Single-angle-of-incidence ellipsometry

Abstract

We introduce single angle-of-incidence (SAI) ellipsometry [U.S. patent application 20070024850 (14 July 2006)] as a technique to completely identify, i.e., totally characterize, film-substrate systems. We show that only one measurement of the ellipsometric function rho at one angle of incidence and one wavelength is totally sufficient to determine the optical constant of the film N1, its thickness d, and the substrate's optical constant N2. Obviously, it is also sufficient for characterizing only the film, determining N1 and d, and for characterizing only the substrate, determining N2 and d, as well as for characterizing only bare substrates. An inverse genetic algorithm (IGA) for complete identification is presented that is based on a physical condition of the transparent-film-absorbing-substrate system . This IGA is used to identify the film-substrate system in four separate cases. We show that removing the film thickness from the fitness function of the genetic algorithm and using the defined optimum population size to characterize the film reduces the computational effort from 20,000 to 69 fitness-function calculations; the number of calculations to characterize an absorbing layer is reduced from 80,000 to 180. This is a very significant reduction and is very welcome in real-time applications. An error analysis is presented that shows that the IGA is resilient to, not affected by, random experimental errors and that it gives very good results in the presence of both random and systematic errors of the ellipsometer system. Experimental results are given that also prove the robustness, stability, and high accuracy of the method. We present data only for the SiO2-Si film-substrate system, but the IGA works for any film-substrate system, physical or not.

Ozone-oxygen gas enhanced passivation of pure iron

“…The cos was mainly correlated with the film thickness and the estimated values of cos for sample treated at a passivation potential of 800 mV (Pa+800) and subsequent oxy-zone treatment (Pa+800 + O 3,2 ) were larger than those of as-deposited sample, Pa−350 sample and Pa−350 + O 3,2 sample. The thickness of the oxidation film and chemical compositions were simulated from the raw data and the optical parameters n (refractive index) and k (extinction coefficient) by using a software supplied along with the ellipsometer [19,20]. The n and k values of oxides and hydroxides were obtained by the baresubstrate analysis [20] of ellipsometry with the chemicals of 99% Fe(OH) 3 (wet amorphous hydroxide), 99% ␥-Fe 2 O 3 (maghemite), 99.9% Fe 3 O 4 (magnetite), 90% ␣-FeOOH (goethite), 99% ␥-FeOOH (lepidocrocite) and 99.9% ␣-Fe 2 O 3 (hematite), These chemicals were purchased from Kojundo Chem.…”

Single-instrument morphology: single-element polarizer (SEP) ellipsometers, reflecsometers, elliptometers, and reflectometers

“…The same instrument with a different DRM would lead to a different ellipsometer, in some cases totally different. For example, combining any experimental technique with the proper heuristic DRM would change a multiple-angle-of-incidence ellipsometer to a single-angle-of-incidence one [16,17]. Therefore, the selection of the DRM is important, and is crucial for some applications; using the ellipsometer in real-time applications, such as a component in a control loop for example.…”

“…The proper selection of the fitness function is crucial for using GAs. In Reference [17], we reported the use of a very efficient GA to fully characterize the film-substrate system with a minimum computational effort; obtaining the optical constants of the film and substrate, in addition to the film thickness.…”

“…In each, the inversion process is composed of tandem sections; an analytic one, followed by either a numerical [22] or heuristic one [17].…”

Single-angle-of-incidence single-element rotating-polarizer (Single SERP) ellipsometer for film-substrate systems

“…Therefore, we always recommend doing an optimization study on µ to minimize the overall computational effort. 25 The optimum population size is associated with the GA itself. A new generation of the same population size µ is repetitively generated from previous generations, starting with the initial one.…”