[Paper Review] Electrothermal Simulation of Bonding Wire Degradation under Uncertain Geometries

Thorben Casper, Herbert De Gersem+5 more|arXiv (Cornell University)|Oct 14, 2016

Electromagnetic Compatibility and Noise Suppression10 references5 citations

TL;DR

This paper proposes a stochastic electrothermal simulation framework using the Finite Integration Technique (FIT) to model bonding wire degradation under geometric uncertainties, treating wires as lumped elements within a spatially distributed field-circuit model. Key results show that manufacturing tolerances in wire length lead to a standard deviation of 4.65 K in temperature, with failure risk increasing when uncertainty bounds cross the critical 523 K threshold after ~26 seconds.

ABSTRACT

In this paper, electrothermal field phenomena in electronic components are considered. This coupling is tackled by multiphysical field simulations using the Finite Integration Technique (FIT). In particular, the design of bonding wires with respect to thermal degradation is investigated. Instead of resolving the wires by the computational grid, lumped element representations are introduced as point-to-point connections in the spatially distributed model. Fabrication tolerances lead to uncertainties of the wires' parameters and influence the operation and reliability of the final product. Based on geometric measurements, the resulting variability of the wire temperatures is determined using the stochastic electrothermal field-circuit model.

Motivation & Objective

• To address the challenge of thermal reliability in IC packaging by modeling electrothermal behavior of bonding wires under fabrication-induced geometric uncertainties.
• To develop a computationally efficient framework that avoids full volumetric meshing of thin wires by using lumped element representations within a coupled electrothermal field simulator.
• To quantify the impact of wire length variability on temperature distribution and failure probability using uncertainty quantification (UQ) techniques.
• To enable early-stage design optimization by predicting expected temperatures and their variability across multiple bonding wires.
• To validate the model using measured data and demonstrate its sensitivity to manufacturing tolerances in real-world IC packages.

Proposed method

• The electrothermal coupling is modeled using the Finite Integration Technique (FIT) for spatial discretization of the electromagnetic and thermal fields.
• Bonding wires are represented as lumped electrical and thermal networks connected via point-to-point links, avoiding fine meshing of thin wires.
• The electrical sub-problem is governed by the current continuity equation with temperature-dependent conductivity, while the thermal sub-problem uses the transient heat equation with Joule heating and boundary heat exchange.
• Uncertainties in wire length are modeled using a probability density function derived from experimental measurements, and propagated via Monte Carlo simulation.
• The system is solved using a time-stepping scheme with 51 time steps up to 50 s, and statistical moments such as expectation and standard deviation are computed over 1,000 Monte Carlo samples.
• The failure threshold is defined at 523 K (250 °C), and the model evaluates whether temperature uncertainty exceeds this limit.

Experimental results

Research questions

• RQ1 How does geometric uncertainty in bonding wire length affect the expected temperature and thermal reliability of IC packages?
• RQ2 What is the magnitude of temperature variation across bonding wires due to manufacturing tolerances, and does it exceed critical failure thresholds?
• RQ3 Can a lumped-element representation of bonding wires be effectively integrated into a full electrothermal field simulation without compromising accuracy?
• RQ4 How do convection and radiation boundary conditions influence the stabilization of temperature over time in the presence of uncertain wire geometries?
• RQ5 To what extent does uncertainty in wire length dominate the overall thermal variability compared to other sources?

Key findings

• The expected temperature of the hottest bonding wire remains below the critical 523 K threshold at steady state (t ≈ 50 s), but uncertainty in wire length leads to significant thermal variation.
• The standard deviation of the temperature in the hottest wire reaches 4.65 K due to geometric uncertainty, indicating substantial variability in thermal response.
• The 6σ deviation band crosses the critical temperature threshold after approximately 26 seconds, indicating a non-negligible risk of thermal failure under uncertainty.
• The Monte Carlo simulation error was estimated at 0.147 K, confirming the statistical reliability of the results with 1,000 samples.
• The spatial temperature distribution at t = 50 s confirms that the shortest wires, located near the chip's contact points, experience the highest temperatures and are most sensitive to geometric variation.
• The model demonstrates that even small geometric deviations can significantly affect thermal performance, highlighting the importance of uncertainty quantification in early IC packaging design.