Convolution based compact thermal model application to the evaluation of the thermal impact of die to die interface including interconnections

Thermal aware design of integrated circuits is essential to avoid reliability issues and failures especially in 3D-technology where active dies are placed on top of each other and more heat is dissipated on the same area available for cooling compared to conventional 2D-packages. A certain number of parameters can be selected to reduce temperature and temperature gradient. This paper is mainly focusing on the thermal impact of the die-to-die interface layer. This consists of adhesive material and arrays of interconnection structures. Besides being used for electrical die-die connections, they can be added to locally improve the low thermal conductivity of the adhesive. Short computational time is preferred for the thermal analysis of different designs: this is why various compact thermal models (CTMs) strategies have been developed. The one presented here, for the steady state temperature evaluation of two dies stacks, is based on convolution and fast Fourier transform. A novel correction methodology is introduced to deal with the material non-homogeneity in the interface layer. Case analyses, as the interface material thermal impact or the maximum achieved temperature as a function of the amount of interconnections, are presented in the paper and can be quickly and easily performed with this CTM.