Beyond Black’s equation: Full-chip EM/SM assessment in 3D IC stack

• EM & SM compact modeling requires knowledge of degradation kinetics.
• Across-die distribution of residual stress is required for accurate SM & EM assessments.
• Methodology for simulating across-die distribution of residual stress is proposed.
• Analytical formulation for the void nucleation time is derived.

Simulation flow for the die-scale assessment of interconnect stress-migration (SM) and electromigration (EM) with an accounted variation of residual stress was developed. Two complimentary methodologies based on finite-element sub-modeling and compact modeling were proposed. A novel EM and SM model which takes into account a vacancy exchange between grain boundaries and grain interior has demonstrated a capability of predicting times for void nucleation at different test conditions while avoiding unreliable assumptions used in the Black’s equation-based assessment.

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