Pattern dependent

We have thus far discussed the diffraction patterns produced by x-rays, neutrons and electrons incident on materials of various kinds. The experimentally interesting problem is, of course, the inverse one given an observed diffraction pattern, what can we infer about the stmctirre of the object that produced it Diffraction patterns depend on the Fourier transfonn of a density distribution, but computing the inverse Fourier transfomi in order to detemiine the density distribution is difficult for two reasons. First, as can be seen from equation (B 1.8.1), the Fourier transfonn is... 

Hwang G S and Glapis K P 1999 Pattern-dependent charging In plasmas IEEE Trans. Plasma Sc/. Special Issue Images In Plasma Science 27 102... 

Glapis K P and Hwang G S 1998 Pattern dependent charging and the role of electron tunneling Japan. J. Appl. Phys. 37 2281... 

Hwang G S and Glapis K P 1998 The Influence of surface currents on pattern-dependent charging and notching J. Appl. Phys. 84 154... 

I he flow pattern depends on the building s relative dimensions long buildings (along wind length, L > 2.5H) versus short buildings L 2.5H). 

The ash deposits resulting from the combustion of solid and oil fuels often contain appreciable quantities of other corrodants in addition to vanadium pentoxide. One of the more important of these is sodium sulphate, and the effects of this constituent in producing sulphur attack have been mentioned. The contents of sodium sulphate and vanadium pentoxide present in fuel oil ash can vary markedly and the relative merits of different materials depend to a great extent upon the proportions of these constituents. Exposure of heat-resisting alloys of varying nickel, chromium and iron contents to ash deposition in the super-heater zones of oil-fired boilers indicated a behaviour pattern depending on the composition of the alloy and of the ash... 

Figure 3. Alfred Mayer s experiments with magnets floating in water (illustrated in one of his publications with this sketch) were the template J. J. Thomson used to develop hi9 first electron configurations (see Figure 4. Mayer found that the magnets adopted different patterns depending on the number introduced, leading Thomson to suspect that similar principles would pertain to electron configurations.

At a given flow condition, different flow patterns were observed which can be classified into five distinct patterns depending on the interfacial configuration liquid alone (or liquid slug), gas core with a smooth thin liquid film, gas core with a smooth thick liquid film, gas core with a ring-shaped liquid film, and gas core with a deformed interface. 

Because it depends on a number of conditions that are themselves inherently variable, runoff tends to vary even more than precipitation, particularly over time. Seasonal runoff patterns depend largely on latitude and altitude of the watershed, due to the importance of snowmelt in runoff peaks. In high-latitude basins or those with significant high-altitude contribut-... 

Although alkyl groups in general increase the rates of electrophilic addition, we have already mentioned (p. 974) that there is a different pattern depending on whether the intermediate is a bridged ion or an open carbocation. For brominations and other electrophilic additions in which the first step of the mechanism is rate determining, the rates for substituted alkenes correlate well with the ionization potentials of the alkenes, which means that steric effects are not important. Where the second step is rate determining [e.g., oxymercuration (15-3), hydroboration (15-17)], steric effects are important. ... 

The interference pattern depends both on the symmetry of the liquid crystal mesophase and on the arrangement of the molecules between the glass cover slips. Three examples are given in Fig. 8. 

The silicates are a large class of solids of great importance in industry as well as science, particularly geology. The prototype silicate is quartz consisting of Si04 tetrahedra which share their comers and edges and are arrayed in various three-dimensional patterns depending on the temperature. In other crystalline minerals the tetrahedra are linked in one-dimensional chains, or two-dimensional sheets. The arrays in these latter cases are combined with various metal ions. 

It should be emphasized that clear-cut situations described in Schemes 1-3 are uncommon and typically the combination of these models needs to be considered for kinetic and mechanistic description of a real system. However, even when one of the limiting cases prevails, each of these models may predict very different formal kinetic patterns depending on where the rate determining step is located. For the same reason, different schemes may be consistent with the same experimental rate law, i.e. thorough formal kinetic description of a reaction and the analysis of the rate law may not be conclusive with respect to the mechanism of the autoxidation process. 

Some genetic conditions are caused by mutations in a single gene. These conditions are usually inherited in one of several straightforward patterns, depending on the gene involved ... 

When a drug is in the bloodstream, it is distributed to various tissues. The distribution pattern depends on a number of factors ... 

It is experimentally obtained by tilting slightly the incident beam starting from a Zone-Axis Pattern. Depending on the presence of broad or sharp lines, 2D (Figure 4a) or 3D (Figure 4b) information is observed. 

The type of diffraction pattern depends on the degree of orientation and the distribution of crystals (if not a single) in the specimen. The following types of electron diffraction patterns may be distinguished ... 

The relative intensities of the [M]+ , [M+l]+ and [M+2]+ ions exhibit a characteristic pattern depending on the elements that make up the ion. For any molecular ion (or fragment) which contains one bromine atom, the mass spectrum will contain two... 

In Section II, we focus first on wafer-scale models, including macroscopic or bulk polish models (e.g., via Preston s equation), as well as mechanistic and empirical approaches to model wafer-scale dependencies and sources of nonuniformity. In Section III, we turn to patterned wafer CMP modeling and discuss the pattern-dependent issues that have been examined we also discuss early work on feature-scale modeling. In Section IV, we focus on die-scale modeling efforts and issues in the context of dielectric planarization. In Section V, we examine issues in modeling pattern-dependent issues in metal polishing. Summary comments on the status and application of CMP modeling are offered in Section VI. 

Fig. 5. Pattern dependent issues in oxide planarization and polishing of shallow trench isolation and metal damascene structures.

Models such as those proposed by Burke, Warnock, and Runnels can be effective in simulating the evolution of step height and film thicknesses around particular features. One limitation with feature based models is that they are difficult to apply over the die scale. In many cases, the features are so small that an attempt to trace their polish evolution is computationally expensive and may be difficult to apply to the entire die. In the next section, we focus on models which seek to address pattern dependencies observed over large regions of the chip or across the entire chip. 

The different polish characteristics of each of the traces demonstrate the significance of layout pattern dependencies in oxide CMP. For example, the L3 profile traces the large step density transitions with dramatic variations in the resulting oxide thickness. In contrast, the blocks along L4 polish at the same rate, underscoring the fact that layout pitch is not a first-order determinant of the polish rate. This is the case for a very large range of pitch... 

Pattern dependency concerns arise at two levels in STI CMP [67] during the oxide overburden polish phase, and when the nitride layer is exposed. In the first stage, the process is similar to interlevel dielectric (ILD) CMP and the characterization and modeling methodologies presented in the previous section are applicable. Once the nitride is exposed, two different materials exist at the same level, and pattern dependency manifestation is more complex. 

A key benefit of accurate CMP models that needs emphasis is the capability to optimize layout design before polishing. Post-CMP ILD thickness variation is a serious concern from both functionality and reliability concerns. An effective method of minimizing this effect is the use of dummy fill patterns that lead to a more equitable pattern density distribution across the chip. Evaluation of such schemes before actual product implementation has become a major use of CMP modeling [53]. Dummy fill is also being investigated for front-end processes where shallow trench isolation CMP suffers from substantial pattern dependencies. 

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