Ivan Ohlídal

Ellipsometric parameters and reflectances of thin films with slightly rough boundaries

Abstract In this theoretical paper, formulae for important optical quantities of single layers with slightly randomly rough boundaries are derived by means of a generalized Rayleigh–Rice theory. Thus the formulae for the specular reflectances and ellipsometric parameters of the layers mentioned are presented. The theoretical results are illustrated by a numerical analysis. Practical features implied by this analysis to be relevant from the experimental point of view are introduced as well. Moreover, relations expressing the flux of scattered light are presented.

3 – Ellipsometry of Thin Film Systems

In this paper, a review of both the important theoretical and experimental results concerning ellipsometry is presented.

Influence of overlayers on determination of the optical constants of ZnSe thin films

In this article a multisample modification of variable angle spectroscopic ellipsometry is used to characterize ZnSe thin films prepared by molecular beam epitaxy on substrates formed by GaAs single crystals. Atomic force microscopy (AFM) is employed to characterize the morphology of the upper boundaries of these films. To interpret the ellipsometric data a relatively complicated physical model that contains a rough overlayer between the ambient and the ZnSe film and a transition layer between the GaAs substrate and the ZnSe film is employed. Several models of dispersion of the optical constants of the overlayers are examined to interpret the ellipsometric data. It is shown that the choice of overlayer dispersion model has a strong influence on determining the optical constants and dielectric function of the ZnSe films in the near-UV region. Within the visible region there are no differences between the overlayer dispersion models regarding determination of the ZnSe optical constants. The spectral depende...

IV: Scattering of Light from Multilayer Systems With Rough Boundaries

Publisher Summary This chapter discusses the scattering of light from multilayer systems with rough boundaries. Multilayer systems are employed in various branches of applied optics and the optics industry. The chapter reviews the important theoretical and experimental results concerning the optics of rough multilayer systems. The physical models of rough boundaries (surfaces) play an important role in the optics of rough multilayer systems. The theoretical approaches enable us to calculate optical quantities corresponding to the rough boundaries and rough thin film systems. The interpretation of experimental data using the theoretical results introduced has been described. Relevant methods for the optical characterization of rough surfaces, rough single layers and rough multilayer systems have been outlined. The chapter also focuses on the scattering of X-rays from rough surfaces and thin film systems with rough boundaries.

Analysis of Slightly Rough Thin Films by Optical Methods and AFM

Abstract. In this paper the analysis of a family of rough silicon single crystal surfaces covered with native oxide layers is performed using a combined optical method based on a multisample treatment of the experimental data obtained using variable angle of spectroscopic ellipsometry and near normal spectroscopic reflectometry. Within this analysis the values of the thicknesses of the native oxide layers are determined together with the values of statistical parameters of roughness, i.e. with the rms values of the heights and the values of the autocorrelation lengths, for all the samples studied. For interpreting experimental data the perturbation Rayleigh–Rice theory and scalar diffraction theory are employed. By means of the results of the analysis achieved using both the theories limitations of the validity of these theories is discussed. The correctness of the values of the statistical parameters determined using the optical method is verified using AFM measurements.

Variable-angle spectroscopic ellipsometry of considerably non-uniform thin films

A theoretical approach for including considerable thickness non-uniformity of thin films into the formulae employed within variable-angle spectroscopic ellipsometry is presented. It is based on a combination of the efficient formulae derived for the thickness distribution density corresponding to a wedge-shaped non-uniformity with dependences of the mean thickness and root mean square (rms) of thickness differences on the angle of incidence that take into account the real non-uniformity of the shape. These dependences are derived using momentum expansion of the thickness distribution density. The derived formulae are tested by means of numerical analysis. An application of this approach is illustrated using the optical characterization of a selected sample of non-uniform SiOxCyHz thin films using phase-modulated ellipsometry.

Influence of lateral dimensions of the irregularities on the optical quantities of rough surfaces

In this paper the influence of lateral dimensions of the irregularities on the optical quantities, i.e. on reflectance, transmittance, scattering losses and ellipsometric ratio of randomly rough surfaces, is discussed in detail. This discussion is based on theoretical (simulated) data calculated using the Rayleigh–Rice theory (RRT). It is shown that the optical quantities mentioned are strongly dependent on the quantities characterizing the lateral dimensions of the irregularities, e.g. on the autocorrelation length. The simulated data are also used to investigate the possibilities and limitations of the scalar diffraction theory (SDT) and effective medium approximation (EMA) in treating the experimental data in practice. On the basis of these theoretical studies it is, moreover, shown that a combination of the SDT and EMA can be employed as a reasonable approximation for describing the interaction of light with randomly rough surfaces. Thus, from the results presented in this paper, it is evident that this combination could be a promising treatment for experimental data corresponding to the optical quantities of randomly rough surfaces.

Theoretical analysis of the atomic force microscopy characterization of columnar thin films

In this paper, the theoretical analysis of the influence of finite linear dimensions of an atomic force microscope tip on profiles of the upper boundaries of columnar thin films and their statistical quantities is performed. This analysis is based on a numerical evaluation of the main statistical quantities, i.e. the standard deviations of the heights and slopes, one-dimensional distributions of the probability density of heights and slopes and power spectral density function, corresponding to a simulated columnar structure of the thin films. It is shown that the strongest misrepresentation of the measured profiles of the upper boundaries of the columnar films originates in the cases when the linear dimensions of the columns are smaller or comparable with the linear dimensions of the tip. Further, it is shown that using a surface reconstruction procedure one can correct (improve) the boundary profiles and their statistical quantities partially. The results of this analysis enable us to perform rough estimation of the errors achieved within atomic force microscopy studies of the real columnar thin films. Moreover, these results allow to estimate the corrections of the statistical quantities mentioned above to be obtained using the surface reconstruction.

Optical properties of diamond-like carbon films containing SiOx

In this paper the optical properties of amorphous DLC films containing SiOx (DLC:SiOx) prepared by plasma enhanced chemical vapour deposition are studied. For this study a combined optical method based on simultaneous interpretation of experimental data obtained within variable angle spectroscopic ellipsometry and near-normal spectroscopic reflectometry is used. The interpretation of these combined experimental data is performed using a new empirical dispersion model of the optical constants characterizing the films under investigation. This dispersion model is based on parameterizing the density of the electronic states belonging to both the valence and conduction bands. It is shown that there are the strong differences between spectral dependences of the optical constants of the DLC films on the one hand and DLC:SiOx films on the other hand. Further, it is shown that the absorption of the DLC:SiOx films is smaller than the absorption of the pure DLC films in the visible. This is explained by the fact that the density of the pi electrons inside the DLC:SiOx films is lower than the density of these electrons in the pure DLC films. It is also found that the existence of small amounts of the silicon and oxygen impurities contained in the DLC films strongly influence their optical properties.

Optical characterization of inhomogeneous thin films of ZrO2 by spectroscopic ellipsometry and spectroscopic reflectometry

In this paper results concerning the optical characterization of inhomogeneous thin films of ZrO2 are presented. The optical characterization of these films is performed using the simultaneous interpretation of experimental data corresponding to variable angle of incidence spectroscopic ellipsometry (VASE) and near-normal incidence spectroscopic reflectometry (NNSR). It is shown that the ZrO2 films exhibit a depth inhomogeneity concerning their refractive indices. Further, it is shown that the ZrO2 films studied can be replaced by the four-layer system from the point of view of satisfactory fits of the experimental data. The values of the thicknesses and spectral dependences of the refractive indices of these four films are determined. Moreover, it is proved that the individual methods, i.e. VASE and especially NNSR, cannot be used separately to characterize the ZrO2 films investigated. The simultaneous treatment of the spectral dependences of the ellipsometric parameters and the reflectance measured for different angles of incidence allows complete optical characterization of these inhomogeneous films to be performed, i.e. only a combination of VASE and NNSR enables us to determine the values of both the refractive indices and the thicknesses of the films replacing the inhomogeneous ZrO2 films investigated from the optical point of view. Copyright