Analytical model for sensor placement on microprocessors

Thermal management in microprocessors has become a major design challenge in recent years. Thermal monitoring through hardware sensors is important, and these sensors must be carefully placed on the chip to account for thermal gradients. In this paper, we present an analytical model that describes the maximum temperature differential between a hot spot and a region of interest based on their distance and processor packaging information. We also use a run-time thermal model, as an illustration of virtual sensors, and examine two benchmarks that exhibit highly concentrated thermal stress. We then use our analytical model to demonstrate the safety margins of the chip. Ultimately, the mathematical expression allows designers to obtain worst-case behavior of thermal heatup and select the optimal location of additional sensors.