# SPICE-Compatible Degradation Modeling Framework for TDDB and LER Effects in Advanced Packaging BEOL Based on Ion Migration Mechanism

## TL;DR

This paper introduces a SPICE-compatible model for predicting dielectric breakdown in semiconductor packaging by simulating metal ion migration and line-edge roughness effects.

## Contribution

A novel SPICE-compatible degradation model integrating ion migration and line-edge roughness effects for accurate lifetime prediction in semiconductor packaging.

## Key findings

- The model accurately predicts resistance changes and lifetime under various stress conditions.
- Incorporating line-edge roughness improves the alignment of predicted lifetime curves with observed device behavior.
- The model's predictions are validated against numerical simulations and show improved accuracy.

## Abstract

The time-dependent dielectric breakdown (TDDB) degradation mechanism, governed by the synergistic interaction of multiphysics fields, plays a pivotal role in the performance degradation and eventual failure of semiconductor devices and advanced packaging back-end-of-line (BEOL) structures. This work specifically focuses on the dielectric breakdown mechanism driven by metal ion migration within inter-metal dielectric layers, a primary contributor to TDDB degradation. A SPICE-compatible modeling approach is developed to accurately capture the dynamics of this ion migration-induced degradation. The proposed model is rooted in the fundamental physics of metal ion migration and the evolution of conductive filaments (CFs) within the dielectric layer under operational stress conditions. By precisely characterizing the degradation behavior induced by TDDB, a SPICE-compatible degradation model is developed. This model facilitates accurate predictions of resistance changes across a range of operational conditions and lifetime, encompassing variations in stress voltages, temperatures, and structural parameters. The predictive capability and accuracy of the model are validated by comparing its calculated results with numerical ones, thereby confirming its applicability. Furthermore, building upon the established degradation model, the impact of line-edge roughness (LER) is incorporated through a process variation model based on the power spectral density (PSD) function. This PSD-derived model provides a quantitative characterization of LER-induced fluctuations in critical device dimensions, enabling a more realistic representation of process-related variability. By integrating this stochastic variability model into the degradation framework, the resulting lifetime prediction model effectively captures reliability variations arising from real-world fabrication non-uniformities. Validation against simulation data demonstrates that the inclusion of LER effects significantly improves the accuracy of predicted lifetime curves, yielding closer alignment with observed device behavior under accelerated stress conditions.