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Manuscript Title: Analysis of spectroscopic ellipsometric measurements.
Authors: M.H.W. Verbruggen, J.M.M. de Nijs
Program title: CENTIPEDE
Catalogue identifier: ACGG_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 69(1992)201
Programming language: C.
Computer: HEWLETT-PACKARD 9000/340.
Operating system: UNIX.
RAM: 100K words
Word size: 64
Keywords: Solid state physics, Experiment, Optics, Spectroscopic Ellipsometry, Effective medium Approximation, Levenberg-marquardt, Linked lists, Fitting algorithm.
Classification: 7.4, 18.

Nature of problem:
The reflection of light at a surface strongly depends on the structural and chemical properties of the surface. Structural features often have a layer-like nature. The chemical properties of the different layers are reflected in the dielectric function that is used for the description of the solid state involved. Mixed layers containing two or more distinguishable compounds, e.g. microcrystallites in a matrix, make part of the problem. Generally, a model in terms of a number of (mixed) layers with a specified composition and thickness on top of a substrate suffices for a correct description of the reflection of light at a surface.

Solution method:
Solving the Maxwell-equations for a reflection at a smooth surface obliges to distinguish two kinds of optical reflections, one parallel and the other perpendicular to the plane spanned by the incident light- beam and the surface normal, the plane of incidence. Both reflections need a complex reflection coefficient rp and rs (senkrecht), for a proper description. In spectroscopic ellipsometry the ratio of both reflection coefficients is measured as a function of photon energy. In our computer program we use a stratified-layer model to calculate the complex reflectance ratio. This theory allows for an adequate matrix representation, the Jones formalism, for all of the involved layers, interfaces and the substrate. Layer thicknesses and dielectric functions have to be entered, and subsequently, the complex reflectance ratio of the surface can be calculated. For mixed layers, one firstly has to calculate the effective dielectric function from the dielectric functions of the various constituents and their respective volume fractions. This can be accomplished by means of an appropriate effective medium theory. As said, the model needs the thickness, the composition and the dielectric functions as input parameters. The dielectric functions can be found in literature, or measured independently. Subsequently, the program optimizes the thicknesses and compositions of the layers as to obtain an optimum agreement between the experimental spectrum and the modeled one. For this purpose a modified Levenberg-Marquardt routine is used. The number of data-points in the ellipsometric spectra may vary from one experiment to another. Similarly, the model that is used for the analysis may be different from case to case. Therefore, good flexibility is highly valued. The application of linked lists ensures us of this flexibility.

As said all dielectric functions have to be known in advance and over the full photon energy range. Furthermore, the dielectric functions are assumed to be isotropic.

Running time:
The time for the test run on the HP9000/340 is about 10 minutes.