Rough multiscale modeling

R7.4.1 (2005). Multiscale Modeling of Two Dimensional Rough Surface Contacts. 

Multiscale Simulations, Fig. 4 Multiscale modeling of channel flow with nanoscale roughness on bottom wall, (a) Physical model abstracted from engineering application (b) streamline comparisons around one roughness the solid lines are from the hybrid modeling, the dashed line on the left is from the full MD simulation, and dashed line on the right is from the full continuum modeling (CFD)... 

Electrodeposition of copper on trenches of microchip interconnects is an important process in modern microelectronics. Thus, KMC models ° and KMC-based multiscale models ° ° have been used to investigate the nucle-ation, surface chemistry, and roughness evolution in this process. However, most KMC models of electrodeposition have not incorporated electrochemical influences and so will not be discussed here. Nonetheless, due to the success of KMC with other electrochemical systems, excellent future opportunities exist for applying KMC to electrodeposition processes. 

Figure 5 shows that there is no way to fit the experimental data assuming that only one type of roughness is presented on the surface. We are thus forced to conclude that, in these experiments the surface has a multiscale roughness, shown schematically in Fig. 6. The structure of this rough surface is a combination of a slight and a strong roughness shown in Fig. 3a,b. When this is taken into account, it is possible to use Eqs. 33, 34,43, and 44 to calculate the shift in resonance frequency and shift in the width of the resonance, and fit the experiments to the calculated curves with properly chosen values of the parameters of strong roughness. The result of such a fit is shown in Fig. 4, curves 2 and 3. For details of the fitting procedure, the limitations associated with the use of a simplified model, and the comparison with STM data see [27].

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