Chapter 12 - Thermal Modeling and Analysis

Abstract

Thermal issues are of significant importance in three-dimensional (3-D) circuits. To understand the implications of heat in the performance of 3-D circuits, the different heat transfer mechanisms in integrated circuits are described. To accurately describe the thermal behavior of 3-D circuits, thermal models of different complexity and accuracy and related thermal analysis methods are presented, including models for liquid cooling. These thermal models include both closed-form analytic models and numerical models. Thermal models that utilize the electro-thermal duality for determining the temperature in a 3-D circuit are also discussed. Moreover, thermal models specific to through silicon vias are described. Thermal analysis techniques that utilize these models, including, for example, the finite element method or the multigrid method, are also presented.