## Total Internal Reflection Ellipsometry

Before discussing TIRE, it is useful to recall two important measurement techniques, one of which is based on the ellipsometric principle and the other on the SPR phenomenon. In brief, ellipsometry can be characterized as a measurement of the change of the state of polarization of light upon reflection on the sample surface (Fig. 1). As the light is not only re-

Fig. 1. The principle of ellipsometry (see text for details). p Parallel, s perpendicular

flected on the surface of a sample but also penetrates into the outermost material under the surface (and is then reflected and refracted further at each interface), the result of an ellipsometric measurement contains information about the optical parameters and morphology of the materials present (often as thin films) within the penetration depth of the light. The experimental data obtained from ellipsometry is usually expressed by the two parameters y and A (called ellipsometric angles). They are defined by the ratio p of the complex-valued reflection coefficients Rp and Rs for light parallel (p) and perpendicular (s) to the plane of incidence, respectively, such that

The amplitude ratio of p is thus given by tan y ,and A is the phase difference between the reflection coefficients in the p- and s-directions.

Ellipsometry is an indirect technique and p contains all information about the structure and type of the investigated material in complex expressions. Thus, in most cases an ellipsometric measurement does not give direct information about one specific property of the sample. One exception is when measurements are performed on a flat ideal, film-free substrate; p can then be directly inverted to provide the complex-valued refractive index of the substrate material. However, in general an appropriate optical model has to be developed and nonlinear regression has to be performed to obtain the values of the parameters of the material under investigation. Nowadays, modeling procedures are often built into the data acquisition software of ellipsometers. Also, databases of optical properties of various materials have been developed over the past decades (Palik 1985, 1991). All this makes ellipsometry a powerful measurement technique. More detailed information about ellipsometry can be found elsewhere (Azzam and Bashara 1987; Tompkins and McGahan 1999; Tompkins and Irene 2005).

Total internal reflection may occur when light is traveling from a medium with higher refractive index to a medium with lower refractive index, given that both media are transparent. Above a certain angle of incidence, called the critical angle, the light is totally reflected back into the higher refractive index medium, and no light passes into the low-index medium. However, due to the so-called evanescent field (Yeh 1988), part of the light penetrates the low-index medium. This forms the basis for the principles behind the SPR and TIRE.

ThemeasurementtechniqueofSPRtakesitsnamefrom thephenomenon with the same name. SPR can be observed in many materials, but it is most significant in free electron materials, especially in metals like silver, gold, and copper. SPR can be excited under conditions of total internal reflection; a typical SPR setup is presented in Fig. 2 (Johansen et al. 2000b).

Photo diode array detector

Photo diode array detector

Fig. 2. Typical surface plasmon resonance setup with a fixed photodiode array detector and a focused light beam. Depending on the actual conditions (i. e., the refractive index of the adsorbed proteins) a surface plasmon can be excited at 0SP(1) or 0SP(2)

The light, which has to be p-polarized is incident through the prism and is reflected at the interface between the glass and the thin metal layer. The requirements for excitation of SPR are fulfilled if the metal has suitable optical properties and thickness. The detector measures the intensity of reflected light. Under certain experimental conditions, which include angle of incidence, wavelength, and the presence and type of overlayer on the surface of the metal layer, all light can be coupled into a surface plasmon wave traveling along the metal surface. In this case no light is reflected and the detector reports zero intensity. When the angle of incidence is varied, a minimum (a "dip") in intensity is observed. The position of the dip turns out to be very sensitive to the presence of an overlayer on the metal surface and can be used for quantification (Johansen et al. 2000a). Nowadays, the SPR technique is widely used for studies of the behavior of proteins on various metal surfaces. Similarly to ellipsometry, this is an indirect technique, so modeling also needs to be applied to obtain information about the investigated material (adsorbed onto the metal surface). As SPR only has one measurement parameter (the changes in the dip position are monitored), it makes this technique powerful in the sensor area. Unfortunately, it is often very hard to obtain more complete information about the investigated material, so complementary techniques need to be applied.

The experimental setup used for TIRE (Fig. 3) is very similar to the SPR setup. However, in addition to the light source, polarizer, and detector, we introduce a second polarizer (called an analyzer), which is necessary to perform ellipsometric measurements. In the ellipsometric configuration described here, the analyzer is rotating. The detector signal is analyzed and provides y and A. In addition, notice that the polarizer azimuth is not in the p-direction as in SPR, but is typically fixed at 45° from the plane of incidence. Immediately one can observe the main difference between detector detector

. / /index matching liquid

^proteins in solution, etc.

. / /index matching liquid

^proteins in solution, etc.

Fig. 3. Schematic view of the total internal reflection ellipsometry (TIRE) system (with a trapezoidal prism as an example). The magnified view (in the circle) shows the index-matching liquid inserted between the prism and glass slide, and the metal layer deposited on the glass slide (see text for details)

the TIRE and SPR techniques on one hand and traditional ellipsometry on the other: measurements are performed from the "back side" of the sample, in comparison to the "front side" measurements made in traditional ellipsometry. This is quite an advantage when in situ studies on protein adsorption are of interest - light does not need to travel through the liquid (which thus is allowed to be opaque), which minimizes disturbances in the measured signal. In comparison to SPR, TIRE provides two parameters, one containing information about intensity (^), quite similar to the intensity measured in SPR, and a second one, the phase difference (A), which is obtainable only in ellipsometry. If the measurement conditions are set so that the SPR effect is utilized, one can combine both techniques to obtain a powerful measurement technique with measurement detection limits normally unreachable for both traditional ellipsometry and SPR (Arwin and Poksinski, unpublished data ). It should be noticed that in principle, the SPR effect is not necessary for the TIRE technique and it will still have some advantages (i. e., measurements is possible in opaque solutions), but the sensitivity will not be as good as when the SPR effect is employed. One should also notice that in most applications of the SPR technique, the angle of incidence is varied (with fixed wavelength), whereas in most cases of TIRE spectroscopy is performed (with a fixed angle of incidence). This should be noticed when comparing the results from both techniques.

The description presented herein is quite brief. However, it should be sufficient to get an overview of the phenomena and theoretical aspects of TIRE. Ellipsometry (Azzam and Bashara 1987; Tompkins and McGahan 1999; Tompkins and Irene 2005) and SPR (Liedberg et al. 1995; Raether 1988) are well-documented techniques, and complementary information about TIRE is also available (Arwin et al. 2004; Nabok et al. 2005; Poksinski et al. 2003; Poksinski and Arwin 2003, 2004; Rekveld 1997).