Có 80+ tài liệu thuộc chủ đề "định tuyến lưới nhiều tín hiệu"
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FIGURE 28.4 Pseudocode of the dynamic programming-based buffered path algorithm.. When a solution with the driver is at the top of the Q, it is the minimum delay solution.. The pseudocode of this algorithm is given in Figure 28.4. Please note that pruning is performed in many steps to remove inferior solutions so that the runtime can be improved. 28.3.2...
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For these regions for which buffer insertion is forbidden, one simply avoids inserting buffer candidate locations on top of the blockage. The purpose is not to improve timing performance but rather to bias van Ginneken style algorithm to insert buffers in regions of the design that are more favorable, such as areas with lower congestion cost.. In fact, because the...
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convexifying the look-up table data with minimum perturbation can be formulated as a convex semidefinite optimization [Roy 2005] problem and hence optimality can be reached in polynomial time. 2 φ( x ) 0 means the Hessian of φ( x ) is positive semidefinite, i.e., all the eigenvalues of the Hessian are greater than or equal to zero.) Thus, the fitting...
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have at least one pin inside a bin, to the perimeter of the bin [SPK03]. It captures the expected congestion at the boundary of the bin rather than that within the bin, in contrast to the pin density metric. In particular, probabilistic estimation is independent of the order in which the nets are considered. In the same vein, the layer...
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In general, the accuracy of placement-based metrics decreases as the level of abstraction of the netlist increases. With the problem of routing congestion getting worse because of the scaling of design sizes and process technologies, a comprehensive congestion management strategy must target congestion through the entire design flow, relying on the appropriate congestion estimators at each stage.. The interested reader...
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This schema was proposed in the earliest papers on rip-up and reroute. The crossing count of a net is the sum of the crossing counts of its connections. Using this bipartite graph, Ting and Tien attempt to find an intelligent subset of nets to rip-up and reroute. Such an issue is endemic to the iterative rip-up-and-reroute schema.. If the routing...
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32.4 SIMPLEX ALGORITHM WITH COLUMN GENERATION. The first algorithm to solve the fractional global routing problem (Equation 32.2) by Hu and Shing in 1985 [15] used the simplex algorithm by Dantzig in 1951 [16] with column generation. The method is limited in the size of the problem instances, and hence Hu and Shing propose a decomposition and cut-and-paste approach.. The...
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A Steiner tree for a net is characterized not only by the edges of the global routing graph, but also each edge of the Steiner tree has a continuous parameter specifying the spacing to each side of the final route. The timing constraints are ensured by bounding the weighted capacitance for subsets of the nets, a constraint similar to the...
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The respective width W c and height H c of the chip can be computed by applying a longest-path algorithm on G H and G V. For dead spaces and routing channels that are not on the critical paths of the constraint graph G H ( G V. After inserting buffers into the selected tile, the information of the constraint...
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Furthermore, 2c c is adopted in the model to account for the worst case coupling effect when all the aggressor nets have different signal transitions from that of the victim net, for which the Miller effect makes the coupling phenomenon more significant by doubling the coupling effect. Let the length of the wire segment e be l e , and...
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34.1 Coupling Noise Phenomenon. 34.1.1 Interconnect Capacitance. 34.1.2 Coupling Noise Injection. 34.2 Noise Analysis. 34.2.1 Noise Calculation. 34.2.2 Failure Criteria. 34.3 Simplifying Models and Analysis. 34.3.1 Simplification of Models. 34.3.1.1 Aggressor Driver Model. 34.3.1.2 Quiet Victim Model (for Functional Noise. 34.3.1.3 Switching Victim Driver Model (for Delay Noise. 34.3.1.4 Receiver Characterization. 34.3.2 Conservative Filtering of Nonrisky Nets. 34.4 Reducing Pessimism...
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FIGURE 34.8 Aggressor driver model.. A small signal analysis of the gate can be performed, wherein a small noise voltage is applied at the output (over a 0 or Vdd bias as appropriate for the output state) and the output current is measured. The ratio of the output current to the applied noise voltage then characterizes the holding resistance. The...
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35.1 Introduction. 35.1.1 Modeling in a Design Flow. 35.1.2 Lithographic Processing. 35.2 Lithographic Modeling. 35.2.1 Introduction. 35.2.2 Lithographic Modeling Fundamentals. 35.2.2.1 Maxwell’s Equations. 35.2.2.2 Propagation. 35.2.2.3 Linearity. 35.2.2.4 Computation by Superposition. 35.2.3 RET Tools. 35.2.3.1 OPC. 35.2.3.2 PSM. 35.2.3.3 OAI. 35.2.3.4 RET Combinations. 35.2.3.5 Polarization. 35.2.4 RET Flow and Computational Lithography. 35.2.5 Mask Manufacturing Flow. 35.2.6 Contour-Based EPE. 35.3 Simulation...
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It can be shown that, when the diffraction pattern of Equation 35.10 is placed at exactly the focal distance in front of the lens, the field at the focal plane (a distance f behind the lens) allows this phase factor to cancel the phase factor in the Fraunhofer diffraction formula, and the field in the image plane becomes. M (...
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FIGURE 35.17 Pitch curve for lines and spaces under a particular OAI approach called QUASAR illumination.. (Adapted from Schellenberg, F.M., Capodieci, L., and Socha, B., Proceedings of the 38th Design Automation Conference, ACM, New York, 2001, pp. 35.2.3.5 Polarization. At this time, there is a fourth independent variable of the EM field that has not yet been as fully exploited...
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FIGURE 35.29 Illustration of the time steps used in the computation of EM fields according to the FDTD Method. properties of air, quartz, and chromium have been measured and can be found in Ref. More critical is the fact that the grid must extend throughout the space to be simulated. If a large system such as an entire lens were...
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Walton, Hierarchical critical area extraction with the EYE tool, in Proceedings of the IEEE Workshop Defect Fault Tolerance in VLSI Systems, pp. Griep, AFFCCA: A tool for critical area analysis with circular defects and lithography deformed layout, in Proceedings of the IEEE International Workshop on Detect and Fault Tolerance in VLSI Systems, pp. Vasudev, Automated optical proximity correction: A rules-based...
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this model takes the topography of the wafer into account and adjusts the polishing rate accordingly, it does not consider the bending of the polishing pad. The model is purely empirical and does not depend on the pressure. This model defines the dependence of the polish rate on the wafer shape. In particular, it takes into account all possible geometrical...
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In the Monte-Carlo approach, a tile is chosen randomly and its content is increment with a predetermined fill amount. The only drawback of the Monte-Carlo method is that it may insert an excessive amount of total fill. A variant of the Monte-Carlo approach is the greedy algorithm. In the presence of two objectives, namely min-variation and min-fill, the intuitive approach...
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36.6.2 I MPACT OF S PATIAL V ARIATION. The 2004 edition of the International Technology Roadmap for Semiconductors (ITRS) [25] lists the control of printed transistor gate length in the lithography process as falling short of expectations for the coming technology generations. This interaction between wafer and die variation, if not considered, leads to erroneous modeling as shown in Figure...