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 SiOxCyHz 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 SiOxCyHz thin film and transition layer. The multiple-beam interference model was used for expressing inhomogeneity of the SiOxCyHz 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 SiOxCyHz 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 SiOxCyHz film and transition layer, profiles of the optical constants of the SiOxCyHz 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.

Ellipsometric characterization of highly non-uniform thin films with the shape of thickness non-uniformity modeled by polynomials.

A common approach to non-uniformity is to assume that the local thicknesses inside the light spot are distributed according to a certain distribution, such as the uniform distribution or the Wigner semicircle distribution. A model considered in this work uses a different approach in which the local thicknesses are given by a polynomial in the coordinates x and y along the surface of the film. An approach using the Gaussian quadrature is very efficient for including the influence of the non-uniformity on the measured ellipsometric quantities. However, the nodes and weights for the Gaussian quadrature must be calculated numerically if the non-uniformity is parameterized by the second or higher degree polynomial. A method for calculating these nodes and weights which is both efficient and numerically stable is presented. The presented method with a model using a second-degree polynomial is demonstrated on the sample of highly non-uniform polymer-like thin film characterized using variable-angle spectroscopic ellipsometry. The results are compared with those obtained using a model assuming the Wigner semicircle distribution.

Measurement of doping profiles by a contactless method of IR reflectance under grazing incidence.

An improved contactless method of the measurement and evaluation of charge carrier profiles in polished wafers by infrared reflectance was developed. The sensitivity of optical reflectance to the incidence angle was theoretically analyzed. A grazing incident angle enhances sensitivity to doping profile parameters. At the same time, the sensitivity to experimental errors sharply increases around the Brewster angle. Therefore, the optimal angle of 65° was chosen. Experimental errors such as unintentional polarization of the measurement beam were minimized by division by reference spectra taken on an undoped sample and further by normalization to a fixed value in the region of 4000 cm-1 to 7000 cm-1. The carrier profile in boron-doped samples was parametrized by 3 parameters and that in phosphorous-doped samples was parametrized by 4 parameters, using additional empirically determined assumptions. As a physical model, the Drude equation is used with two parameters assumed to be concentration-dependent: relaxation time and contribution from band-to-band excitations. The model parameters were calibrated independently by infrared ellipsometry. The presented method gives results in satisfactory agreement with the profiles measured by the electrochemical capacitance-voltage method.

Universal dispersion model for characterization of optical thin films over a wide spectral range: application to hafnia.

A dispersion model capable of expressing the dielectric response of a broad class of optical materials in a wide spectral range from far IR to vacuum UV is described in detail. The application of this universal dispersion model to a specific material is demonstrated using the ellipsometric and spectrophotometric characterization of a hafnia film prepared by vacuum evaporation on silicon substrate. The characterization utilizes simultaneous processing of data from multiple techniques and instruments covering the wide spectral range and includes the characterization of roughness, nonuniformity, transition layer, and native oxide layer on the back of the substrate. It is shown how the combination of measurements in light reflected from both sides of the sample and transmitted light allows the separation of weak absorption in films and substrates. This approach is particularly useful in the IR region where the absorption structures in films and substrates often overlap and a prior measurement of the bare substrate may be otherwise necessary for precise separation. Individual phenomena that contribute to the dielectric response, i.e., interband electronic transitions, electronic excitations involving the localized states, and phonon absorption, are discussed in detail. A quantitative analysis of absorption on localized states, permitting the separation of transitions between localized states from transitions between localized and extended states, is utilized to obtain estimates of the density of localized states and film stoichiometry.

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.

Influence of cross-correlation effects on the optical quantities of rough films.

Within the Rayleigh-Rice theory the influence of layer boundary roughness on coherently reflected light is expressed using very complex formulae. Therefore we deal with the simplification of these formulae by employing an approximation based on neglecting cross-correlation effects between both the rough boundaries. It is shown that if the mean distance of the boundaries (mean thickness) is sufficiently large in comparison with the lateral dimensions of the roughness it is possible to describe the individual boundaries of the layers by matrices corresponding to isolated rough surfaces. This fact enables us to simplify the formulae for the optical quantities in a substantial way, which also simplifies the numerical calculation needed for the inverse problem. This statement is illustrated by means of a numerical analysis simulating ellipsometric and reflectometric data of rough silicon dioxide layers placed onto silicon single crystal substrates.

Models of dielectric response in disordered solids.

Two dispersion models of disordered solids, one parameterizing density of states (PDOS) and the other parameterizing joint density of states (PJDOS), are presented. Using these models, not only the complex dielectric function of the materials, but also some information about their electronic structure can be obtained. The numerical integration is necessary in the PDOS model. If analytical expressions are required the presented PJDOS model is, for some materials, a suitable option still providing information about the electronic structure of the material. It is demonstrated that the PDOS model can be successfully applied to a wide variety of materials. In this paper, its application to diamond-like carbon (DLC), a-Si and SiO2-like materials are discussed in detail. Unlike the PDOS model, the presented PJDOS model represents a special case of parameterization that can be applied to limited types of materials, for example DLC, ultrananocrystalline diamond (UNCD) and SiO2-like.