Thermal correlation between measurements and FEM simulations in 3D ICs

This paper presents a comparison between electrical measurements, which are carried out with embedded in-situ sensors, and thermal numerical simulations. The objectives of this study are firstly to calibrate the Finite Element model by comparing the measurement results with those from simulations through a Design Of Experiments (DOE), and then to provide thermal recommendations on the studied parameters thanks to the calibrated numerical model. The primary objective of the DOE is to quantify the sensitivity of modeling parameters. Results show a strong influence of the silicon thickness, the convective heat transfer coefficient of the bottom surface, the thickness of the thermal insulation and the position of the hot spots relative to the sensors. The boundary conditions, particularly the heat transfer coefficient are also identified as significant parameters. Once the main factor set determined, the second objective of this study is to weight quantitatively the influence of key parameters. Finally, by providing a numerical and experimental comparison, this paper provides validated values of boundary conditions to be applied in the numerical simulations. These are considered to be the most difficult to obtain, while they have a huge influence on the simulation results, and this work allows to provide reliable thermal recommendations on designs to manage self-heating challenges.