A Force-Directed-Based Optimization Scheme for Thermal Placement Design of MCMs

Thermal management becomes exceptionally critical to both the reliability and operation performance of electronic packages, particularly for multichip modules (MCMs), as packaging and power densities continue increase while packaging dimension continues decrease. The underlying goal of the study is to pursue the minimum system temperature design of MCMs containing a number of chips of equal and/or unequal power through the optimal chip placement design. To deal with the thermal design problems, an effective indirect optimization approach that integrates a modified force-directed (FD) thermal model, a finite-element (FE) technique and an exterior penalty method (EPM) is proposed. In the modified FD thermal model, a novel representation of the repulsive and attractive forces is proposed, and the sum of these forces in the design system, representing the total system chip junction temperature, constructs the objective of the optimization problems. Together with some geometry constraints, the constrained optimization problems are formed, and furthermore, transformed into unconstrained optimization problems using an EPM. The solution of the optimization problems is sought through a direct, iterative search scheme with two proposed placement strategies. The alternative goal of the study is to address the feature and feasibility of these two proposed placement strategies for the current problems. The applicability of the proposed optimization approach is demonstrated through several design applications, and their results are extensively compared against the published data. It turns out that the current optimization approach can be very effective and robust in providing thermal optimal design of MCMs with a minimal total chip junction temperature through optimal chip placement