Interposer Thermal Warpage Calculator
Advanced 2.5D Multi-Die Packaging: Predict thermal bending curvature ($\kappa$), peak out-of-plane warpage ($\delta$), and shadow moiré coplanarity per JEDEC J-STD-020.
Package Footprint & Dimensions
Material CTE & Reflow Temperature
Thermal Warpage & Coplanarity Results
Recommended Tools & Equipment
Tested hardware and components for high reliability
Package Warpage & Timoshenko Bimetallic Bending Theory
Heterogeneous multi-die systems (such as TSMC CoWoS or Intel EMIB) must maintain strict flatness to ensure reliable microbump and BGA ball attachment.
1. Timoshenko Elastic Bending Formulation
m = t_si / t_sub, n = E_si / E_sub, h = t_si + t_sub κ = 6 · (Δα · ΔT) · (1 + m)² / [ h · ( 3(1+m)² + (1 + m·n)·(m² + 1/(m·n)) ) ]
2. Peak Out-of-Plane Displacement
δ = ( κ · D_diagonal² ) / 8 [meters]
Frequently Asked Questions
What causes thermal warpage in 2.5D semiconductor interposer packages?
Thermal warpage is driven by mismatch in Coefficient of Thermal Expansion (CTE) between materials. Single-crystal silicon has a low CTE ($\approx 2.6\,\text{ppm}/\text{K}$), while the underlying organic laminate substrate has a much higher CTE ($14\sim 18\,\text{ppm}/\text{K}$). When cooling from solder reflow ($260^\circ\text{C}$) to room temperature ($25^\circ\text{C}$), the substrate shrinks more than the silicon, bending the package into a concave "smile" bow.
Why is out-of-plane warpage critical for motherboard surface mount assembly?
During BGA reflow on the system motherboard, if package corners bow upward by more than $100\sim 150\,\mu\text{m}$, corner solder balls fail to touch the PCB pads, causing "open" solder joints. Conversely, excessive center depression can squeeze adjacent balls together, causing bridging shorts.
How does Shadow Moiré optical interferometry measure warpage?
Shadow Moiré projects light through a high-precision reference optical grating onto the package surface inside a thermal chamber. Geometric interference fringes form between the grating and its shadow, allowing non-contact mapping of out-of-plane displacement ($\delta$) across the entire package during the complete $-40^\circ\text{C}$ to $+260^\circ\text{C}$ reflow profile.