CLIP: integer-programming-based optimal layout synthesis of 2D CMOS cells

A novel technique, CLIP, is presented for the automatic generation of optimal layouts of CMOS cells in the two-dimensional (2D) style. CLIP is based on integer-linear programming (ILP) and solves both the width and height minimization problems for 2D cells. Width minimization is formulated in a precise form that combines all factors influencing the 2D cell width—transistor placement, diffusion sharing, and vertical interrow connections—in a common problem space; this space is then searched in a systematic manner by the branch-and-bound algorithms used by ILP solvers. For height minimization, cell height is modeled accurately in terms of the horizontal wire routing density, and a minimum-height layout is found from among all layouts of minimum width. For exact width minimization alone, CLIP's run times are in seconds for large circuits with 30 or more transistors. For both height and width optimization, CLIP is practical for circuits with up to 20 transistors. To extend CLIP to larger circuits, hierarchical methods are necessary. Since CLIP is optimum under the modeling assumptions, its layouts are significantly better than those generated by other, heuristic, layout tools.