Coupled Simulation of Transient Heat Flow and Electric Currents in Thin Wires: Application to Bond Wires in Microelectronic Chip Packaging

TL;DR

This paper develops a coupled 1D-3D simulation method for modeling transient heat flow and electric currents in thin wires, specifically applied to bond wires in microelectronic chip packaging, addressing numerical challenges due to geometric scales.

Contribution

It introduces a stable coupling scheme for 1D and 3D electrothermal problems using de Rham currents, enabling efficient simulation of bond wires in microelectronics.

Findings

The coupling scheme achieves stable and physical solutions.

Numerical errors and convergence rates are characterized.

Application to industrial chip packaging demonstrates practical relevance.

Abstract

This work addresses the simulation of heat flow and electric currents in thin wires. An important application is the use of bond wires in microelectronic chip packaging. The heat distribution is modeled by an electrothermal coupled problem, which poses numerical challenges due to the presence of different geometric scales. The necessity of very fine grids is relaxed by solving and embedding a 1D sub-problem along the wire into the surrounding 3D geometry. The arising singularities are described using de Rham currents. It is shown that the problem is related to fluid flow in porous 3D media with 1D fractures [C. D'Angelo, SIAM Journal on Numerical Analysis 50.1, pp. 194-215, 2012]. A careful formulation of the 1D-3D coupling condition is essential to obtain a stable scheme that yields a physical solution. Elliptic model problems are used to investigate the numerical errors and the corresponding convergence rates. Additionally, the transient electrothermal simulation of a simplified microelectronic chip package as used in industrial applications is presented.