General thermal force model with experimental studies

Thermal force has proven to be a useful concept for managing the package-level thermal placement problem. However, the previous thermal force model is based on insulated edge boundary condition; thus it is only suitable to face-cooled packages. A general thermal force model is proposed to extend the applicability of the thermal force to cover general cooling conditions by introducing the concept of the heat transparency of a boundary /spl tau/. By managing /spl tau/, the present method generates a series of thermal-force-equilibrium placements fitting to situations from face-cooled to edge-cooled packages. Experimental results indicate that for generating the reliability-best placements, the best /spl tau/'s are in the range 0 /spl les/ /spl tau/ /spl les/ 0.05 for face-cooled packages and in the range 0.1 /spl les/ /spl tau/ /spl les/ 0.25 for the volumetric-cooled packages. For edge-cooled packages, the best /spl tau/'s are the largest values of /spl tau/ that can achieve convergent thermal-force-equilibrium placements.