Transient thermal transport in a three-dimensional integrated circuit (3D IC) with unequally sized die

Thermal modeling of three-dimensional integrated circuits (3D ICs) is of much interest due to the nature of heterogeneous integration and the growing rate of heat dissipation. There is a lack of past work specifically on thermal modeling of 3D ICs with unequally sized die. This work presents transient modeling of thermal transport in a general multilayer 3D IC with die of different widths normal to the thickness direction. The governing energy equations are solved in the Laplace domain by deriving a set of algebraic equations for the series coefficients for the temperature field. Interfacial conditions between adjacent die and adiabatic conditions along the overhanging edges are accounted for. Under special conditions, results are shown to agree well with past work on steady conditions, as well as on equally sized die. The model is used to predict transient thermal response of a representative two-die 3D IC to heat generation due to dynamic workload. The effect of practical considerations are investigated, including transient heat generation spikes and interfacial contact resistance. The theoretical model developed in this work improves the understanding of thermal transport in 3D ICs, and may contribute towards improved thermal analysis tools for 3D ICs.