Fast Analytical Modeling of Dynamic Thermal Behavior of Semiconductor Devices and Circuits

This paper presents a set of closed-form analytical expressions to approximate the transient solution to the heat equation without requiring any computationally intensive series summation. The parameters of these expressions can be easily extracted from the physical layout for constructing a thermal impedance matrix to be used in a self-consistent electrothermal circuit simulation of a large number of heat sources. These formulations are derived by assuming a small heat source compared to the chip area in a homogeneous chip with the boundary conditions of an adiabatic top and an isothermal bottom. The derivation allows heat sources to be located at a certain depth from the chip top. The expressions have been verified by comparison with 3-D numerical simulations.