Thermal expansion behavior is one of the most critical properties determining the long-term reliability of underfill adhesives in flip-chip, BGA, and wafer-level packaging. This article provides a comprehensive technical evaluation of underfill adhesive thermal expansion, including coefficient of thermal expansion (CTE) measurement below and above the glass transition temperature (Tg) by thermomechanical analysis (TMA) in accordance with ASTM E831 and ISO 11359-2. It covers sample preparation, testing items, test methods, data interpretation, and typical application scenarios to support material selection and packaging qualification.
Technical Overview
Underfill adhesives are epoxy-based polymer materials dispensed beneath flip-chip dies, ball grid arrays (BGA), and chip-scale packages (CSP) to mechanically couple the silicon die to the substrate. Their primary function is to redistribute thermomechanical stress away from solder interconnects, dramatically improving thermal cycling fatigue life. The effectiveness of this stress redistribution depends almost entirely on the coefficient of thermal expansion (CTE) of the cured underfill relative to the surrounding materials.
In a typical assembly, the silicon die exhibits a CTE of approximately 2.6 ppm/°C, eutectic or lead-free solder joints fall in the range of 20–23 ppm/°C, and organic laminate substrates expand at 14–17 ppm/°C. The cured underfill must fill this gap: a CTE below the glass transition temperature (CTE1) of roughly 25–45 ppm/°C is generally targeted. Above Tg, polymer chain mobility increases sharply and the expansion coefficient (CTE2) can rise to 80–150 ppm/°C or higher, which is why both Tg and the two CTE segments must be evaluated together. An underfill with an excessively high CTE above Tg can generate compressive stress on the die during reflow or high-temperature operation, causing die cracking or delamination.
This experimental evaluation therefore focuses on three interdependent outputs: CTE1, CTE2, and Tg, measured primarily by thermomechanical analysis (TMA) and cross-verified by differential scanning calorimetry (DSC) and dynamic mechanical analysis (DMA) where required.
Testing Samples
Capillary Flow Underfill Bulk Specimens
Liquid capillary underfills are cast into silicone or PTFE molds and cured according to the supplier-recommended schedule, followed by the specified post-cure. Cylindrical specimens of 5 mm diameter and 5–10 mm height, or rectangular prisms with two flat, parallel, and perpendicular end faces, are machined or ground to ensure uniform load contact. Any surface irregularity introduces measurement error, so end-face parallelism within a few micrometers is required.
No-Flow Underfill Specimens
No-flow and fluxing underfills are cured through a simulated reflow profile with a peak temperature of 200–250 °C rather than an oven bake. Bulk specimens must replicate this cure history so that the measured CTE and Tg reflect the actual degree of cure achieved in production. Residual unreacted monomer depresses Tg and inflates CTE2, making cure-verification by DSC a prerequisite before thermal expansion testing.
Molded Underfill Compounds
Molded underfill (MU) materials are transfer-molded or compression-molded into plaques or cylindrical pellets, then post-cured. Specimens are cut from the mid-thickness region of the plaque to avoid molded-in skin effects and flow-induced filler orientation, both of which can bias CTE results. Silica filler loading above 60–70 wt% is common in these materials, so specimen-to-specimen homogeneity must be confirmed.
Assembled Test Vehicles and Conditioned Samples
For verification purposes, actual flip-chip or BGA assemblies may be sectioned and analyzed to confirm that the in-situ underfill behaves like the bulk specimen. In addition, subsets of specimens are moisture preconditioned per industry-standard moisture sensitivity leveling practices (for example, 85 °C/85% RH for 168 hours or 30 °C/70% RH for 192 hours) to evaluate how absorbed moisture shifts Tg and expansion behavior.
Testing Items
The complete thermal expansion evaluation typically includes the following items:
- Coefficient of thermal expansion below Tg (CTE1, α1), reported in ppm/°C
- Coefficient of thermal expansion above Tg (CTE2, α2), reported in ppm/°C
- Glass transition temperature (Tg) determined from the TMA inflection point
- Tg cross-verification by DSC midpoint (ISO 11357-2 / ASTM E1356) and tan-delta peak by DMA where specified
- Total linear dimensional change (ΔL/L0) across the full test temperature range
- Thermal expansion hysteresis and CTE drift over repeated heating cycles
- Effect of moisture preconditioning on CTE1, CTE2, and Tg
- Degree of cure verification by residual exotherm, as a pre-test screening item
Testing Methods
Thermomechanical Analysis (TMA) Procedure
CTE and Tg are measured by TMA following ASTM E831 and ISO 11359-2 (with corresponding GB/T thermal analysis method equivalents). Specimens are conditioned at 23 ± 2 °C and 50 ± 5% relative humidity for at least 24 hours before testing. A low-expansion quartz expansion probe with a 3 mm tip applies a static force of typically 0.05 N or less to ensure contact without indentation of the polymer surface.
The furnace is purged with nitrogen at 20–50 mL/min. Specimens are cooled to the starting temperature, commonly −50 °C, held for thermal stabilization, then heated to 250 °C (or a ceiling at least 30 °C above the expected Tg but below the degradation onset) at a linear rate of 5 °C/min. A first conditioning scan is performed to erase mechanical and thermal history from curing and specimen preparation; reported values are taken from the subsequent scan. Instrument calibration is validated with a certified reference material such as sapphire for expansion accuracy and indium for temperature accuracy. A minimum of three to five replicate specimens per material lot are tested, and results are reported as mean value with standard deviation.
Data Reduction and Calculation
The linear CTE is calculated from the slope of the dimension-versus-temperature curve: α = (1/L0) × (ΔL/ΔT), where L0 is the initial specimen length at the reference temperature. CTE1 is the linear regression slope over the temperature region at least 20–30 °C below the Tg inflection, and CTE2 is the slope at least 20–30 °C above it. Tg from TMA is reported as the inflection point of the transition region, which is typically 5–15 °C higher than the DSC midpoint for the same material. Any non-linearity, shrinkage event, or post-cure exotherm observed during the scan is noted, as it may indicate incomplete cure or residual stress relief.
Acceptance Guidelines
While acceptance limits are product-specific, general industry guidelines for reliability-focused underfills are: CTE1 of 25–45 ppm/°C, CTE2 below approximately 100–120 ppm/°C, Tg of 90–150 °C depending on application temperature, and CTE drift below 10% across three consecutive heating cycles. Materials intended for automotive or high-temperature packaging are additionally screened for CTE stability after moisture preconditioning and after extended thermal aging at 150 °C or above. Independent verification of these properties can be performed by accredited third-party laboratories using the same ASTM and ISO methods.
Applications
Thermal expansion test data for underfill adhesives directly support the following applications:
- Material selection and comparative benchmarking for flip-chip underfill in mobile processors, application processors, and advanced-node logic devices
- Corner and edge bonding reinforcement of BGA and CSP packages where CTE-driven board-level bending controls solder joint life
- Stacked-die, package-on-package, and 3D packaging architectures with tight CTE mismatch budgets between thin dies, through-silicon vias, and molding compounds
- Automotive power electronics and high-temperature underfills requiring stable CTE and high Tg across the −40 °C to 150 °C operating envelope
- Incoming material inspection, supplier qualification, and lot acceptance testing at packaging factories and accredited third-party laboratories
- Input data for finite element simulation of package warpage, die stress, and solder joint creep-fatigue life prediction
FAQ
Why must the underfill CTE be matched between silicon and the substrate?
If the underfill CTE is too close to silicon, it cannot effectively couple the die to the board and stress remains concentrated in the solder joints. If it is too close to the laminate, thermal cycling induces excessive tensile stress at the die passivation interface, causing delamination or die cracking. A CTE1 of 25–45 ppm/°C provides an engineered intermediate value that distributes strain through the encapsulant rather than the interconnects.
What is the difference between CTE1 and CTE2?
CTE1 is the expansion coefficient in the glassy state below Tg, where the polymer network is rigid and expansion is low. CTE2 is the expansion coefficient in the rubbery state above Tg, where segmental mobility increases and expansion rises sharply. Both values, and the Tg that separates them, are needed to predict behavior across the full operating and reflow temperature range.
Why is the first TMA heating scan discarded?
The first scan relieves residual stress and completes minor post-cure reactions introduced by specimen machining and cure history, which produces a non-linear dimension change that does not represent the intrinsic material behavior. Reporting from the second scan yields reproducible CTE1, CTE2, and Tg values suitable for specification and comparison.
How does moisture absorption affect the results?
Absorbed moisture plasticizes the epoxy network, lowering Tg by 10–30 °C and increasing CTE2, particularly for highly filled capillary underfills. Testing both as-molded and moisture-conditioned specimens reveals whether a material will retain adequate dimensional stability through humid preconditioning and solder reflow during assembly.
How many specimens are required for a valid evaluation?
A minimum of three replicate specimens is standard, and five is preferred for qualification programs. Specimens should come from different cure batches or mold locations when lot-to-lot consistency is being evaluated, and results should be reported as mean plus or minus one standard deviation against the specification limits.