Length scales spanning

As understanding of the CMP process improves, one can expect a great deal of work in all aspects of CMP modeling and simulation. These improvements are likely to extend over many length scales spanning wafer-level polish and uniformity concerns to die-level prediction to microscopic feature, chemical, and mechanical interactions. 

FIGURE 26.12 Schematic diagram illustrating the various hierarchies of the gridless particle methods and their resolved length-scales, spanning from nanometers to macroscopic dimensions. 

We have investigated the electrochemistry of adsorbed AQDS on HOPG surfaces at three different length scales, spanning the macroscale to nanoscale [79]. In the macroscopic measurements, four different grades of HOPG, specifically... 

Another realistic approach is to constnict pseiidopotentials using density fiinctional tlieory. The implementation of the Kolm-Sham equations to condensed matter phases without the pseiidopotential approximation is not easy owing to the dramatic span in length scales of the wavefimction and the energy range of the eigenvalues. The pseiidopotential eliminates this problem by removing tlie core electrons from the problem and results in a much sunpler problem [27]. 

As for all disordered complex macromolecular materials, polymers can be characterized by a hierarchy of different length and time scales, and these scales span an extremely wide range, as outlined in Fig. 1.1 [15]. The diffusion... 

Next, we discuss strategies to make maximal use of simple unbiased movesets for conformational sampling of biomacromolecules. We provide an example to illustrate how the inclusion of conformational fluctuations spanning multiple length scales can improve the quality of sampling. We conclude with a discussion of the metrics and guidelines that can be used to optimize a moveset for a given system. 

As a consequence, much less effort has been devoted to model these interactions, compared with electrostatics. This picture changes when interfaces are considered. Although the magnitude of those contributions will not be significantly affected, their variations through the interface span different length scales for the different interactions. Therefore the picture of a predominant electrostatic contribution could change at the interface. This has in fact been observed [11,17,18],... 

F.F. Abraham et al Spanning the continuum to quantum length scales in a dynamic simulation of brittle fracture. Europhys. Lett. 44, 783-787 (1998)... 

Figure 4.3.1 Catalyst characterization under reaction conditions spans all length scales from real reactors to the atomic structure with the catalytically active site as well as many orders in timescales considering long-term behavior in a real process and rapid changes of the structure and extremely fast surface processes.

As was mentioned earlier, designing mesoporous materials with structural features that span several length scales could benefit perceived device applications. In this context a three-way-templating strategy that facilitates selected area... 

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