Analysis of inhomogeneous thin films of ZrO2by the combined optical method and atomic force microscopy

Optics of Inhomogeneous Thin Films with Defects: Application to Optical Characterization

This review paper is devoted to optics of inhomogeneous thin films exhibiting defects consisting in transition layers, overlayers, thickness nonuniformity, boundary roughness and uniaxial anisotropy. The theoretical approaches enabling the inclusion of these defects into formulae expressing the optical quantities of these inhomogeneous thin films are summarized. These approaches are based on the recursive and matrix formalisms for the transition layers and overlayers, averaging of the elements of the Mueller matrix using local thickness distribution or polynomial formulation for the thickness nonuniformity, scalar diffraction theory and Rayleigh-Rice theory or their combination for boundary roughness and Yeh matrix formalism for uniaxial anisotropy. The theoretical results are illustrated using selected examples of the optical characterization of the inhomogeneous polymer-like thin films exhibiting the combination of the transition layers and thickness nonuniformity and inhomogeneous thin films of nonstoichiometric silicon nitride with the combination of boundary roughness and uniaxial anisotropy. This characterization is realized by variable angle spectroscopic ellipsometry and spectroscopic reflectometry. It is shown that using these optical techniques, the complete optical characterization of the mentioned thin films can be performed. Thus, it is presented that the values of all the parameters characterizing these films can be determined.

Ellipsometric characterization of inhomogeneous thin films with complicated thickness non-uniformity: application to inhomogeneous polymer-like thin films

The method of variable angle spectroscopic ellipsometry usable for the complete optical characterization of inhomogeneous thin films exhibiting complicated thickness non-uniformity together with transition layers at their lower boundaries is presented in this paper. The inhomogeneity of these films is described by means of the multiple-beam interference model. The thickness non-uniformity is taken into account by averaging the elements of the Mueller matrix along the area of the light spot of the ellipsometer on the films. The local thicknesses are expressed using polynomials in the coordinates along the surfaces of the films. The efficiency of the method is illustrated by means of the optical characterization of a selected sample of the polymer-like thin film of SiO_xC_yH_z prepared by plasma enhanced chemical vapor deposition onto the silicon single crystal substrate. The Campi-Coriasso dispersion model is used to determine the spectral dependencies of the optical constants at the upper and lower boundaries of this film. The profiles of these optical constants are determined too. The thickness non-uniformity is described using a model with local thicknesses given by the polynomial with at most quadratic terms. In this way it is possible to determine the geometry of the upper boundary. The thickness and spectral dependencies of the optical constants of the transition layer are determined as well. Imaging spectroscopic reflectometry is utilized for confirming the results concerning the thickness non-uniformity obtained using ellipsometry.

Spectroscopic ellipsometry of inhomogeneous thin films exhibiting thickness non-uniformity and transition layers

In this paper the complete optical characterization of an inhomogeneous polymer-like thin film of SiO_xC_yH_z exhibiting a thickness non-uniformity and transition layer at the boundary between the silicon substrate and this film is performed using variable angle spectroscopic ellipsometry. The Campi-Coriasso dispersion model was utilized for describing the spectral dependencies of the optical constants of the SiO_xC_yH_z thin film and transition layer. The multiple-beam interference model was used for expressing inhomogeneity of the SiO_xC_yH_z thin film. The thickness non-uniformity of this film was taken into account by means of the averaging of the elements of the Mueller matrix performed using the thickness distribution for the wedge-shaped non-uniformity. The spectral dependencies of the optical constants of the SiO_xC_yH_z thin film at the upper and lower boundaries together with the spectral dependencies of the optical constants of the transition layer were determined. Furthermore, the thickness values of the SiO_xC_yH_z film and transition layer, profiles of the optical constants of the SiO_xC_yH_z thin film and the rms value of local thicknesses corresponding to its thickness non-uniformity were determined. Thus, all the parameters characterizing this complicated film were determined without any auxiliary methods.

Measurement of thickness distribution, optical constants, and roughness parameters of rough nonuniform ZnSe thin films

Epitaxial ZnSe thin films exhibiting two important defects, i.e., boundary roughness and thickness nonuniformity, prepared on GaAs substrates, are optically characterized using a combination of variable-angle spectroscopic ellipsometry, spectroscopic near-normal reflectometry, and imaging spectroscopic reflectometry (ISR). The influence of boundary roughness is incorporated into optical quantity formulas by the Rayleigh-Rice theory. Thickness nonuniformity is included using averaging of the unnormalized Mueller matrices. The dispersion model of the optical constants of the ZnSe films is based on parametrization of the joint density of electronic states. Very thin overlayers represented by thin films with identically rough boundaries are taken into account on the upper boundaries of the ZnSe films. Standard optical techniques are used to determine the spectral dependencies of the optical constants of the ZnSe films, together with the parameters of roughness and thickness nonuniformity. ISR is then used to find the maps of the local thickness and local rms value of height irregularities. The values of roughness parameters, determined using the standard techniques and ISR, are verified by a comparison with results obtained by atomic force microscopy.

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.