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532                                        Chapter 12 Integrated Circuit Design


        is an important first step in the layout of an integrated circuit. It is the process of
        determining the shapes and relative positions of the modules so that the chip size
        becomes small and a desired aspect ratio of the chip is obtained. I/O pin locations,
        timing constraints, power dissipation, temperature gradients, and wire density
        estimates are other factors guiding the relative placement.
            Most of the early systems developed for layout
        focused on minimizing the chip area. However, perfor-
        mance issues—in particular, speed and power con-
        sumption have recently become a major concern.
        Notice that a smaller chip represents a smaller capac-
        itive load and may therefore be potentially faster and
        consume less power than a larger chip. Floor planning
        is used to verify the feasibility of a design without
        performing the detailed layout and design of all the
        blocks and functions.
            The next step, referred to as placement, is deter-
        mining the precise positions and orientations of the
        modules. The goal is to complete the placement and
        interconnections in the smallest possible area consis-
        tent with a set of technological and performance con-
        straints.
                                                          Figure 12.1 Main steps in
            Wire routing is usually partitioned into two steps:
                                                                     the layout of
        global and detailed. Global routing of the nets involves
                                                                     VLSI circuits
        selecting the particular routing regions each net will go
        through. Thereafter, in the detailed routing step, the
        actual or relative locations of all interconnections are determined. Often the entire
        routing process is carried out in a symbolic form which is technology-independent.
        In the subsequent steps, the wires and contacts are given their actual sizes and any
        surplus area is removed by compaction. Often, detailed routing and compaction are
        combined into a single step. Naturally, all these steps are mutually dependent.
            Unfortunately, most problems in floor planning, placement, and routing are
        NP-complete problems (i.e., large problems can not be solved in reasonable time).
        Thus, in practice various heuristic algorithms are used. A heuristic algorithm
        explores only a small region of the configuration space by sequentially generating
        a new configuration according to a set of rules. Hence, a heuristic algorithm can
        not be guaranteed to find the global optimum.


        12.2.1 Floor Planning and Placement

        The floor planning problem is defined as the problem of determining the geometry,
        locations, aspect ratios, and pin positions for all modules, so that all the con-
        straints, listed shortly, are satisfied and so that a weighted sum of the total chip
        area, net length, delay, and power dissipation is minimized. Placement is a special,
        more restricted, case of floor planning.
            The floor planning constraints are

            Q A set of modules with variable geometry, pin positions, estimated delays,
               and power dissipation
            Q Constraints on the positions of some of the modules
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