Cauchy model

SE-measurements were done with a Spectral Ellip-someter ES4G from Sopra, with a Xenon high-pressure 1 2174-01 light source from Hamamatsu, a double monochromator with a slit width of 400 xm, a spectral range from 230-930 nm and a spectral resolution of 0.05 nm. The evaluation of the measurements was carried out by Film Wizard 32 with the Cauchy-model. The observation of the relative changes in the refractive index at 589.3 nm was sufficient to monitor the sorption of the analytes. 

Using a four-phase model consisting of ambient/simple grade/film/ substrate, we fit the data to obtain the dispersion of optical constants for each films in the range of 1.55-6.53 eV. The Cauchy model was used as a model for the substrate and fixed during the fitting. The Cody-Lorentz (CL) model [14] was used as a model for the film. 

Equation (6.10) applies equally well to both high and low birefringence LC materials in the off-resonance region. For low birefringence (An <0.12) LC mixtures, the X terms are insignificant and can be omitted. Thus, Hg and n each have only two fitting parameters. The two-coefficient Cauchy model has the following simple forms [13] ... 

For most LC displays [14], the cell gap is controlled at aroimd 4 pm so that the required birefringence is smaller than 0.12. Thus Equation (6.13) can be used to describe the wave-length-dependent refractive indices. For infrared applications, high birefringence LC mixtures are required [15]. Under such circumstances, the three-coefficient extended Cauchy model (Equation (6.10)) should be used. 

Figure 6.2 Wavelength-dependent refractive indices of 5CB at T= 25.1 C. Open and closed circles are experimental data for and n , respectively. Solid line represents the three-band model and dashed lines are for the extended Cauchy model. The fitting parameters are listed in Table 6.1. Li and Wu 2004. Reproduced with permission from the American Institute of Physics.

Figure 6.9 Wavelength-dependent refractive index of NOA65 and the ordinary refractive index of E48, E44, and E7 at T= 20°C. The open squares, upward-triangles, fiUed circles, and downward-triangles are the measured refractive index of E48, E44, NOA65 and E7, respectively. The solid lines represent the fittings using the extended Cauchy model (Equation (6.10)). The fitting parameters are listed in Table 6.3.

J. Li and S. T. Wu, Two-coefficient Cauchy model for low birefringence liquid crystals, J. Appl Phys. 

A Variable Angle Spectroscopic EUipsometer of the type M200-F (J.A. Woollam Co. Inc., Lincoln, USA) with a spectral range from 245 to 995 nm was used to determine the thickness of the adsorbed polymer layers. Measurements were performed in ambient at three different angles (65, 70, and 75° with respect to the surface normal). For each polymer adlayer, i.e. Sil-PEG (from toluene), Sil-PEG (from acidic aqueous solution), and PLL-g-PEG (from aqueous HEPES buffer), five samples were prepared to obtain statistical data. The measurements were fitted with multilayer models using WVASE32 analysis software. The analysis of optical constants was based on a bulk silicon/ SiOj, layer, fitted in accordance with the Jellison model. After adsorption of the molecules, the adlayer thickness was determined using a Cauchy model A = 1.45, B = 0.01, C = 0). 

Lorentz model Sellmeier model Cauchy model... 

To select suitable dispersion model, such Sellimeier model, Cauchy model, Lorentz model, Drude model, effective medium approximation (EMA) model etc., for each layer. Which dispersion model should be selected for a certain layer depends on the specific type of the film and we will discuss later in detail. In the model, some parameters are known and the others are unknown. The unknown parameters will be determined through mathematical inversion method. 

Cauchy model is regarded as an approximate function of Sellmeier model. It was an empirical model first proposed by A. L. Cauchy. The equation of the model is expressed as ... 

Schmidt et al. [136] also reported room-temperature spectroscopic ellipsometry results on pulsed laser deposition-grown wurtzite MgxZni xO (0thin films. The refractive index data were fit to a three-term Cauchy approximation type formula (Equation 3.105), and the anisotropic Cauchy model parameters A, B, and C for ZnO were obtained as 1.916,1.76, and 3.9 for E J c and 1.844,1.81, and 3.6 for... 

Stimulated Emission in ZnO 195 Table 3.9 Cauchy model parameters for the Mg ni /3 alloy system. 

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