Integrated Circuit manufacturing complexities have resulted in decreasing product yields and reliabilities. This process has been accelerated with the advent of very deep sub-micron technologies coupled with the introduction of newer materials and technologies like copper interconnects, siliconon-insulator and increased wafer sizes. The need to improve product yields has been recognized and currently some yield enhancement techniques are used in industry CAD tools. Still, the signi cant increase in problem size implies that considerable time and e ort can be saved if the designer could predict the yield of each design stage. In this paper we undertake an e ort to derive bounds on the yield of the routing for a given placement. When the design is routed, resulting in a yield which is signi cantly smaller than the bound, the designer can choose to change the router cost functions, modify the placement or even re-design the unit in an attempt to increase the yield. We compare the bounds on yield obtained for a set of standard b enchmarks against exact yield values for the vanilla" routings, and the run times needed t o c alculate the two. The results indicate that reasonably good estimates of yield can be obtained in signi cantly lower amounts of run time. The accuracy of the estimates increases when larger designs are c onsidered as the simplifying assumptions made in the model no longer in uence the estimates signi cantly. 1: IntroductionThe need to improve product yields has been an important problem facing the semiconductor manufacturing industry 1 . Traditional yield models have focussed on the wafer yields as a function of defect densities, defect clustering and die area 1, 2, 3 . With his pioneering e ort, Stapper showed that some of the yield detractors are in uenced by h o w a design is laid out 2 . Based on this observation, substantial work 7 has been done to introduce the yield as a secondary objective t o t h e traditional objectives of minimizing area and improving performance of designs. Most of the work 4, 5, 6, 8 has focused on developing e cient yield estimation and enhancement techniques. These approaches are widely used in the industry and have helped improve manufacturability signi cantly. Unfortunately, instead of being able to identify the actual cause of the yield detractors, the above e orts minimize the e ects on product yields due to the design style being used. The next section attempts to motivate the need for alternative approaches to help locate the cause of yield degradation due to the design methodology used. 2: MotivationOne of the factors that in uence the magnitude of yield detractors is the design methodology being adopted to create a design. A t ypical layout synthesis design ow comprises of several substages like oorplanning, placement, routing, and compaction. Since most of these stages except

This report describes the integration of new solid and interface-cohesive mechanics systems into MOOSE. The purpose of these new systems is to support the ability of MOOSE to run full-field crystal plasticity finite element method simulations of key material processes in high temperature metallic materials. These simulations could be used to help accurately predict the performance of key high temperature structural materials in future advanced nuclear reactor components. Previous work implemented preliminary versions of many of these systems in MOOSE Apps. The current work reports on their integration into the main MOOSE tensor mechanics module along with associated improvements to the basic formulations and numerical implementations. Finally, the report provides an example of the full-field crystal plasticity simulations now possible in MOOSE, including examples of realistic geometries requiring millions of degrees of freedom to resolve the microstructural features and macroscale geometry.

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Generally, structures are not founded on ground level like that used in the Author's experiments. Although only qualitative results were aimed at, a proper depth of foundation would have been more realistic and might have had an appreciable effect on the dynamic soil-structure interaction.26. In 9 6 the Author states that it is often assumed that the resonant frequency for any one mode is invariant but the results in Fig. 3 show that this is not valid. The variation of the resonant frequency with the angle of excitation is a maximum of about 0.5 Hz. We feel that this may be due to the eccentrically fixed steel platform on the top of the tower and also due to measurement error. 27.Regarding the dependence of resonant frequency on amplitude (8 7), Table 1 for the rigid base tests shows that the changes in resonant frequency with amplitude are not appreciable for either mode. Only for the flexible base (125" mode) is there an appreciable change which may be attributed to the compaction of soil. 28.The assumption that structural damping can be idealized using a viscous model analogy is not far from true. Figure 5 shows that the relation between peak to peak amplitude of motion and cycle number (from 20-140 cycles) is almost linear.29. There appears to be a contradiction in 5 12 as regards the directional properties. It is evident that they do depend on the foundation.30. The difficulty of interpreting the characteristics of soil-structure interaction of the actual structure based on the model performance is indicated in 14. The scaling factor can be reliably determined only by conducting tests on other models to different scales.31. Regarding the soil-structure interaction being beneficial or not, in 16 and 17 the Author only indicates the two possibilities. What are his own conclusions?32. We feel that it would be highly beneficial to obtain a correlation between the power, frequency and damping characteristics of the soil. Perhaps this could be achieved by subjecting the structure to random vibrations (similar to natural conditions) under various foundation conditions and analysing the power spectrum.