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YAP+: Pad-Layout-Aware Yield Modeling and Simulation for Hybrid Bonding

Zhichao Chen, Puneet Gupta

TL;DR

YAP+ tackles the challenge of predicting copper-copper hybrid-bonding yield by introducing a pad-layout-aware, physics-driven near-analytical framework that jointly models overlay errors, Cu recess variations, and particle-induced defects for W2W and D2W bonding. The approach combines explicit mechanics-based models with a dilation-based critical-area method to handle arbitrary pad layouts, supported by an open-source simulator that achieves over 1000x runtime speedups while maintaining high accuracy. Key contributions include the first HB-specific yield model, a dilation-based critical-area computation, and comprehensive case studies on pad layouts, bonding pitch, and redundancy strategies. The framework enables practical co-optimization of packaging processes and chiplet architectures, promising substantial gains in yield and system-level design flexibility in 2.5D/3D integration contexts.

Abstract

Three-dimensional (3D) integration continues to advance Moore's Law by facilitating dense interconnects and enabling multi-tier system architectures. Among the various integration approaches, Cu-Cu hybrid bonding has emerged as a leading solution for achieving high interconnect density in chiplet integration. In this work, we present YAP+, a yield modeling framework specifically tailored for wafer-to-wafer (W2W) and die-to-wafer (D2W) hybrid bonding processes. YAP+ incorporates a comprehensive set of yield-impacting failure mechanisms, including overlay misalignment, particle defects, Cu recess variations, surface roughness, and Cu pad density. Furthermore, YAP+ supports pad layout-aware yield analysis, considering critical, redundant, and dummy pads across arbitrary 2D physical layout patterns. To support practical evaluation, we developed an open-source yield simulator, demonstrating that our near-analytical model matches simulation accuracy while achieving over 1,000x speedup in runtime. This performance makes YAP+ a valuable tool for co-optimizing packaging technologies, assembly design rules, and system-level design strategies. Beyond W2W-D2W comparisons, we leverage YAP+ to investigate the impact of pad layout patterns, bonding pitch, and pad ratios across different pad types, and explore the benefits of strategically placing redundant pad replicas.

YAP+: Pad-Layout-Aware Yield Modeling and Simulation for Hybrid Bonding

TL;DR

YAP+ tackles the challenge of predicting copper-copper hybrid-bonding yield by introducing a pad-layout-aware, physics-driven near-analytical framework that jointly models overlay errors, Cu recess variations, and particle-induced defects for W2W and D2W bonding. The approach combines explicit mechanics-based models with a dilation-based critical-area method to handle arbitrary pad layouts, supported by an open-source simulator that achieves over 1000x runtime speedups while maintaining high accuracy. Key contributions include the first HB-specific yield model, a dilation-based critical-area computation, and comprehensive case studies on pad layouts, bonding pitch, and redundancy strategies. The framework enables practical co-optimization of packaging processes and chiplet architectures, promising substantial gains in yield and system-level design flexibility in 2.5D/3D integration contexts.

Abstract

Three-dimensional (3D) integration continues to advance Moore's Law by facilitating dense interconnects and enabling multi-tier system architectures. Among the various integration approaches, Cu-Cu hybrid bonding has emerged as a leading solution for achieving high interconnect density in chiplet integration. In this work, we present YAP+, a yield modeling framework specifically tailored for wafer-to-wafer (W2W) and die-to-wafer (D2W) hybrid bonding processes. YAP+ incorporates a comprehensive set of yield-impacting failure mechanisms, including overlay misalignment, particle defects, Cu recess variations, surface roughness, and Cu pad density. Furthermore, YAP+ supports pad layout-aware yield analysis, considering critical, redundant, and dummy pads across arbitrary 2D physical layout patterns. To support practical evaluation, we developed an open-source yield simulator, demonstrating that our near-analytical model matches simulation accuracy while achieving over 1,000x speedup in runtime. This performance makes YAP+ a valuable tool for co-optimizing packaging technologies, assembly design rules, and system-level design strategies. Beyond W2W-D2W comparisons, we leverage YAP+ to investigate the impact of pad layout patterns, bonding pitch, and pad ratios across different pad types, and explore the benefits of strategically placing redundant pad replicas.

Paper Structure

This paper contains 29 sections, 32 equations, 18 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Overview of Failure Mechanisms of Hybrid Bonding
  3. Overlay Errors
  4. Cu Recess Variations
  5. Particle Defects
  6. YAP+ Yield Model
  7. Overlay Model
  8. Cu Recess Model
  9. Calculation of $\zeta_-$
  10. Calculation of $\zeta_+$
  11. Defect Model
  12. Defect Shape Modeling
  13. Dilation-based Critical Area Calculation
  14. Overall Bonding Yield Model
  15. D2W Hybrid Bonding Yield Models
  16. ...and 14 more sections

Figures (18)

  • Figure 1: Failure mechanism of Overlay errors.
  • Figure 2: Failure mechanism of Cu recess variations.
  • Figure 3: Failure mechanism of particle defects.
  • Figure 4: Simulation workflow and the validation of modeling yield on various input parameter sets.
  • Figure 5: Correlation results of the overlay model and the Cu recess model with the simulation data for W2W HB.
  • ...and 13 more figures