Post-Silicon Estimation of Spatiotemporal Temperature Variations Using MIMO Thermal Filters

This paper experimentally demonstrates a methodology for proactive estimation of spatiotemporal variations in junction temperature of a silicon chip using multi-input multi-output (MIMO) thermal filters. The presented approach performs on-chip measurements to estimate the relations between power and temperature variations in the frequency domain to construct a MIMO thermal filter. The extracted filter is then used to predict spatiotemporal temperature variations from a known power pattern, even for locations without temperature sensors. The accuracy of the proposed approach is verified through a thermal emulator designed in 130-nm CMOS technology with on-chip digitally controllable power (heat) generators and temperature sensors. Using the proposed MIMO thermal filter, spatiotemporal temperature variations are accurately estimated with small error bound even at locations with no temperature sensors.