms, (20) Harke, M.; Teppner, R.; Schulz, O.; Motschmann, H.; Orendi, H. Rev. Sci. Instrum. 1997, 68, 3130.
Benjamins et al.
Figure 1. (a) Schematic illustration of the used ellipsometer setup: Q, quarterwave plate; P, polarizer; C, compensator; A, analyzer. (b) Modified Optrel ellipsometer. For practical reasons, the goniometer was turned upside down, so that the optical components now hang down from the laser and detector arms. The advantage with this mounting is an increased clearance below the arms, which increases the accessible range of the angle of incidence. (c) Cross section of the measuring cell. respectively, facilitated the light passage between air and solution. Three different types of light guides were tested: (1) solid glass rods with polished planar end surfaces (5 mm diameter and 50 mm length); (2) glass tubes with glued 1 mm thick end windows (5 mm diameter and 50 mm length); (3) glass tubes with glued 0.15 mm thick end windows (made from a cover glass of the type used in light microscopy). The tubes (or rods) used as light guides were immersed into the solution (through the air-liquid interface) in such a way that light passes inside the tubes and enters the solution perpendicularly through the glass window mounted on the laser arm. The light should again pass perpendicularly through the other light guide after being reflected at the studied interface. When measurements were performed on the air-liquid interface, these glass tubes were of course situated in the ambient air. The light guides were tightly fixed to the respective arms in front of the laser and the detector (Figure 1b). The light guide holders were adjustable, to be able to fine tune the alignment of the tubes. We will return to the alignment procedure below. A specially designed circular measuring cell with a diameter of 80 mm allowed for measurements in a large angle of incidence (Φin) interval: 35° < Φin < 70°. Furthermore, the measuring cell was designed to ensure a planar liquid surface. This was achieved by a stainless steel rim, which was wetted by the aqueous phase and covered by a Teflon ring that was wetted by the oil as shown in Figure 1c. The instrument was mounted on a damped optical table (RS4000 sealed hole tabletop with tuned damping placed on stabilizers (high-performance laminar flow isolator) Newport, Irvine, CA) to counteract the effect of ambient vibrations. This is important as air-liquid or liquid-liquid interfaces are easily disturbed mechanically. Aligning the standard optical components has been done according to the recommendations of the manufacturer, with
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the exception of the procedure of calibrating the angle of incidence, Φin. Instead of defining 0° as the position when the beam is reflected back from a liquid surface below the goniometer into the laser, as judged visually, the following procedure was applied. The arms were positioned at any fixed angle of incidence close to the Brewster angle of the air-water interface and an ellipsometry measurement was performed on a clean water surface. The reflection of light at each interface can be described by the Fresnel reflection coefficients, rp and rs for the p and s components, respectively, where p means parallel and s means perpendicular to the plane of incidence.
nj cos φi - ni cos φj rpij ) nj cos φi + ni cos φj
(1)
ni cos φi - nj cos φj ni cos φi + nj cos φj
(2)
rsij )
tpij )
2ni cos φi nj cos φi + ni cos φj
(3)
tsij )
2ni cos φi ni cos φi + nj cos φj
(4)
These coefficients depend on the angles of incidence φi and refraction φj and the refractive indices ni and nj of the media on both sides of the interface. For an interface the ratio F ) rp/rs is related to the ellipsometer angles ∆ and Ψ as
rp ) tan Ψei∆ ) tan Ψ(cos ∆ + i sin ∆) rs
(5)
By combining eqs 1, 2, and 5 and Snell’s law (ni sin φi ) nj sin φj), we can get an analytical expression for the refractive index of the reflecting material (n2) surrounded by a medium (n0).
n2 ) n0 tan Φin
(
4F 1sin2 Φin (1 + F)2
the detector slightly off-center, which will not result in any significant errors in the ellipsometric measurements. This will be discussed in detail below.
Results and Discussion
In a similar way transmission tp and ts coefficients can be described.
F)
Figure 2. Refraction at an air-solution interface. The line separating air and solution indicates the cuvette window.
)
1/2
(6)
For a clean interface between two dielectric media, the reflection coefficients are real quantities, while they become complex for a semiconductor, a metal, or any material that absorbs light at the used wavelength. Thus for dielectric media that do not absorb light, ∆ will be 180° below and 0° (or 360° depending on the definition of the angles) above the Brewster angle as obvious from eq 5, that is, F ) (tan Ψ. The recorded Ψ and ∆ values and the refractive index for pure water were used to calculate the value for Φ, correct to the third decimal, from eq 6 using an iterative procedure. The light guide on the laser arm was aligned with the aid of an adjustable mirror placed at the opposite side of the room as follows: (1) The laser arm is adjusted in a horizontal position and the detector arm is moved upward so that it does not block the light path. (2) The mirror is aligned by adjusting it so that the light beam reflected from the mirror coincides with the laser beam at the light guide window. (3) The light guide is then adjusted so that reflection from the end of the light guide on the mirror exactly coincides with the direct beam. This method will allow us to align the light guide with a precision of about (1 mrad. The light guide on the detector arm is aligned by first placing both the laser and detector arms in a horizontal position and then adjusting it until the light reflected against the end of the light guide coincides with the incoming laser beam. This alignment is not as accurate as the alignment of the light guide on the laser arm as the optical path is considerably shorter. However, a misalignment here will mainly cause the beam to hit
Influence of the Light Guides on the Ellipsometry Measurements. If the difference in refractive index between the two media that surround an interface is small, the changes in Ψ and ∆ will also be small and sensitive to optical errors in the ellipsometer. Therefore, to be able to measure on interfaces such as the oil-water interface, it is of the utmost importance to minimize all sources of optical errors in the ellipsometer. The introduction of light guides on the laser and detector arms can have a considerable effect on the ellipsometric measurements, especially if the guides are not well constructed and aligned. We will here give a short description of the different optical errors that are introduced by a light guide, in a light beam’s amplitude and phase. We will first start to examine the effect of a single light guide. Case 1. A major error in the determination of the phase shift is introduced when the glass in the light guide is birefringent. The shift of ∆, δ∆, due to birefringence depends on the orientation of the optical axis of the light guide as
δ∆ e
2πd (np - ns) λ
(7)
where d is the thickness of the window, np - ns is the difference of the refractive index of the glass in the p and s direction, respectively, and λ is the wavelength of the light. The effect of birefringence on the other ellipsometric parameter, Ψ, is relatively small and will be neglected. To reduce the errors in ∆, the difference between the refractive index in the p and s directions needs to be very small and the windows of the light guide have to be as thin as possible. However, since birefringence can be induced by mechanical stress, either from fabrication of the glass or from manufacturing the light guides, it is difficult to completely avoid this type of error. Case 2. The light guide used as the entrance window into the test solution, which in our setup is mounted on the laser arm, is the one that is most sensitive to a misalignment. Misalignment of this window will also change the direction of the light beam and therefore the angle of incidence by δΦ; see Figure 2. The introduced error, δΦ, is proportional to the angle of misalignment of the entrance window, Φmis
(
δΦ ) - 1 -
)
1 Φ nsolution mis
(8)
where nsolution is the refractive index of the solution into which the light guide is immersed. The error in Ψ and ∆ from this misalignment depends on the angle of incidence, nsolution, and the optical properties of the reflecting surface in the test solution. From this point of view a misalignment of the light guide on the detector arm is of less importance
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and will not affect the actual angle of incidence but mainly cause the beam to hit the detector slightly off-center. Case 3. Another type of error that is introduced when a light guide is not aligned perpendicular to the light beam is a difference in transmittance between the p and s directions. This difference will mainly introduce an error in the determination of the ellipsometric parameter Ψ. Snell’s law and the equations for the reflection and transmission coefficients at an interface, eqs 1-4, can be used to determine the magnitude of the Ψ-error, δΨ, as a function of the angle of incidence. At small misalignments, δΨ depends on the angle of misalignment, Φmis, as (see also Appendix A)
δΨ ≈ K1 sin2 Φmis
Figure 3. Multireflections between two light guides, where sin and sout indicate the distance between light guide and surface before and after reflection, respectively.
(9a)
where the value of the parameter K1 depends on the refractive index of the glass in the window, n1, as well as on the refractive index of the two surrounding media, n0 and n2.
K1 ≈
1 4
(( ) ( 1-
n0 n1
2
))
n0 n0 n1 n2
+
2
(9b)
The index 0 denotes the medium outside the entrance interface and 2 the medium outside the exit interface. Case 4. If a light guide is misaligned, the multiple reflections between the two parallel interfaces of the window in the light guide will change the amplitude and phase of the p and s directions differently. These differences will introduce errors in both of the two ellipsometric parameters, Ψ and ∆. The introduced errors δΨ and δ∆, respectively, can, at small angles of misalignment, Φmis, be written as (see also appendix A)
δΨ ≈ -K2 cos 2β sin2 Φmis
(10a)
δ∆ ≈ 2K2 sin 2β sin2 Φmis
(10b)
where
K2 )
(
1
and
β≈
)
n02 (n1 - n0)(n1 - n2) n1 n1 + n 2 (n1 + n0)(n1 + n2) n0 n2
(
)
n02 2πdn1 1 - 0.5 2 sin2 Φmis λ n 1
(11a)
(11b)
We here note that δΨ and δ∆ obtained from eq 10 oscillate with Φmis as discussed further below and as shown in Figure 6. This completes our discussion about errors introduced by a single light guide. An additional error occurs when the beam has to pass two light guides. This is due to the multiple reflections between the two light guides, as indicated in Figure 3. The effect on the observed ellipsometric parameters Ψobs and ∆obs from these multiple reflections is (see also Appendix B)
tan Ψobsej∆obs ≈ tan Ψej∆ (1 + r102rs2(tan2 Ψej2∆ - 1)e-j2β12) (12) where Ψ and ∆ are the ellipsometric parameters of the studied interface, r10 is the reflection coefficient of the glass-solution interface, and rs and rs are the reflection
Figure 4. Effect of multireflections between two light guides on the observed Ψobs and ∆obs values, obtained from eqs 12 and 13, as a function of the distance variation, δ(sin+sout). The reflecting surface is a silica plate with a 30 nm silicon layer in water. The parameters used for the calculations were Φin ) 65°, Ψ ) 15.457°, ∆ ) 146.350°, and r10rs ) 0.085.
coefficients of the studied interface, where rp/rs tan Ψej∆. The parameter β12 depends on the optical path between the two light guides. The parameter β12 is defined as
β12 ) 2πn1(sin + sout)/λ
(13)
The Ψobs and ∆obs values, obtained from eqs 12 and 13, as a function of the distance variation, δ(sin + sout) are shown in Figure 4 for a silica plate with a 30 nm thick silicon layer in water at Φin ) 65° (Ψ ) 15.457°, ∆ ) 146.350°, and r10rs ) 0.085). It is obvious that multiple reflections between the two light guides can introduce large errors in the observed Ψobs and ∆obs values. Figure 4 and eq 12 also show that the errors in Ψ and ∆ are periodic, with the periodicity of 2n(sin + sout)/λ. This periodicity in Ψ and ∆ requires that the light’s coherence length is sufficiently long so that several rays, in the laser beam, can interfere with each other. However, if both light guides are not aligned perfectly perpendicular to the laser beam, that is if the optical path for different rays in the beam differs by more than a wavelength, the reflected rays will be out of phase by half a period or more. This means that the amplitude of the oscillation and the error will be strongly reduced. It can be shown that a very small tilt of the light guide on the detector arm (
