RMS roughness

Parameters measured Surface topography (rms roughness, rms slope, and power spectrum of structure) scattered light line shape of periodic structure (width, side wall angle, height, and period)... 

Although the power spectral density contains information about the surface roughness, it is often convenient to describe the surface roughness in terms of a single number or quantity. The most commonly used surface-finish parameter is the root-mean-squared (rms) roughness a. The rms roughness is given in terms of the instrument s band width and modulation transfer function, M(p, q) as... 

Different values of will result if the integral limits (i.e., band width) or modulation transfer function in the integral change. All surface characterization instruments have a band width and modulation transfer function. If rms roughness values for the same surface obtained using different instruments are to be compared, optimally the band widths and modulation transfer functions would be the same they should at least be known. In the case of isotropic surface structure, the spatial frequencies p and q are identical, and a single spatial frequency (/>) or spatial wavelength d= /p) is used to describe the lateral dimension of structure of the sample. 

The importance of instrument band width is illustrated by considering the rms roughness of the two samples of Figure 2. If the rms roughness is calculated over the... 

Study [1], it was reported that with increasing ion dose density from 10" to lO ions/cm, RMS roughness of the ion beam bombarded membrane increased from 21 to 204 nm without changing ionic conductivity of the membrane. 

The Si wafer industry has achieved very flat Si surfaces by electropolishing a root-mean-square (rms) roughness of 0.3 nm is customary, even for highly-doped degenerate Si. For a 100-nm Au layer deposited atop a 10-nm Ti adhesion layer atop an electropolished Si wafer, an rms roughness of 0.4 nm was measured by AFM [38]. 

The comparison of continuum and atomistic models by Luan and Robbins demonstrates that the atomic details of this contact can have a significant influence on the calculated friction. However, those calculations did not explore atomically rough surfaces, which are most likely found in real engineering contacts. The effect of roughness has been investigated recently by Qi et al. in a study of the friction at the interface between two Ni(100) surfaces.85 Two models were considered in that work. In the first model, both surfaces were atomically flat i.e., the rms roughness was 0.0 A. In the... 

To quantitatively characterize the surface roughness of the Pt films, the rms roughness cr of the electrodes was evaluated and the resulting values are indicated in Figures 10a, 10b and 10c, respectively. From the comparison between height fluctuation of all the film... 

Root mean square (rms) roughness SEM Scanning electron microscope... 

Tapping-mode atomic force microscopy studies showed that as these hyperbranched PAA films became somewhat less smooth as they increased in thickness through successive grafting stages [24]. For example, a very smooth initial single-crystal Au(lll) surface with a root mean square (RMS) roughness of 0.2 nm (over a 2 xm x 2 im area) had its roughness increased to... 

Figure 13.5(d) presents experimental stiffness measurements using differential UFM for three high modulus surfaces sapphire, Si(100) and LiF(lOO) (Dinelli et al. 2000b). The samples were probed with the same silicon tip on a V-shaped cantilever (nominally cantilever stiffness was kc - 2.8 nN nm 1,and radius of curvature R = 10 nm). The surface RMS roughness of the surfaces was less than 0.2 nm over a few square micrometres for all three samples. The relative difference between the three sets of data reveals that the elastic properties of these three materials can be distinguished by differential UFM the relative independence of the applied force may indicate the fact that the tip had been flattened by extended contact with such hard samples. 

Fig. 13.7. GaSb-InAs superlattice (a) AFM (b) UFM with periodicity of 40 nm (arrow i) and 8nm (arrow ii). The topographical image shows that the surface is very flat (RMS roughness < 0.2 nm over 1 pm2 area). Wider layers (arrow i) are barely visible whereas the finer ones (arrow ii) are not visible at all. The very fine superlattice (arrow ii) of layers only 4 nm wide is observable in the UFM image (Dinelli er a/.

Fig. 4. Left Tunneling density of states measured at 60 mK at the Au surface of Nb-Au bilayer samples with a varying Au thickness Ln. Data from the 130 and 200 nm samples are not shown for ease of reading. Right, top Schematic cross section of the full Nb-Au bilayers sample. Right, bottom STM image (410 x 410 nm2) at 100 mK of the sample with a Au thickness of 72 nm. The rms roughness for this image is 3.4 nm.

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