Root-mean-square roughness

On average, the reflectivity decays in proportion to 0 or since both interfaces are sharp. However, if either surfaces is rough, then marked deviations are seen and the reflectivity is damped by a factor of exp -2k o, where a is the root-mean-square roughness. Thus, the reflectivity is very sensitive to surface roughness and to concentration gradients at interfaces. 

Figure 3 shows an optical profiler trace of the same portion of the wafer sample analyzed by the mechanical profiler. The resulting line scan in Figure 3a is similar to that for the mechanical system. The average and root-mean-square roughness are... 

Another characteristic of a polymer surface is the surface structure and topography. With amorphous polymers it is possible to prepare very smooth and flat surfaces (see Sect. 2.4). One example is the PMIM-picture shown in Fig. 7a where the root-mean-square roughness is better than 0.8 ran. Similar values are obtained from XR-measurements of polymer surfaces [44, 61, 62], Those values compare quite well with observed roughnesses of low molecular weight materials. Thus for instance, the roughness of a water surface is determined by XR to 0.32 nm... 

Fig. 7a, b. PMIM-image of (a) a poly-p-bromostyrene surface [118], (b) a PS/polybutadiene diblock copolymer, PS-b-PB, at approximately 100 fold magnification. The lateral resolution is of the order of 1 pm while the height resolution is of the order of 0.6 nm. The root-mean-square roughness averaged over the area shown is 0.8 nm in (a) close to the resolution limit of the technique. It is much larger (10 nm) in (b) due to the formation of steps after annealing. The scale in z-direction in (a) and (b) is different by a factor of 7... 

PET and PEN have an inherent surface smoothness of less than 1 nm, in terms of both Roughness Average (Ro) and Root Mean Square Roughness (Rq), using... 

One assembly example is polyethylenamine (PEI)-mediated self-assembly of FePt nanoparticles [56]. PEI is an all -NH-based polymer that can replace oleate/oleylamine molecules around FePt nanoparticles and attach to hydrophilic glass or silicon oxide surface through ionic interactions [52], A PEI/FePt assembly is readily fabricated by dipping the substrate alternately into PEI solution and FePt nanoparticle dispersion. Figure 10 shows the assembly process and TEM images of the 4 nm Fes8Pt42 nanoparticle self-assemblies on silicon oxide surfaces. Characterizations of the layered structures with X-ray reflectivity and AFM indicate that PEI-mediated FePt assemblies have controlled thickness and the surfaces of the assemblies are smooth with root mean square roughness less than 2 nm. 

Table 8.1. Surface properties of the etched ZnO Al films shown in Fig. 8.8. Root mean square roughness (ArrrlK), haze at a wavelength of 700 nm, and resulting short circuit current density, when applied in 1.1pm thick pc-Si I1 solar cells...

Measurements by Atomic Force Microscopy (in tappingmode, using a standard silicon tip with a radius of 10 nm) of the surface topography of both the lower and the upper interface (the surface of the aluminum electrode and that of the polymer film, respectively) revealed a typical root-mean square roughness of 3 nm or less... 

Fig. 10 (a) Representative AFM image of a PMPS-h-PI surface (root mean square roughness over imaged area, 0.071 nm). (b) Profile of PMPS-b-PI surface along line drawn in (a). Maximum distance between domain peaks 22.0 nm minimum distance 16.8 nm. Reproduced from [74], Hioms and Martinez (2003) Synth Met 139 463... 

Figure 19.2 Self-similarity analysis for nanotextured silver surfaces prepared in different ways. The root mean square roughness inferred from atomic force microscopy is plotted versus measurement area. The various surfaces are 100 nm thick evaporated silver films (solid squares, red line)-, 5.2 nm thick evaporated silver films (open circles, green line) nanoparticle films assembled from colloid attachment to self-assembled monolayers (solid circles, blue line) films from deliberate precipitation of silver colloid (solid up-triangles, black line) Tollens reaction films (open down-triangles, orange line). Lines with slopes H = 1.0 and H = l.S representing two-dimensional and 1.5 dimensional surfaces respectively are...

Figure 31. Optical image (a) and the corresponding surface topography by AFM (b) of a PS film of 239 nm as prepared (left column), after 4 hours at 180°C in a pure nitrogen atmosphere (middle column) and after 4 hours at 180°C under air flow (right column). Rq represents the root-mean-square roughness, (c) Linecuts in the AFM images presented above.

This film shows a low root mean square roughness (RMS) of only 2.2 nm. 

Table 6.1 Root-mean-square roughness (Rrms) the mean roughness (RJ for both swivel cruciforms calculated using Veeco software and using AFM images shown in Figures 6.6a-d and 6.7a-d.

The term in front of the bracket is the well-known Kanazawa expression (Eq. 61). The correction terms inside the brackets take care of roughness at the interface of the hquid k is the lateral correlation length of roughness (where the spectriun of spatial frequencies is assiuned to be Gaussian), hr is the root-mean-square roughness, and 8 = 2r]l pco)) / is the penetration... 

The phase measurement interference microscopy (PMIM) is mainly used for surface analysis. A resolution depth of 0.6 nm can be achieved, whereas the lateral resolution is only in the range of about 1 ftm [White et al., 1990]. A laser beam in the microscope is reflected from the sample surface and simultaneously from a semitransparent smooth reference surface [Stamm, 1992]. The interference pattern is recorded which can be converted into a contour map of the sample surface, e.g., to determine the root-mean-square roughness of materials. 

ROOT-MEAN-SQUARE ROUGHNESS VALUES, OBTAINED BY DIFFERENT MEASURING METHODS, FOR SEVERAL SUBSTRATES ... 

Surface roughness is the deviation of a surface from perfect flatness. It is often defined as a RMS (root mean square) roughness as this parameter is obtained directly... 

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