Optical reflectance and ellipsometric

Characterization of Materials, Thin Films, and Interfaces by Optical Reflectance and Ellipsometric Techniques... 

A good review article on optical constants and their measurement is that by Bell (1967). Determination of optical constants from reflectance measurements is treated by Wendlandt and Hecht (1966) and from internal reflection spectroscopy by Harrick (1967). Ellipsometric techniques are discussed at length by Azzam and Bashara (1977). 

At planar interfaces there are four main types of linear optical signals that are detected by different techniques. Three of them are related to reflection and one to attenuated total reflection. In reflection methods the basic measurable parameters are related to rp and rs - the complex am-phtudes of the reflection coefficients of the light polarized parallel p) and perpendicular s) to the incidence plane, respectively (Fig. 17). These are reflection coefficient = rs(p), phase of reflected light 5j(p) = (l/2/)lnK(p)/rf(p), ellipsometric parameters = tan rp/rs and A =... 

This equation is the so-called basic ellipsometric equation. It contains R and R which depend on the optical properties of the reflecting system, the wavelength of the light X the angle of incidence cp and the experimentally measurable parameters Pand A. For the reflection at a clean interface, the Rp and R are the Fresnel coefficients (246) of the single uncovered interface. They depend only on the refractive indices of the two adjacent phases and the angle of incidence. For systems that do not absorb light the optical constants of the two bulk phases (ambient and substrate media) are usually obtained from the experimental values of P and A for the clean interface (denoted by subscript 0 via Eq. (111). For a layer-covered interface, multiple reflections and refractions take place within the layer (Fig. 24). 

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. 

So far we introduced two quantitites which account for changes in the state of reflection upon reflection. We also discussed how these quantities can be measured. The next chapter deals with the theory of reflection and illustrates means for a calculation of the ellipsometric angles of a given optical layer system. 

Some of the basic facts of optics pertaining to ellipsometry will be presented briefly in this and the following subsections. Detailed treatment of the optical principles and the derivation of the equations for the reflection and the refraction of light can be found in standard textbooks on optics or electromagnetic radiation. A short summary of optical principles for ellipsometry was presented in a previous review on ellipsometric optics with special reference to electrochemical systems by the present author. ... 

Ellipsometric techniques in which amplitude ratios and phase shifts for reflected light are directly measured as opposed to the previous technique in which the phase shift is indirectly obtained. This is difficult to do over large wavelength regions because of requirements on optical elements such as polarizers and retarders. 

With ellipsometry the polarization state of reflected radiation rather than just its intensity, is experimentally determined. Ellipsometry is not so much another experimental technique but a more thorough variety of the traditional ones, whether external or internal reflection. Two results per resolution element, namely the ellipsometric parameters (cf. Eq. 6.4-17) and A, are derived independently from the measurements. These can further be evaluated for the two optical functions of the medium behind the reflecting surface or other two data of a more complex sample. In any case there is no information necessary from other spectral ranges as it is for Kramers-Kronig relations. In comparison to the conventional reflection experiment, ellipsometry grants more information with a more reliable basis, e.g. since no standards are needed. 

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. 

Ellipsometric Determination of Film Thickness. The principal use of the ellipsometer was to study the upper edge of the films on vertical plates where the thickness became less than 1000 A. and could not be observed with the interference microscope. The ellipsometric measurement of film thickness is described in the literature [4,6]. For the purposes to which the technique was applied here, the approximate equation given by Drude [6] relating the film thickness and refractive index with the optical parameters of the incident and reflected light was entirely adequate. In order to use the Drude approximations it was necessary to assume the refractive index of the liquid film to be the same as that of bulk liquid. These approximate equations are highly inaccurate for film thickness greater than 100 A. 

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