Fast Transient Convolution-Based Thermal Modeling Methodology for Including the Package Thermal Impact in 3D ICs

The relevance of accurate prediction of the thermal behavior of microelectronic systems has been increasing since the introduction of 3D integrated circuits (ICs). Different modeling strategies have been implemented to this scope, aiming both to increase accuracy and to reduce computational time. In this paper, a transient fast thermal model methodology for packaged 3D stacked ICs is presented. It can be considered as a multiscale strategy, whose core is constituted by a highly resolved, convolution-based algorithm. This allows to compute the temperature increase due to a generic, time varying, power map in a stack configuration. On top of this, the time-dependent package thermal spreading and capacitive effect is included via correction profiles. These corrections are based on the ratio between the thermal responses of the package and of the stack configurations to uniform, impulsive, power dissipation at different time steps. Validation with respect to finite-element method results shows good accuracy. An error metric, to estimate a priori the need to include the package impact on top of the convolution-based approach, has also been developed. Alternative but similar algorithms, which place themselves in between the solutions with and without the package impact, both from an accuracy and from a computational time point of view, are also shortly presented in this paper.