Thermal Modeling of Memory Access Operations in Microprocessors

Abstract

A large fraction of energy consumed in modern microelectronic devices and systems is taken up by memory access operations, which is expected to cause significant temperature rise. Since memory access operations are very short in duration, this is expected to inherently be a transient thermal phenomenon. Despite the critical importance of thermal management in microelectronics, not much work exists on understanding the nature of thermal transport during memory access operations. In this work, a mathematical model to predict the transient temperature rise within a 3D memory chip is presented. Most heat-generating memory access processes occur over a short timescale for which the thermal penetration depth is shorter than the die thickness. This enables the modeling of such processes independent of the nature of chip cooling by treating the chip as a semi-infinite medium. A semi-infinite Green’s function model is developed for one bank of memory on a single layer of a block of the memory chip. This model is validated against finite element simulation results. Validation is also carried out by comparison of the model against the analytical solution for a limiting case. The analytical model is used to analyze transient thermal effects of various memory access processes for multiple banks. These results will help develop an understanding of optimal layouts and processes for 3D memory chips, eventually leading to co-design tools that simultaneously improve thermal and electrical performance of 3D memory chips.