Theoretical model based thermal studies on stacked dies

A generic thermal resistance based theoretical model is proposed for n ges 3 stacked dies. The model assumes same die to die thermal resistance between adjacent dies. It also includes external thermal resistances. This model is solved to establish the relation between thermal resistances and total heat flow from top and bottom of package. The hottest die location is related to the ratio of total heat going through top of the package, ´F´. This relation is found to be stair case like linear function. Lower and upper bounds to the temperature drop within the die stack are established. Two definitions of package thermal metrics are proposed. Both are shown to have a quadratic variation with the fraction of total heat going through top of the package (F). The results form a scientific basis for steady state thermal characterization of 3D stacked dies under complete range of external thermal boundary conditions