# Semiconductor FE Model Verification — Final Technical Summary

2026-10-11. This summary consolidates actual Phase 1/2 evidence; no new FE solutions were performed. The original **L1/C3, four-interface Bonded MPC** result remains the official baseline. L2 is a verification case, not a replacement.

## Model and assumptions

The original FE stack is Si / SAC305 / continuous Top Cu / AlN / Bottom Cu. Chip and solder footprints are 10×10 mm; substrate layers are 20×20 mm. Thicknesses from bottom to top are 0.30/0.60/0.30/0.15/0.50 mm. The FE thickness axis is +Y. D2 display-model wire bonds, terminals and patterned copper islands are absent from this FE geometry. Materials use constant isotropic linear-elastic properties. E01, E04 — source index

A uniform Si volumetric heat source totals 5 W. The Bottom Cu underside has equivalent convection, h=1000 W/(m²·K), ambient 25°C. A steady-state temperature field drives a small-deformation static structural solution with stress-free reference 25°C. Bonded MPC provides ideal structural bonding; thermal MPC enforces ideal temperature continuity, not validated finite interface resistance. These assumptions do not reproduce a verified cooling system or installed product. E01–E04

## Constraint-reference independence

Case A uses global displacements at (0,0,0): XYZ=0; (20,0,0): YZ=0; (0,0,−20): Y=0, in mm. Case B mirrors these anchors to (20,0,−20), (0,0,−20), (20,0,0). Both six-scalar rigid-motion constraint matrices have rank six. Mesh, materials, MPC interfaces and imported temperatures were unchanged. These constraints define a displacement reference, not a clamped face or actual mounting. E02

Rigid translation and infinitesimal rotation do not change symmetric displacement gradients. With unchanged thermal strain, elastic strain and stress should therefore be unchanged. Actual results support this: both solder peaks are **26.497303519 MPa**; nodal means differ by **−4.325×10⁻⁹ MPa**. The largest all-body stress-component difference is **2.5 Pa**; elastic-strain difference **6.18×10⁻¹¹**. Removing fitted rigid motion from all 23,108 nodes leaves a maximum displacement residual **1.20×10⁻⁸ μm**. Anchor reactions are approximately 10⁻⁹ N. Raw Umax happens to agree for the mirrored symmetric cases; this is not a general independence criterion. E02, E06

## Mesh sensitivity: final all-MPC formulation

L1 has 23,108 nodes/3,504 solid elements; L2 has 59,265/10,000. L2 used a fresh thermal solution on its own mesh and verified node/coordinate mapping to structural analysis. E03–E05

| Quantity | L1 extracted | L2 | Change |
|---|---:|---:|---:|
| Tmax / °C | 38.786160 | 38.776649 | −0.009511°C |
| Umax / μm, Case A | 3.191468 | 3.177515 | -0.437% |
| Solder von Mises peak / MPa | 26.497304 | 26.676049 | +0.675% |
| Solder unique-node mean / MPa | 16.989327 | 16.847271 | -0.836% |

The official Mechanical-export Tmax remains **38.7861595°C**; its approximately 5.6×10⁻⁷°C difference from the L1 RTH extraction is storage precision, not another case. Both meshes balance approximately 5 W input and convection output. The nodal mean includes reconstructed Hex20 midside-node stress components and is not a volume average. E01, E03, E06, E07

## Corner stress and credibility limits

All four upper solder-interface corners exhibit nearly equal peaks. A single Max marker does not imply a unique asymmetric hotspot. Small displacement does not imply low stress: stress depends on displacement gradients and thermal mismatch. Material discontinuities and sharp bonded corners produce strong local gradients. E01–E04, E06

Despite only +0.675% peak sensitivity, a fixed near-corner reconstructed sample changes −17.67%; a fixed 1×1×0.15 mm corner-region volume estimate changes −2.14%. These are postprocessing estimates, not additional FE solutions or Mechanical nodal averages. L1/L2 interface interpolation discretization also differs. Two mesh levels do not establish asymptotic convergence, an error bound, or prove/exclude a mathematical singularity. E03, E04, E06

The work provides targeted **solution verification**, not comprehensive solver-code verification or experimental **validation**. Validation would require product-specific mounting, cooling, material characterization and measurements. No physical tests were used. [NASA V&V distinction](https://www.grc.nasa.gov/www/wind/valid/tutorial/overview.html); [verification methodology](https://www.grc.nasa.gov/www/wind/valid/tutorial/verassess.html).

SAC305 plasticity, creep, thermal cycling, manufacturing residual stress and actual mounting are not modeled. No solder fatigue life or product qualification claim is supported. D6 baseline numbers remain valid for the stated model; clarify “region average” as a unique-node mean, identify the Case A displacement reference and retain corner/mesh-sensitivity caveats. No videos were edited. E01–E07


## Public attachment scope

Evidence identifiers E01–E07 refer to retained project records. Raw FE projects, node-level data, solver logs and internal scripts are not public attachments.