Modelling of Skin Effect in On-Chip VLSI RLC Global Interconnect

Abstract

This paper addresses one of the aspects of the high frequency effects, namely the skin effect. The basic problem with skin effect is that it attenuates the high frequency components of a signal more than that of the low frequency components. Due to the increase in operating frequency and die sizes, RC models are becoming insufficient for analysis of global VLSI interconnects. Accurate noise modelling for RLC lines is thus critical for timing and signal integrity analysis. Skin effect basically affects the resistance and also the inductance, which in turn affects the system integrity in particular and its response as a whole. The current distribution inside the conductor changes as frequency increases. These changes produced in the conductors are known as skin and proximity effect. Till now the skin effect has been neglected for the modelling the on-chip interconnects. But with the increase in frequency to the GHz range, the skin effect has become prominent in performance parameter modelling. In this paper, firstly a crosstalk noise formula for on chip VLSI interconnects has been proposed without considering the skin effect. The voltage response at the output node is analytically derived and then the skin effect on the line resistance is analysed. From that an efficient and novel model is derived to estimate the crosstalk in the on-chip interconnects. On-chip inductive effects are becoming predominant in deep submicron interconnects due to increasing clock speeds; circuit complexity and decreasing interconnect lengths. Inductance causes noise in the signal waveforms, which can adversely affect the performance of the circuit and signal integrity. In this paper, we have also proposed a novel analytical model to find the impact of the skin effect on the noise in RLC interconnect without considering the skin effect on inductance because the value of the resistance increases dramatically compared to that of the value of inductance. In this work, the resistance variation due to the skin effect is considered in two wire transmission line model. The correlation between the skin effect and the noise induced is also discussed. The simulation results justify the efficacy of the proposed crosstalk noise model in the presence of skin effect.