With the continual scaling of devices and interconnects, accurate analysis and effective optimization of the temperature distribution of a ULSI chip are increasingly important in predicting and ensuring the performance and reliability of the chip before fabrication. Motivated by the design challenges, this dissertation aims at a detailed study of the areas of thermal analysis, modeling, and optimization of ULSI chips. In particular, this dissertation introduces LOTAGre, a high-efficiency [special characters omitted] (n lg n) multilayer Green's function-based thermal analysis method. LOTAGre can analyze ULSI chips consisting of multilayer heterogeneous heat conduction materials, with either wire-bonding packaging or flip-chip packaging, under uniform or nonuniform ambient temperatures. By integrating the eigen-expansion technique and the transmission line theory, this dissertation derives the multilayer heat conduction Green's function, including the s-domain version which can be used to compute the thermal transfer impedance between two arbitrary locations in the chip and establish compact thermal models for the critical components in the chip.

To aid interconnect thermal analysis, this dissertation introduces a new Schafft-type interconnect temperature distribution model which is very flexible in addressing the effects of chip packaging, surrounding ambient temperatures, and the temperature gradients within the interconnect. An efficient [special characters omitted] (n) method is introduced to solve the interconnect temperature distribution from the model.

To optimize the chip temperature distribution, this dissertation introduces an optimal power budget model that determines the optimal allocation of cell powers to different regions of the chip so that the resultant temperature distribution most closely approximates the target temperature distribution for the chip. The generalized minimal residue method and the conjugate gradient method are employed to construct top-level and front-level thermal optimizers to solve the optimal power budget efficiently. Finally, the dissertation describes the procedure to incorporate the optimal power budget model into the widely distributed Capo placement tool to enable thermal optimization in the cell placement stage.