Ellipsometry model

Fig. 7.29. Top Reflectivity at normal incidence of two PLD grown Bragg mirrors with 5.5 and 10.5 YSZ-MgO layer pairs obtained from the ellipsometry model analysis. By doubling the layer number, the reflectivity was increased from 90 to 99%. The UV-vis ellipsometry data were fitted best with layer thicknesses of 38-46 nm YSZ/48-54nm MgO for the 5.5 layer pair Bragg, and 46.4 0.7 nm YSZ and 51.9 0.5 nm MgO for the 10.5 pair Bragg. Measured and calculated by R. Schmidt-Grand. Bottom SNMS isotope intensity depth profile of this 5.5 x YSZ/MgO Bragg structure...

A quite different means for the experimental determination of surface excess quantities is ellipsometry. The technique is discussed in Section IV-3D, and it is sufficient to note here that the method allows the calculation of the thickness of an adsorbed film from the ellipticity produced in light reflected from the film covered surface. If this thickness, t, is known, F may be calculated from the relationship F = t/V, where V is the molecular volume. This last may be estimated either from molecular models or from the bulk liquid density. 

In recent years, high-resolution x-ray diffraction has become a powerful method for studying layered strnctnres, films, interfaces, and surfaces. X-ray reflectivity involves the measurement of the angnlar dependence of the intensity of the x-ray beam reflected by planar interfaces. If there are multiple interfaces, interference between the reflected x-rays at the interfaces prodnces a series of minima and maxima, which allow determination of the thickness of the film. More detailed information about the film can be obtained by fitting the reflectivity curve to a model of the electron density profile. Usually, x-ray reflectivity scans are performed with a synchrotron light source. As with ellipsometry, x-ray reflectivity provides good vertical resolution [14,20] but poor lateral resolution, which is limited by the size of the probing beam, usually several tens of micrometers. 

Plasma analysis is essential in order to compare plasma parameters with simulated or calculated parameters. From the optical emission of the plasma one may infer pathways of chemical reactions in the plasma. Electrical measurements with electrostatic probes are able to verify the electrical properties of the plasma. Further, mass spectrometry on neutrals, radicals, and ions, either present in or coming out of the plasma, will elucidate even more of the chemistry involved, and will shed at least some light on the relation between plasma and material properties. Together with ellipsometry experiments, all these plasma analysis techniques provide a basis for the model of deposition. 

Thus, ellipsometry gives direct evidence for a model of the initial stages of polythiophene growth, disproving the conclusions based purely on coulo-metry. In the same paper, Hamnett and Hillman were able to obtain valuable and complementary information not just on the initial stages of the polymerisation but also on the mechanism of the subsequent nucleation and growth. The unique piece of information that the ellipsometer was able to extract, the changes in film thickness (in real time), when combined with coulometric data allowed a wealth of information to be deduced, e.g. with respect to the film composition, and ably showed the power of the technique. 

Whereas the XSW technique takes advantage of the standing wave established on the total reflection of X-rays from a mirror surface, a conceptually more straightforward approach is that of simply specularly reflecting an X-ray beam from an electrode coated with the film of interest, measuring the ratio of the intensities of the incident and reflected rays, and fitting the data, using the Fresnel equations, to a suitable model an approach similar to optical ellipsometry. 

One of the drawbacks of ellipsometry is that the raw data cannot be directly converted from the reciprocal space into the direct space. Rather, in order to obtain an accurate ellipsometric thickness measurement, one needs to guess a reasonable dielectric constant profile inside the sample, calculate A and and compare them to the experimentally measured A and values (note that the dielectric profile is related to the index of refraction profile, which in turn bears information about the concentration of the present species). This procedure is repeated until satisfactory agreement between the modeled and the experimental values is found. However, this trial-and-error process is complicated by an ambiguity in determining the true dielectric constant profiles that mimic the experimentally measured values. In what follows we will analyze the data qualitatively and point out trends that can be observed from the experimental measurements. We will demonstrate that this... 

It is easy to figure out why this is. The theory of ellipsometry assumes that the surface is atomically flat. It is possible to model roughness as a series of declivities in the surface. These are taken as being full of solution. Thus, the ellipsometer sees pools of solution where it assumes the electrode surface should be. Especially in the determination of submonolayers, the result can contain significant errors in n and K that have been calculated on the assumption of a completely smooth surface (Brusic and Cahan, 1969). 

No carbon was recorded for the D-treated film. The O/Si composition ratio was found to be 2.08 and is attributed to the extent of condensation as the organic phase has been removed completely. Based on the amount of Si for sample D and assuming a density of 2.3 g cm3 for amorphous SiC>2, the top layer would correspond to a thickness of 154 nm, if a dense layer is assumed. As the actual layer thickness is 458 nm, this would imply a porosity of 66%. Here a considerable discrepancy with the porosity obtained from ellipsometry is evident. In this respect it should be noted that the RBS measurement was done more to the edge of the sample than ellisometry, where the thickness is smaller than in the centre. Further, the refractive index determined with ellipsometry is very accurate. However, the relation of porosity with refractive index depends on the model used. 

DePalma and Tillman investigated self-assembled monolayer films from three silanes, tridecafluorooctyltrichlorosilane, undecyltrichlorosilane, and octadecyl-trichlorosilane, on silicon, a popular model substrate for such studies with great relevance to potential semiconductor coating applications. They characterized the films by ellipsometry and contact angle measurements (data for trideca-fluorooctyltrichlorosilane are included in Table 1), but more usefully from an applicational viewpoint, they carried out friction and wear measurements with a pin-on-disk device where the silicon wafer substrate, coated with monolayer, is moved under a spherical glass slider. Optical microscopy was used to assess wear. Table 2 summarizes DePalma and Tillman s data and their comparison with the classical self-assembled monolayer friction studies of Levine and Zisman [18]. 

Ellipsometry determines a certain average thickness th of the adsorbed layer. However, what is important for the evaluation of polymer conformations in this layer is the root-mean square thickness t. Hence, it is necessary to find a way of relating t to th. McCrackin and Colson66 studied this problem for several distributions of segments and found tnn, = th/l-5 for the exponential distribution and t - th/1.74 for the Gaussian distribution. Takahashi et al.67 showed that t = th/1.63 for the one-train and two-tail model (see Eqs. (B-110) and (B-lll)). 

The main experimental technique applied in this chapter is SE. Several textbooks were written on SE [73,114-118], Therefore, only some basic concepts are described. SE examines the relative phase change of a polarized light beam upon reflection (or transmission) at a sample surface. In Fig. 3.4 the setup of an ellipsometry experiment is shown. Upon model analysis of the experimental data, the DFs and thicknesses of the sample constituents can be extracted. Two different experimental approaches have to be distinguished, standard and generalized ellipsometry. 

In Spectral Ellipsometry, changes in the state of polarisation of white light upon reflection at surfaces are monitored. This enables separation of the refractive index and physical thickness by modelling of a layer system. To handle correlations between layer thickness and refractive index, adequate layer thicknesses have to be guaranteed to avoid physically unreasonable solutions of the fitting due to local minima. 

Our approach to this problem involves a detailed mechanistic study of model systems, in order to identify the (electro)chemical parameters and the physicochemical processes of importance. This approach takes advantage of one of the major developments in electrochemical science over the last two decades, namely the simultaneous application of /ton-electrochemical techniques to study interfaces maintained under electrochemical control [3-5]. In general terms, spectroscopic methods have provided insight into the detailed structure at a variety of levels, from atomic to morphological, of surface-bound films. Other in situ methods, such as ellipsometry [6], neutron reflectivity [7] and the electrochemical quartz crystal microbalance (EQCM) [8-10], have provided insight into the overall penetration of mobile species (ions, solvent and other small molecules) into polymer films, along with spatial distributions of these mobile species and of the polymer itself. Of these techniques, the one upon which we rely directly here is the EQCM, whose operation and capability we now briefly review. 

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