A Model for Interlevel Coupling Noise in Multilevel Interconnect Structures

In multilevel interconnect structures, the interconnect layers are practically always perpendicular to each other. Due to the capacitive coupling between adjacent layers, the switching activity in one layer produces noise in the others. Often, this interlevel coupling noise is implicitly neglected: only the parallel neighbors of a victim line are considered noisy while the perpendicular conductors located in the layers above and below the victim are assumed to behave as quiet metal planes. However, the error due to this assumption is unclear. It has never been rigorously analyzed or quantified. This paper examines the interlevel coupling noise present at the far end of a victim when a large number of perpendicular aggressors are randomly switching. Each aggressor is modeled as a Markov chain and the victim is modeled as a resistance-inductance-capacitance transmission line. The result is a novel closed-form expression for the power-spectral density of the random switching noise produced by the perpendicular aggressors. It is used to rigorously show that the quiet metal plane assumption is statistically very good when the number of orthogonal aggressors is large and when they are toggling independently. The validity of the quiet metal plane assumption is also discussed when the orthogonal aggressors form wide buses that can be considered sufficiently correlated to produce deterministic simultaneous switching noise