tailieunhanh - Handbook of algorithms for physical design automation part 75

Handbook of Algorithms for Physical Design Automation part 75 provides a detailed overview of VLSI physical design automation, emphasizing state-of-the-art techniques, trends and improvements that have emerged during the previous decade. After a brief introduction to the modern physical design problem, basic algorithmic techniques, and partitioning, the book discusses significant advances in floorplanning representations and describes recent formulations of the floorplanning problem. The text also addresses issues of placement, net layout and optimization, routing multiple signal nets, manufacturability, physical synthesis, special nets, and designing for specialized technologies. It includes a personal perspective from Ralph Otten as he looks back on. | 722 Handbook of Algorithms for Physical Design Automation E E E E t 0 x 0 x Ax x 2 Ax x 3 Ax H H H t At x Ax x Ax x Ax E E E E t At t At E E E E t 2 At x 0 x A0 x 2 Ax x 3 Ax FIGURE Illustration of the time steps used in the computation of EM fields according to the FDTD Method. Adapted from Taflove A. and Hagness . Computational Electrodynamics The Finite-Difference Time-Domain Method Artech House Boston 2005. With permission. properties of air quartz and chromium have been measured and can be found in Ref. 94 this tends to not be a practical drawback to its use. 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 to be simulated point by point the amount of computation would be gigantic. Lens propagation is well described by the approximations described previously in Section and using the Hopkins method of Section . To use the more accurate results of the FDTD simulation where it matters at the mask and more particularly at the patterned surface of the mask a grid can be set up to only simulate the thin region at the quartz chrome air interface of the photomask using fine grids . grid spacing of 5 nm for illumination wavelength k 193 nm . The scattering of the mask patterning structures can then be accurately computed locally using the FDTD method and a replacement for the mask function a new M x y can be generated from the results at the bottom of the simulation window. This M x y will have the amplitude and phase information as generated by the FDTD simulator and the angular spectrum . Fourier transform of this complex function can be used in the established equations. Another problem lies with the treatment of the boundary conditions. Normally such a program would assume the edges are contiguous with another domain periodically repeated from the grid under simulation. If this is actually the case on the photomask . with .