Parameter Ellipsometry

For the thin surface oxide film which absorbs light, the estimation of three unknown parameters ate required which are a teal part (refractive index, ni) of complex refractive index, Nj = 2-j 2. an imaginary part (extinction coefficient, and thickness of the 

To overcome this difficulty, several methods are proposed for obtaining the three unknowns without assumptions. First, one has to measure reflectance, R, in addition to F and A. During the oxide film formation, the reflectance change, AR, is measured with the changes of F and A. Since lo in Eq. (18) corresponds to the reflection intensity from the sample surface, the photometric ellipsometer can easily be modified to the simultaneous measurement of reflectance. For the nulling ellipsometer, however, it is difficult to simultaneously measure the reflectance with F and A. From the three parameters of F, A, and R, one can calculate the three unknowns, h, and d with help of computer program. 

For the other technique for the estimation, multiple-incidence angles method has been apphed. The T and A are measnied by several angles of incidence (( )i) and the optimal values of ri2. 2, and d were calculated by the sets of Fi and Ai at each angle, ( )i,i. 

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Other workers have studied polythiophene electropolymerization with two-parameter ellipsometry. The importance of experimental conditions in the... 

Combined Reflectance-Ellipsometry (Three-Parameter Ellipsometry) Method... 

This modified ellipsometry is the combined reflectance-ellipso-metry technique, also known as the three-parameter ellipsometry (TPE) in contrast to the conventional two-parameter ellipsometry. Since it was first introduced in 1971 by Paik and Bockris to study passivation film formed anodically on cobalt, TPE has proven to be a powerful technique for determining all three unknowns from purely optical measurements alone. The measurements for A, and R are made with the same experimental setup as for the conventional ellipsometer, with minor modifications of the measurement routine if necessary. Here, R is the reflectance at the same angle of incidence as for the A and if/ measurements. Therefore, no alignment change is necessary for additional measurement of R. With some automatic ellipsometers (see Section III.5), all three measurements can be recorded simultaneously. It should be emphasized once more that A, ij/, and R are mutually independent functions, despite the fact that both il/ and R are defined by combinations of and r. ... 

Thus, the four equations (19a)-(19d) are reduced to (20a) and (20b), which are the equations used in conventional two-parameter ellipsometry two equations are lost in the process of taking the ratio r /r This is where the problem originates. However, because r and r can be determined from a light intensity measurement, along with A, it is possible to use three equations, namely (19a), (19b), and (20b), to determine three unknowns. Alternatively, Eqs. (16b), (20a), and (20b) can be used in conjunction with measurements of R, A, and ij/. The latter method is preferred in... 

Three-parameter ellipsometry is based on the fact that there can be three independent equations and there are three unknown variables pertaining to a surface film. All three equations are related to actual quantities measured with a fixed set of wavelength and angle of incidence. Gottesfeld et al measured and R which are and respectively, and A. In another of their works, measurements of R and R in addition to A and were made. This amounts to a redundant use of the equations because the ij/ function is not independent of the R and R functions, but these four measurements may serve to enhance the accuracy of determination by suppressing measurement errors. 

The combined ellipsometry-reflectance method—three-parameter ellipsometry—has been subject to error analysis. Cahan showed that, while it is possible in principle to obtain an unambiguous solution for the optical constants and thickness of a film by three-parameter ellipsometry, the method does not guarantee that a solution can be obtained in practice. He also pointed out, by working with sample data from electrochemically produced films, that the numbers obtained as the solution are not necessarily physically real when the three-layer model is inadequate for the particular system. Chung, Lee, and Paik" studied the forward and reverse sensitivity analyses for three-parameter ellipsometry to obtain the forward sensitivity coefficients (dMldoi) > and the reverse sensitivity coefficients for a passive film on nickel (here... 

The most important factor turned out to be the judicious choice of the angle of incidence. Thus, the sensitivity analysis confirms the earlier proposition that, for a successful application of three-parameter ellipsometry, it is essential to choose an incident angle that is well below the principal angle of incidence. At the principal angle of incidence, the relative phase retardation A is near 90° and the sensitivity in the A measurement is near maximum. Therefore, angles near the principal angle are most often... 

Anodic films on platinum were analyzed with ellipsometry and related techniquesand by three-parameter ellipsometry. The film formed in sulfuric acid solution at potentials higher than about 1.0 V versus NHE was found to be extremely thin (2 5 A, depending on potential) and light-absorbing ( 2.8, 1.7). 

Thickness (x) and the Optical Constants (it, k) of Anodic Films on Metab Determined by Three-Parameter Ellipsometry... 

Table 2 is a summary of the optical constants and thickness of the anodic films on various metal surfaces determined by the three-parameter ellipsometry. 

The optical principles and equations used in the technique are concisely summarized. The combined reflectance-ellipsometry (three-parameter ellipsometry) method and spectroscopic ellip-sometry are expected to be applied to an increasing number of studies in interfacial electrochemistry. The importance of proper experimental conditions, especially the proper choice of incidence angle is emphasized. Instrumentation, experimental methods, and error and sensitivity problems are dealt with. Some typical and recent applications in electrochemistry are reviewed. 

Figure 16. Change of fihn thickness of passive oxide formed in pH 8.4 horate solution as a function of time. The refractive index (n2) and extinctio index (k2) of the film which was simultaneously estimated from the 3-parameter ellipsometry was also plotted. Reprinted from K. Azumi, T. Ohtsuka, and N. Sato, pH dependence of Thickness of Passive Films on Iron Measurement hy three Parameter Reflectrometry , Denki Kagaku, 53 (1985) 700, Copyright 1985 with permission from The Electrochemical Soc. of Japan.

Figure 18. Change of (a) potential E and current density (B) ellipso-metric parameters, Pand A, and reflectance, ARJRo = (R(f)-RoyR

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