Thermo-Mechanical Stress in Cu TSV Arrays

Heterogeneous Integration course, SSIs M.Sc. · Autumn 2024 · Academic project · Individual

3D COMSOL study of thermal-expansion mismatch stress in copper through-silicon-via arrays over a 25 to 400 C cycle, comparing an SiO2 liner against a compliant polymer liner.

COMSOL
TSV
3D integration
Stress analysis
Packaging

Overview

Through-silicon vias make 3D integration possible, but copper expands about six times faster than silicon when heated. This study quantifies what that mismatch does to stress around a via array during a thermal cycle, and whether a compliant liner helps.

Technical approach

3D COMSOL model of a four-via Cu TSV array (about 30 um vias) in a silicon domain with an SiO2 liner
Thermal cycle from 25 C up to 400 C and back, with copper plasticity included
Repeat with a compliant polymer-like liner (3 GPa modulus, higher CTE) for comparison
Compared von Mises stress, displacement, and plastic strain fields

Results

Peak von Mises stress of about 700 MPa concentrated near the copper via boundaries at 400 C, well above the copper yield strength used (250 MPa), with residual stress around 150 MPa after cool-down
The compliant liner dropped peak via stress to about 100 MPa with no plastic strain, at the cost of process complexity
Results connect directly to keep-out-zone rules for active devices near TSVs in 3D ICs

Media

COMSOL von Mises stress plot of a copper TSV array with SiO2 liner — Von Mises stress around the Cu TSV array with an SiO2 liner, compared across the thermal cycle.

COMSOL displacement slice plot of the TSV array at 400 C — Displacement slices through the via array at 400 C.

COMSOL equivalent strain plot at 400 C — Equivalent plastic strain at 400 C, concentrated at the via boundaries.

COMSOL slice plot of stress through the TSV array at 400 C — Stress slices through the via array at 400 C with the SiO2 liner.

COMSOL slice plot of residual stress after cooling — Residual stress slices after cool-down to 25 C.

COMSOL displacement plot of the TSV array — Displacement field around the vias (SiO2 liner).

COMSOL von Mises stress plot at 400 C — Von Mises stress at the 400 C peak of the thermal cycle.