Effect of Roughness on Ellipsometry Analysis

Spectroscopic ellipsometry (SE) [1, 2] is a powerful non-destructive technique to determine the structure of silicon-based materials such as amorphous silicon (a-Si) and hydrogenated amorphous silicon (a-Si :H). In analyzing the SE spectra, the Bruggeman effective medium approximation (EMA) [3, 4] is usually used to model a thin film as a mixture of amorphous silicon and voids. In these models, however, precise knowledge of the dielectric functions of the various components is required in order to obtain reliable estimation of the structural parameters. This requirement is particular critical to the amorphous component because the structure of amorphous silicon is known to depend considerably on the preparation procedures [5]. So far, the dielectric functions used for modeling a-Si1 x :Hx have been based on certain dielectric functions without consideration of the preparation method. It may not be clear, particularly for thin films of amorphous silicon prepared by novel method, whether it is relaxed or unrelaxed dielectric functions which are appropriate for the modeling. In the present work the scope of the problem is assessed by constructing dielectric functions for relaxed and unrelaxed a-Si1 x :Hx thin films using measured a-Si dielectric functions, and fitting, respectively, using simulated dielectric functions for bulk unrelaxed and relaxed a-Si1 x :Hx on the surface roughness and void concentration parameters. The tetrahedron model [3, 4] is applied to construct the complex dielectric functions for relaxed (e 1⁄4 e1r þ ie2r) and unrelaxed (e 1⁄4 e1ur þ ie2ur) a-Si1 x :Hx, by using the dielectric functions for relaxed and unrelaxed a-Si [5], respectively. For details we refer to the work of Mui and Smith [3], [4]. The complex dielectric functions constructed for relaxed and unrelaxed a-Si1 x :Hx components with various hydrogen concentrations are shown in Fig. 1. It is seen that the relaxed and unrelaxed spectra exhibit different peak position and amplitude. Moreover, as the hydrogen content increases, the complex dielectric functions shift to higher photon energy with lower peak values. The complex dielectric functions for the relaxed (unrelaxed) a-Si1–x :Hx film are constructed using a three-layer structure: the first layer is a surface roughness layer, modeled using the EMA, consisting of 50% voids, 50% layer 2. Layer 2 is modeled using the EMA, consisting of a mixture of relaxed (unrelaxed) a-Si1 x :Hx and voids. The substrate is smooth silicon dioxide (SiO2). Fractional void concentrations in layer 2 are varied from 0.01 to 0.26 in the simulations. The thickness of layer 1 is set to be 0.001 mm, while the film thickness (layer 2) is fixed at 1 mm. The incidence angle is set to be 75 . The constructed complex dielectric functions for relaxed a-Si1 x :Hx films are then fitted using unrelaxed a-Si :H spectra, applying a nonlinear regression based on the Levenberg-Marquardt method [6], and vice-versa. In order to avoid interference caused by the interface, the fits are done above 1.75 eV. We denote the void concentration and the thickness of the surface roughness by Cvoid and TR respectively. The fitting error of the void concentration and the thickness of surface roughness are denoted by DCvoid and DTR, respectively, i.e. Cvoid 1⁄4 Cconstructed void Cfit void , similarly for DTR. In order to reveal the quality of the modeling, we define

This chapter reviews the use of spectroscopic ellipsometry (SE) as a characterization tool for nanoparticle-polymer and nanoparticle-SAM hybrids. The development of such materials is based on the drive toward technological applications of new functional organic materials in solar cells, flat screen displays, sensors and organic electronics. For many of these application the optical properties of the materials are of critical importance for the device operation. In this respect, an accurate and complete determination of the frequency-dependent complex dielectric function, \(\varepsilon ( \omega ) = \varepsilon ' + i \varepsilon ''\), of the materials over a wide spectral range is the primary goal of SE characterization. The major focus of the chapter will be to present optical models that are needed to analyze the data; specifically to develop models that describe the effective dielectric function of a film of NPs supported by, or embedded in, an organic matrix. Starting with the Mie solution to Maxwell’s equations, examples of various nanoparticle scattering cross-sections are presented to show the influence of the particle size and material properties. Modeling composites then requires making the step from individual NPs to arrays and composites by using the effective medium approximation. Finally the origin of anisotropy will be described and models for the dielectric tensor elements presented. Examples from the literature will be referred to throughout.

Roughness and chemistry of silicon and polysilicon surfaces etched in high-density plasma: XPS, AFM and ellipsometry analysis

Different types of land cover are associated with different surface roughness, which produce variations in the frictional force on the wind. Therefore, mean wind profiles at low levels often differ markedly over short distances where there is a gradient in surface roughness. Horizontal gradients in surface roughness may produce vertical vorticity, circulation, and horizontal divergence. The effect of roughness on vertical wind shear and storm-relative helicity is also qualitatively important and may lead to large gradients in helicity over short distances. Recent studies also suggest an important role of friction in tornadogenesis.
 We show conceptually and theoretically how gradients in surface roughness produce quasi-ambient convergence and vertical vorticity, and gradients in vertical shear and storm-relative helicity. We then present observational data and numerical simulations that demonstrate the effects of surface roughness on the kinematics and shear of boundary-layer flow, for future work examining the importance of these processes for tornadogenesis.

Although there has been significant progress on the individual effects of surface roughness and boundary slippage on the hydrodynamic lubrication performance of pivoted pad thrust bearings, the coupled effect of these two factors remains unclear. This is particularly important for preventing wear in large pivoted pad thrust bearings under heavy-load and thin-film conditions. In this work, a rough surface lubrication numerical model is developed for the pivoted pad thrust bearing with consideration of boundary slippage by combining the average flow model and the modified limiting shear stress model. The nonlinear slip control function in the modified limiting shear stress model is presented by the interface shear stress, which is obtained by the average flow Reynolds equation. The coupled effects of surface roughness and boundary slippage on hydrodynamic lubrication performance are studied under different conditions. Our results show that the rough thrust pad surface helps to control the slip region and maintain lubrication performance, while the rough collar surface extends the slip region and causes a severe adverse effect on lubrication performance. However, a reasonably designed slip/nonslip configuration on a thrust pad surface is helpful for controlling the slip region on the thrust pad surface. At this point, a rough collar surface can significantly increase the improvement effect of the slip/nonslip configuration on lubrication performance. Additionally, boundary slippage can be prevented if both surfaces are rough. The coupled effects of surface roughness and boundary slippage can be used to design pivoted pad thrust bearings to improve lubrication performance.

This paper describes a study of the adhesion between elastic solids and the effect of roughness in reducing the adhesion. The experiments were carried out between optically smooth rubber spheres and a hard smooth flat surface of Perspex which could be roughened to various degrees. The radius of the rubber spheres was varied by a factor of 8, their elastic modulus by a factor of 10, while the centre line average (c.l.a.)of the roughened Perspex surface was varied from 0.12 to 1.5 μm. The results show that c.l.a. roughnesses which are small compared with the overall deformation occurring at the region of the rubber-Perspex contact can produce an extremely large reduction in adhesion. The effect is more marked for rubbers of higher modulus. On the other hand the curvature of the sphere (over the range examined) has little influence. For this reason and because the analytical problem of a sphere on a rough flat is extremely complicated a theoretical analysis has been developed for the simpler case of a smooth flat in contact with a rough flat surface. As in Greenwood & Williamson (1966) the rough surface is modelled by asperities all of the same radius of curvature and with heights following a Gaussian distribution of standard deviation σ. The overall contact force is obtained by applying the contact theory of Johnson, Kendall & Roberts (1971) to each individual asperity. The theory predicts that the adhesion expressed as a fraction of the maximum value depends upon a single parameter, 1/Δ e ,which is the ratio between a and the elastic displacement δ C that the tip of an asperity can sustain before it pulls off from the other surface. The analysis shows that the adhesion parameter may also be regarded as representing the statistical average of a competition between the compressive forces exerted by the higher asperities trying to prize the surfaces apart and the adhesive forces between the lower asperities trying to hold the surfaces together. Although the theory is derived for two nominally plane surfaces it is found to fit the experimental results for a sphere on a flat reasonably well.

The effective medium approximation (EMA) has been widely applied to model the effect of a solid sample with surface roughness in spectroscopic ellipsometry (SE). There are two specific cases to utilize the EMA model. One is utilizing the EMA model to perform the inversion of the optical constants of solid samples from the SE measurements. Another is utilizing the EMA model to estimate the thickness of the rough layer at solid surface from the SE measurements under the condition in which the optical constants of samples are known. For the first case, the thickness of the rough layer is usually assumed to be the root mean square (rms) roughness as measured by atomic force microscopy (AFM). We theoretically investigate the error of the EMA model to estimate optical constants for different surface morphologies and materials. Because the EMA model only accounts for the height irregularities of rough surfaces but neglects the effect of the lateral irregularities on electromagnetic scattering from rough surfaces, it is difficult to obtain high-precision results for optical constants. Moreover, the inversion error of optical constants by using the EMA model is difficult to evaluate. In the second case, the thickness of the rough layer is estimated by using the EMA model from the SE measurements, called the EMA model roughness. We show that the EMA model roughness generally has a deviation from the rms roughness as measured by AFM. Some correlated relationships are established between the EMA model roughness and the morphological parameters of rough surfaces. It is found that these relationships have similar forms but not identical coefficients for different materials. The results from this work may facilitate a better understanding and utilization for the EMA model in SE.

Boron doping effects on microcrystalline silicon film roughness studied by spectroscopic ellipsometry

Effect of roughness and shape factor on flotation characteristics of glass beads

Optical properties and band structure of Ge 1− yC y and Ge-rich Si 1− x− yGe xC y alloys

ABSTRACTWell characterized rough surfaces of aluminum films have been studied by the nondestructive technique of Spectroscopie Ellipsometry (SE). The roughness of the aluminum specimens had been characterized earlier by Total Integrated Scattering and Stylus Profilometry techniques to obtain numerical estimates of ras roughness and autocovariance lengths. The present SE measurements on these specimens were carried out at a number of angles of incidence in the range 30–80° and at a number of discrete wavelengths in the spectral range 300–650nm. The SE results were then analyzed by the scalar theory of diffraction from random rough surfaces by treating the surface as a simple random rough surface. The results of such analyses of the SE measurements are compared with the results of the earlier characterization techniques.

Optical simulation of external quantum efficiency spectra of CuIn1−xGaxSe2 solar cells from spectroscopic ellipsometry inputs

The effect of surface material and roughness on the conductance of a channel at molecular flow was measured for N2, Ar, He, and H2. The experimental results were compared with the results of Monte Carlo calculations. The channel consisted of two parallel disks with different surfaces including polished stainless steel (SS), roughly polished SS, quartz, Ti, Cu, Al, alumina with smooth surface, alumina with rough surface, Au coating, Pt coating, and diamondlike carbon (DLC) coating. The conductances of the experimental channel depended on the slope of the surface roughness, rather than the arithmetic surface roughness (Ra) or the material. In the case of smooth surfaces, such as polished SS, quartz, and DLC coating, the experimental results for N2, Ar, and H2 show good agreement with the calculation, assuming diffuse reflection. The momentum accommodation coefficients on these surfaces for N2, Ar, and H2 were estimated to be in the range from 0.98 to 1.00, based on the assumption that specular reflection was simply included in diffuse reflection. The conductance for He, however, was 3%–5% larger than that of the calculation. The momentum accommodation coefficient for He was similarly estimated to be in the range from 0.95 to 0.97.

Specular x-ray reflectivity (XRR) measurements were used to study the density and surface roughness of ultrathin hydrogen-free amorphous carbon films deposited by sputtering, of thickness varying from 25 to 325 Å. The film thickness and surface roughness obtained from XRR measurements are in good agreement with that found by spectroscopic ellipsometry (SE) and atomic force microscopy. The results for the film composition obtained from SE and XRR are supported by stress measurements. Films (especially those with thickness below 100 Å) deposited with positive substrate bias voltage were found to exhibit a reduction in density, sp3 C–C bonding, and internal compressive stresses and an increase in surface roughness by increasing film thickness.

Optical constants of electroplated gold from spectroscopic ellipsometry