Integrated circuit white space redistribution for temperature optimization

Thermal problems are important for integrated circuits with high power densities. Three-dimensional stacked-wafer integrated circuit technology reduces interconnect lengths and improves performance compared to two-dimensional integration. However, it intensifies thermal problems. One remedy is to redistribute white space during floorplanning. In this paper, we propose a two-phase algorithm to redistribute white space. In the first phase, the lateral heat flow white space redistribution problem is formulated as a minimum cycle ratio problem, in which the maximum power density is minimized. Since this phase only considers lateral heat flow, it also works for traditional two-dimensional integrated circuits. In the second phase, to consider inter-layer heat flow in three-dimensional integrated circuits, we discretize the chip into an array of tiles and use a dynamic programming algorithm to minimize the maximum stacked tile power consumption. We compared our algorithms with a previously proposed technique based on mathematical programming. Our iterative minimum cycle ratio algorithm achieves 35% more reduction in peak temperature. Our two-phase algorithm achieves 4.21× reduction in peak temperature for three-dimensional integrated circuits compared to applying the first phase, alone.