Analysis of multiple-angle ellipsometry of uniaxial ultrathin organic films at the air-water interface and determination of the refractive indices of behenic acid monolayers

Abstract

Multiple-angle ellipsometry of uniaxial ultrathin films is discussed analytically and by computer analysis. The various relations between angle of incidence, layer thickness, and refractive indices are presented. It is shown that multiple-angle ellipsometry conveys sets of experimental data well suited for computer analysis with high redundancy by exposing systematic experimental errors. The ellipsometric data allow no unique characterization of ultrathin, uniaxial, nonabsorbing films and it is demonstrated that the derived layer thickness depends strongly on assumptions of the layer anisotropy. For typical experimental results the allowed range of combinations of the refractive index values as a function of an assumed layer thickness is presented. Calculations show that certain combinations of refractive indices will result in an ellipsometric angle &A = 0 for all angles of incidence. Some of these combinations are physically realistic and might in fact be experimentally accessible. The potential of ellipsometric experiments to characterize ultrathin films is demonstrated by combining the method with data known from X-ray diffraction. Thus we have determined the refractive indices for a behenic acid monolayer in the S and CS phase, respectively, to nxS = 1.47, n2S = 1.54 and nxCS = 1.48, nPCS = 1.56. These values are deduced from the measured ellipsometric angles, a Lorentz-Lorenz approximation for the refractive indices, and structural data known from X-ray measurements.

Structural Conformation of Bovine Serum Albumin Layers at the Air–Water Interface Studied by Neutron Reflection

“…We cannot explain this discrepancy but we note that it is not easy to observe protein adsorption at the air-water interface with ellipsometry because of the lack of contrast in refractive index between the adsorbed layer and the water substrate. The difficulties at the higher concentration region may be caused by the inability of ellipsometry to make an unambiguous separation of coverage and the protein distribution profile along the surface normal direction (27). Not surprisingly, there is also a large discrepancy between their layer thicknesses and the neutron results.…”

Ellipsometry and Infrared Reflection Absorption Spectroscopy of Adsorbed Layers of Soluble Surfactants at the Air–Water Interface

“…The Lorentz-Lorenz equation was used for modeling the monolayers as being composed of two different species, the adsorbed molecule and water (36). This equation has also been used for estimating the ordinary and extraordinary refractive indices of anisotropic solid monolayers (37,38). In this article, three different algorithms are used for determining the relative difference in the determined parameters ( , d 1 , n 1 , and the surface coverage, θ ) when other parameters are fixed.…”

Alignment of Hexatic Langmuir Monolayers under Shear

“…The reflectivity of a Langmuir monolayer under BAM conditions can be calculated using the transfer matrix formalism [11][12][13] assuming the monolayer to be a uniaxial anisotropic medium. The length of the C 22 molecules (d 27.5Å) and the dielectric tensor of the monolayer (e Ќ 2.16 and e k 2.37) have been measured using multiple-angle ellipsometry [14]. The reflectivity also depends on the value of the polar tilt, which changes with the surface pressure of the monolayer.…”