Lecture 4 n Physical design automation n Algorithms

Lecture 4 n Physical design automation n Algorithms n n Device and interconnect modeling n n Important for the performance-driven layout Simulation and numerical computation n 1/4/2022 Graph theory Data structure Optimization methods Evaluation of the design VLSI Physical Design 1

Lecture 4 (cont. ) n Algorithms n Optimum solution and approximation solution n n Time complexity of an algorithm n n n Running time must be controlled in polynomial time NP-complete class Heuristic algorithms n n 1/4/2022 Global optimal and local optimal Based on the experience and the understanding of the problem Practical approach VLSI Physical Design 2

n Examples n n 1/4/2022 The shortest path in a graph can be computed in a polynomial time The maximum flow in a graph can be computed in polynomial time The minimum partition of a graph has not been computed in polynomial time Traveling salesman problem has not been solved in polynomial time VLSI Physical Design 3

Lecture 4 (cont. ) n Device and interconnect modeling n Parasitic parameter computation n Modeling n n Lumped model Distributed model Transmission line model Design rules n 1/4/2022 3 D computation is needed for deep-submicron-process Need knowledge of EM field and numerical analysis To simplify the design VLSI Physical Design 4

Lecture 4 (cont. ) n Simulation and numerical computation n n SPICE Special purpose simulator n n Delay and noise computation n n Use the closed formula Package analysis n 1/4/2022 In house tool Simulator for the clock network Simulator for the mixed-signal circuit Nsoft, HP, … VLSI Physical Design 5

n Interconnect model example 1/4/2022 VLSI Physical Design 6