Statistical Interconnect Timing Analysis Based On Symbolic Method

An efficient yet accurate statistical timing model for IC interconnects is proposed in this paper. When considering process variations, interconnect physical parameters must be modeled as random variables, which makes interconnect delays become random variables with certain PDF. In order to get the PDF of the interconnect delay, a creative new symbolic delay calculation algorithm, expressing delays as closed functions of interconnect physical parameters, is employed. And based on closed-form delay metrics, delay is represented directly as function of physical parameters. Then by using a quadratic model to approximate the delay, we managed to obtain its PDF directly through Characteristic Function and Fourier Transform technique. This method can be used to handle interconnect circuits with more than 300,000 nodes with a high efficiency. And as compared to Monte Carlo Simulation, this method has a fairly good accuracy with only 1% error.