Ellipsometry data analysis

Ellipsometry is very sensitive to sample surface and interface structures. Hence, to incorporate these structures into an optical model for the investigated sample is necessary in ellipsometry data analysis. The effective medium approximation (EMA) [66] has been applied to calculating the complex refractive indices and dielectric constants of surface roughness and interface layers. In addition, the volume fractions in composite materials can be got from ellipsometry analysis using EMA. 

The ellipsometry data analysis procedure consists of the following steps [6,7] ... 

Jellison GE (1998) Spectroscopic ellipsometry data analysis measured vs. calculated quantities. Thin Solid Films 313-314 33-39. 

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...

The following chapter presents the basics of ellipsometry and discusses some recent advances. The article covers the formalism and theory used for data analysis as well as instrumentation. The treatment is also designed to familiarize newcomers to this field. The experimental focus is on adsorption layers at the air-water and oil-water interface. Selected examples are discussed to illustrate the potential as well as the limits of this technique. The authors hope, that this article contributes to a wider use of this technique in the colloidal physics and chemistry community. Many problems in our field of science can be tackled with this technique. 

In short, ellipsometry applied to adsorption layers of ionic soluble surfactants does not measure the surface excess. The ellipsometric signal may show a non-monotonic behaviour which is caused by a redistribution of the ions between compact and diffuse layer. The data analysis within the classical model of a charged double layer yields an estimate of the prevailing ion distribution. 

Rapid advances in computer technolc during the past decades have made possible the automation of ellipsometry instruments and data analysis [5]. Developments in spectroscopic ellipsometry, based on rapid data collection, can offer the real-time characterization of dynamic behavior of thin layers [33,34], including the evaluation of structural changes, phase separation, or the swelling of polymer films [17]. 

In this chapter, we will provide an overview of principles, measurement techniques, data analysis procedures for ellipsometry, and introduce the related applications of ellipsometry, especially in the field of stoichiometry. 

Fig.2 shows the process of ellipsometry data fitting and model analysis, and it includes the following steps ... 

Optical constants are closely related to the wavelength of incident light, and it is known as the dispersion relation. In the analysis of ellipsometry data, it is an important step to select appropriate dispersion model for the investigated samples if the dielectric function is unknown. 

Constructing an optical model. In the data analysis procedure in ellipsometry, an optical model corresponding to the investigated sample structures must be constructed firstly. An optical model is represented by the complex refractive index and layer thickness of each layer, normally, it consists of an air/thin film/ substrate structure. It should be decided if any layer is anisotropac at this stage, and whether or not interface layers are to be modeled as a single effective medium approximation, or is a more complicated graded interface to be used for the sample. 

This chapter introduces the principles, measurement techniques, data analysis procedures for ellipsometry, and provides the related applications of ellipsometry, esp>ecially in the field of stoichiometry. As examples, we give an overview of the various eUijjsometiy applications in stoichiometry for surface and interfaces, alloys and compwsites, etc. It s shown that ellipsometry, either alone or in combination with other techniques, is now a mature technique which has been successfully applied to large variety applications. There will be a bright future for ellipsometry as its combine accuracy, speed, and proven reliability with the huge advantage of nondestructive characterization. 

Many earlier attempts to utilize reflectance data in combination with ellipsometry data seem to have failed because of improper experimental conditions which resulted in poor resolution. In particular, the proper choice of an angle of incidence has been found to be crucially important for achieving high resolution, as will be discussed in connection with error analysis in Section III.6. The often-used angle of incidence near the principal angle of incidence for many metals) turns out to be an extremely... 

Double films formed on InP were studied by applying ex situ ellipsometry after successive etching steps of the thermally formed oxide by an HF solution. From calculations based on a four-phase model (see Appendix A1 for treatment of two and more layers), the existence of an easily etched outer layer with smaller refractive index and a more durable inner layer with larger index was shown, which is consistent with XPS analysis. In the same work, in situ ellipsometry data was shown to be explained by the presence of a liquid layer when a microscopic model based on the Lorentz-Lorenz relation was used. Other ellipsometric studies of double films, such as double films of Si02 and Si3N4 on Si, have been reported. 

Ellipsometry experiments produce values that are not useful by themselves computers must be used to obtain useful quantities such as thin film thickness or the optical functions of materials. The advent of modern computers has resulted in the invention of several spectroscopic ellipsometers and the creation of more realistic analysis programs required to understand spectroscopic ellipsometry data. 

Any ellipsometer will only measure characteristics of the light reflected from or light transmitted through the sample. Ellipsometers do not measure film thicknesses or optical functions of materials, although these parameters can often be inferred very accurately from the ellipsometry measurements. Data analysis is an essential part of any ellipsometry experiment. 

Dielectric constants of metals, semiconductors and insulators can be detennined from ellipsometry measurements [38, 39]. Since the dielectric constant can vary depending on the way in which a fihn is grown, the measurement of accurate film thicknesses relies on having accurate values of the dielectric constant. One connnon procedure for detennining dielectric constants is by using a Kramers-Kronig analysis of spectroscopic reflectance data [39]. This method suffers from the series-tennination error as well as the difficulty of making corrections for the presence of overlayer contaminants. The ellipsometry method is for the most part free of both these sources of error and thus yields the most accurate values to date [39]. 

Manual null ellipsometry is accurate but infrequently done, due to the length of time needed to acquire sufficient data for any meaningffil materials analysis. Automated null ellipsometers are used, for example, in the infrared, but are still slow. Numerous versions of last automated ellipsometers have been built. Examples... 

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. 

Ellipsometry, a classical technique that is commonly employed in the study of thin films on solid supports, has long been used to investigate Langmuir monolayers. The relative ease with which such measurements can now be carried out, and their high sensitivity and high spatial resolution, has led to renewed interest in the method. Rasing et al. have recently described studies on PDA in which the phase retardation was measured as a function of the surface pressure. Fluctuations in the signal can be correlated with the texture of the monolayer, and estimates of the sizes of the domains and their character can be obtained from quantitative analysis of the data. 

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