All-Digital Circuits for Measurement of Spatial Variation in Digital Circuits

Abstract

Increased variation in CMOS processes due to scaling results in greater reliance on accurate variation models in developing circuit methods to mitigate variation. This paper investigates spatial variation in digital circuit performance: we describe a test-chip in 90 nm CMOS containing all-digital measurement circuits capable of extracting accurate variation data. Specifically, we use replicated 64-bit Kogge-Stone adders, ring oscillators (ROs) of varying gate type and stage length and an all-digital, sub-picosecond resolution delay measurement circuit to provide this data. Measurement data from the test-chips indicate that 1) relative variation is significantly larger in low-voltage domains, 2) within-die variation is spatially uncorrelated, and 3) die-to-die (or global) variation is strongly correlated, but degrades toward uncorrelated as the power-supply voltage is lowered. Lastly, extended analysis of the data reveals that systematic effects such as layout pattern dependencies or circuit structure can be misinterpreted as random but spatially-correlated variation. This suggests that circuit designers will reap more benefit from design tools capable of modeling systematic, position-dependent variation rather than spatially correlated, distance-dependent variation.