Ellipsometric thicknesses method

Figure 3. SPM topography images (2x2 microns) of three different islandlike PS brushes prepared by grafting-to method, effective ellipsometric thickness of PS layer 7.5M).5 nm.

The confrontation of this elegant prediction by experiment has taken many years to complete because all experimental techniques available at that time did not have the proper spatial resolution. Spectroscopic methods such as EPR, NMR, IR are only sensitive to the fraction of monomers attached to the wall. Ellipsometry measures the first moment of the monomer distribution and vields an average length called the ellipsometric thickness Hydrodynamic methods, based on flow restric-tion in capillaries covered by the adsorbed layer, yield another average length related to the maximum extension of the adsorbed layer To study concentration profiles at the solid-liquid interface, one has thus to devise special tools. 

Studies have been made on the rate of growth of oxide films on different crystal faces of a metal using ellipsometric methods. The rate was indeed different for (100), (101), (110), and (311) faces of copper [162] moreover, the film on a (311) surface was anisotropic in that its apparent thickness varied with the angle of rotation about the film normal. 

Peyser and Stromberg63 used the ATR method to measure the thickness of a polystyrene layer adsorbed on a quartz surface from cyclohexane solution at 35 °C and compared it with the thickness obtained by ellipsometry. Good agreement was observed although the ellipsometric measurements were made for the chrome plate. 

The technique can also be used for multilayered structures. The corresponding equations are then more complicated and are usually applied to inorganic semiconductors [36-38] due to their better defined interfaces and geometry compared with organic semiconductors. In the case of transparent media (k = 0), the ellipsometric equations can be used to determine both n and the thickness of the film with sensitivity below 1 A. This is much better than can be achieved by methods based on 7Z and T, thus reducing the uncertainty in the n determination. Several examples of ellipsometry applied to CPs are reported in the literature [32,43,44],... 

By combining this technique with capacitive coupling or ultrasound reflection, wafer thickness and wafer flatness information is also obtained. A further step is to wafer-map the data. Using optical scanning, surface defect maps are generated (2.) and insulator thickness variations are measured ellipsometrically and displayed. As discussed further on, recombination lifetime maps can also be generated by non-contacting methods. 

For example, the ellipsometric technique was used to determine the interfacial thickness in SAN/PA blends, compatibilized by addition of SMA [Yukioka and Inoue, 1991, 1993]. A thin bi-layer film of SMA/SAN was prepared then mounted on a thick PA substrate. The interfacial thickness varied with the compatibilization time from A1 = 2 to 30 nm. The method was also used to study the interphasial thickness variation in PCL blends with CTBN or CTBR. Without a reactive modifier (aminopropyltriethoxysilane, APS), the measured thickness was A1 = 3 nm, upon addition increasing to 6 nm [Okamoto and Inoue, 1993]. 

Many ingenious methods have been introduced to study protein adsorption. If the kinetics of the adsorption process are important, the ellipsometric method introduced by Rothen (3) is probably the best. In this method protein adsorption can be studied ijn situ from a solution. The method has been used to study the kinetics of both the adsorption of protein in single layers and in double layers that can occur in the immune-reaction. When protein such as bovine serum albumin (BSA) was adsorbed from a dilute solution onto a surface, after a delay of a few seconds, steady-state diffusion controlled the adsorption process and, consequently, the amount bound to the surface increased linearly with time. However, as the surface became covered, adsorption slowed down, because it was now limited by the number of available sites on the surface. The final layer of BSA was roughly 2 nanometer thick. 

Although the optical properties of the adsorbed layer by evaluation of the ellipsometric data obtained are quite interesting for its characterization, for inter-facial science the information about the amount adsorbed at an interface is especially important. In the calculation of this quantity, however, the problem appears to be of a proper proportionality between the layer properties provided by ellipsometry and the adsorbed amount. Recently, it was shown that for ultrathin adsorbed layers of conventional soluble surfactants ellipsometry is insufficient and additional experimental methods are required (245,250). Relatively thick layers are also often not homogeneous in the bulk (substrate) normal to the interface. In this case the refractive index and the thickness of the layer calculated from the experimental values of 8 A and 8 A represent mean optical quantities. If, additionally, the relractive index n is a linear function of the solute concentration in the layer ... 

In principle ellipsometric measurements are a way of determining film thickness in situ, as a function of redox state, and this was an early driving force behind attempts to apply ellipsometry to electroactive polymers. The thickness of an electroactive polymer film is a highly significant parameter. As a function of the redox state of the material, thickness can be expected to vary with, among other parameters, polymer tertiary structure and solvent and ion populations. Nonoptical methods of determining film thickness are rather unsatisfactory, since they are invariably made ex situ. 

The ellipsometric method has been developed by Yukioka and Inoue (1991, 1994). The principles of the technique and the model used for calculating the thickness of the interphase are schematically illustrated in Figs. 4.13 and 4.14, respectively. The retardation (A) and reflection ratio (tan(i/<)) can be determined from the ellipsometric readings. The adopted model assumes the existence of four layers air, thin polymer-1, interphase, and thick polymer-2 (see Fig. 4.14). In the interphase the refractive index is assumed to be an average n = iti+ ni)H. Thus, one can compute the best value of the interfacial thickness, do, to fit the observed values of A and tan( ). The following relations were derived for the computation of d ... 

The inversion of the Drude equations, that is the estimation of unknown thicknesses or optical constants from ellipsometric measurements, relies upon the application of computer-intensive search and optimization methods, which are well within the capabilities of personal computers. The software for solving a wide variety of film problems is now available as part of the instrumentation package from a good number of ellipsometer manufacturers. This has resulted in the fast-widening scope of ellipsometry as reflected in the number of publications in which the technique is dominant. 

More direct methods than kinetic ones have also been tried in order to get a picture of the morphology. Ellipsometry is an excellent tool for determining thickness of films. Because the charge Q used for making the films should be related directly to thickness if the growth is uniform, ellipsometric constants can be used... 

In the broadest sense, ellipsometry is concerned with measurement and analysis ofthe state of elliptical polarization of light (Rothen, 1964). However, it is generally used to mean a method, based on analysis of elliptical polarization, to determine the properties of thin films (particularly the thickness) on dielectric or metal surfaces. The basic theory derives from the work of Lord Rayleigh and Paul Drude in the late 19 century. L(xd Rayleigh had inferred the presence of viscous films of minute thickness on water surfaces, and devised an experiment whereby the effect of these films on the polarization state of a reflected beam could be measured with great precision. Drude, meanwhile, was interested in the reflection of light from thin films oi solids, and derived, based on Maxwell s equations, the fundamental formulae on which ellipsometric instruments are based. 

Ellipsometry is a high-precision optical characterization technique, the potential of which has not yet been sufficiently exploited in polymer science. It is a rapid and nondestructive experimental method for the analysis of surfaces and thin films. Besides the determination of film thickness with high sensitivity ( 0.1 nm), optical parameters related to material properties can also be evaluated [1]. The facts that ellipsometric measurements can be performed under any ambient conditions, and require no special sample preparation procedures, provide a definite advantage over other surface science techniques [2—4]. 

With regards to stratified systems, it is noticeable that the layer thickness can, in principle, be determined by using the ellipsometric method. However, this does not hold for ultrathin films (monolayers and multilayers) because the infiuence of anisotropy, molecular density, and thickness cannot be discriminated in this case [68]. 

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