Variance Analysis in 3-D Integration: A Statistically Unified Model With Distance Correlations

Variability is a challenge for future scaling as process dimensions reduce. The emerging 3-D sequential stacking technology is more than Moore's scaling alternative. The 3-D design flow requires the partitioning of the netlist between the tiers. This paper presents the variability analysis of circuits partitioned into different levels. A comparison among local and global variations effects on ring oscillators (ROs) and SRAM is demonstrated. The across-chip variations and correlation range are shown as a critical point for the 3-D very large-scale integrated circuits, where the local variability is dominant. The correlations between devices due to the distances or the allocation into different tiers are directly taken into account in the SPICE model due to a statically unified model applied to 3-D circuits based on Monte Carlo simulations. Design wise, the 3-D integration can further decrease the circuit variability as shown in RO output frequency and SRAM static noise margin.