Deterministic, Solver-Accurate Thermal and Warpage Analysis at Manufacturing Resolution for Advanced 2.5D HBM Packages

Thermal management has become the defining bottleneck in high-performance computing (HPC) and AI accelerator packaging.

Modern packages integrate high-power ASICs with multiple High Bandwidth Memory (HBM) stacks on a silicon interposer, creating tightly coupled thermal and mechanical interactions. Die-to-die thermal crosstalk elevates HBM junction temperatures, while coefficient of thermal expansion (CTE) mismatch between the epoxy moulding compound, silicon interposer, and organic substrate drives thermo-mechanical warpage that threatens solder joint integrity and long-term reliability.

Each HBM stack now comprises a base die with up to 16 vertically stacked memory dies—compared to four in prior generations—concentrating active silicon in a confined vertical column adjacent to the ASIC. As systems integrate four or more HBM stacks per device, aggregate thermal design power exceeds 1 kW.

At these scales, thermal behavior is governed by fine-grained spatial effects, including tier-level hotspot formation, vertical heat conduction through TSVs, and anisotropic resistance across BEOL layers and micro-bump arrays. Capturing these effects requires simulation at manufacturing resolution.

Conventional finite element analysis (FEA) cannot meet this requirement due to two fundamental limitations:

• Computational scale: Package geometries with hundreds of billions of degrees of freedom make high-fidelity FEA impractical for iterative design workflows.
• Model fidelity: Standard FEA workflows rely on homogenization, collapsing BEOL layers and micro-bump arrays into isotropic slabs. These approximations remove critical anisotropy and obscure the localized thermal effects that drive HBM reliability risks.

As a result, thermal analysis remains both too slow and too coarse to support modern design cycles.

This work evaluates Vinci, a system for deterministic, solver-accurate physics computation directly on manufacturing-resolution geometry, using a representative 2.5D package.

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Fig 1: Explicit representation of the multi-layer stackup including BEOL metal layers, micro-bump arrays, and TSVs at manufacturing resolution — no geometry simplification. Source: Vinci