Paper LB-WeA9
Numerical Ellipsometry: N-K Plane Analysis of Transparent Conducting Films for Solar Applications

Wednesday, October 20, 2010, 4:40 pm, Room Cimmaron

This work presents a new kind of ellipsometric data analysis applied to an Indium Tin Oxide thin film, characterized by an energy window of electromagnetic transparency capable of passing solar energy and at the same time having usable electron conductivity elsewhere. The work presents very recent advances in the n-k plane data analysis method that allow greatly improved accuracy in modeling these films for multiple layers. Solution accuracy is orders of magnitude better than least squares, the method in common use. It is well known that such materials are optically opaque (have high extinction coefficients, k) both at energies higher than the high energy window edge and at energies below the lower window edge. Such materials present a particular challenge to ellipsometry data analysis due to these different optical behaviors across the measurement wavelength range. Data reported here were taken on an Indium Tin Oxide (ITO) film grown on a silicon substrate to a nominal thickness of 400 nm. Measurements were taken at 293 wavelengths, every 5 nm from 280 to 1700 nm, and at each of three incidence angles of 55°, 65°, and 75°. Thus at each wavelength (experiment) there are three measurements providing 6 real numbers, three each of Ψ and Δ. Each Ψ-Δ pair results in set of solution curves on different root and logarithm planes, for which the one containing the film solution is readily identifiable. If measurements had no experimental uncertainty, the three curves per experiment would intersect at the value of film n, k, and d. In actual fact they come close to intersecting and have a point of closest approach. In cases for which the intersection is well defined, and there are six real number unknowns which may, in principle, be determined. We have chosen the six variables to represent the thickness and optical properties of two layers on the substrate, one computation per wavelength. In the transparent region from approximately 300 to 980 nm the ITO matches a 2 layer film divided into two near-equal thicknesses with somewhat differing index real part and with an extinction coefficient near zero. At longer wavelengths the film corresponds to an absorbing layer which appears vertically inhomogeneous but which cannot be well characterized due to the light interaction depths at the three incidence angles. Results will be presented across the entire measurement wavelength range.