Coefficient of Thermal Expansion (CTE) Testing of Underfill Adhesives: Experimental Methods, Standar

The coefficient of thermal expansion (CTE) is one of the most critical thermomechanical parameters for underfill adhesives used in flip-chip, BGA, and wafer-level packaging, because it directly governs solder joint stress and thermal cycling reliability. This article provides a comprehensive technical overview of underfill CTE testing experiments, covering specimen preparation, test items, measurement methods based on ASTM E831 and ISO 11359-2 thermomechanical analysis, typical acceptance values, and practical application guidance for electronics packaging engineers.

Technical Overview

Underfill adhesives are epoxy-based thermosetting materials, typically loaded with 50–80 wt% of fused silica filler, that are dispensed or pre-applied beneath silicon die and ball grid array (BGA) components to reinforce solder interconnections. By coupling the die to the substrate, the cured underfill redistributes thermomechanical strain away from the solder joints, dramatically improving resistance to thermal cycling, mechanical shock, and board-level flexure.

The coefficient of thermal expansion (CTE) quantifies the fractional dimensional change of the material per unit temperature change and is defined as alpha = (1/L0) × (ΔL / ΔT), where L0 is the initial specimen length and ΔL is the dimensional change over the temperature interval ΔT. The result is expressed in parts per million per degree Celsius (ppm/°C).

For cured underfill adhesives, two distinct CTE regions are reported: alpha 1 (α1) below the glass transition temperature (Tg), which is the value relevant to normal device operation, and alpha 2 (α2) above Tg, where the softened polymer network expands significantly faster. Typical commercial underfills exhibit α1 of approximately 20–45 ppm/°C and α2 of approximately 80–150 ppm/°C.

CTE control is essential because of the inherent mismatch within the package: silicon expands at roughly 2.6 ppm/°C, eutectic and SAC solder alloys at approximately 21–23 ppm/°C, and organic substrates at roughly 14–17 ppm/°C. An underfill with a well-matched CTE minimizes shear strain on solder joints during reflow and power cycling. Poorly matched or incompletely characterized CTE values are a frequent root cause of premature solder fatigue, die cracking, and delamination, which is why CTE testing is a mandatory item in underfill qualification and incoming material inspection.

Testing Samples

Cured Bulk Specimens

CTE is measured on fully cured, void-free bulk coupons representative of the underfill in its cured state. The material is cast into flat molds and cured according to the supplier-recommended schedule, for example 150 °C for 1 hour or 165 °C for 30 minutes, followed by any specified post-cure. Deviation from the specified cure profile changes the crosslink density and can shift both Tg and CTE, so the actual time–temperature history must be documented in the test report.

Specimen Preparation

Two-component systems are weighed and mixed at the specified ratio, then vacuum-degassed to eliminate entrapped air bubbles. Single-component snap-cure or no-flow formulations are used directly. After casting, the cured plaque is cut or ground to produce specimens with flat, parallel measuring faces. Conditioning prior to testing is performed at 23 ± 2 °C and 50 ± 5% relative humidity in accordance with ISO 291 or ASTM D618.

Specimen Geometry and Quantity

• Specimen measuring surface: typically 3–6 mm square or circular
• Specimen thickness: typically 1–3 mm, uniform within 0.02 mm
• Measuring faces parallel and free of voids, cracks, and filler segregation
• Minimum of three specimens per condition to assess repeatability
• Specimens inspected under a stereo microscope to confirm freedom from defects

Testing Items

A complete underfill CTE test experiment typically includes the following measured and reported items:

• Linear CTE below Tg (α1), ppm/°C
• Linear CTE above Tg (α2), ppm/°C
• Glass transition temperature (Tg) determined from the CTE inflection, per ASTM E1545
• Full dimensional change versus temperature curve from ambient to the maximum test temperature
• Cross-check of Tg by differential scanning calorimetry (ASTM E1356 or ISO 11357-2) or DMA where required
• Verification of complete cure through residual exotherm analysis, where applicable
• Optional directional comparison (through-thickness versus in-plane) to evaluate filler-induced anisotropy

The test report should state the cure conditions, specimen dimensions, temperature range and heating rate, applied probe force, the specific temperature intervals used for slope calculation, calibration reference materials, and the mean and scatter of replicate specimens.

Testing Methods

Thermomechanical Analysis (TMA) — ASTM E831 / ISO 11359-2

Thermomechanical analysis is the industry-preferred method for underfill CTE because it requires only small specimens and simultaneously yields α1, α2, and Tg in a single experiment. A flat-tipped quartz expansion probe applies a low static force, typically 0.01–0.1 N, on the specimen while a linear variable displacement transducer monitors thickness change with sub-micrometer resolution. The specimen is heated at a controlled rate, commonly 5 °C/min, under nitrogen purge from a starting temperature below room temperature (for example −50 °C) up to 200–250 °C, depending on the expected Tg.

CTE is calculated from the slope of the dimension-versus-temperature curve over a defined interval below Tg (for example 40–100 °C) and over a defined interval above Tg (for example Tg + 20 °C to Tg + 60 °C). Where residual curing stress or moisture is a concern, a first heating scan is used for conditioning and the second scan is used for measurement. The instrument is calibrated for temperature and length change using certified reference materials such as aluminum (approximately 23 ppm/°C) and fused silica (approximately 0.5 ppm/°C).

Quartz Dilatometry — ASTM D696 / GB/T 1036

The quartz dilatometer method measures CTE over a moderate temperature interval around room temperature, typically −30 °C to +30 °C, using specimens 50–125 mm in length. It offers excellent precision but is generally impractical for small cured underfill coupons, so it is mainly used as an independent cross-check or for molded bulk plaques when higher accuracy at room temperature is required.

Supplementary Tg Verification by DSC and DMA

Because α2 depends strongly on Tg, the Tg value is often confirmed by complementary techniques. DSC per ASTM E1356, ISO 11357-2, or GB/T 19466.2 detects the step change in heat capacity and also reveals any residual cure exotherm, confirming completeness of polymerization. Dynamic mechanical analysis per ASTM E1640 or ISO 6721-11 provides Tg from the viscoelastic modulus transition and is preferred when the underfill is highly filled and the TMA inflection is weak.

Test Procedure Summary

• Verify full cure and inspect specimens for defects
• Condition specimens at 23 ± 2 °C and 50 ± 5% RH
• Measure specimen dimensions and record orientation
• Calibrate the TMA for temperature, force, and displacement
• Load specimen, apply low-force expansion probe, purge with nitrogen
• Heat at 5 °C/min across the specified temperature range
• Compute α1, α2, and Tg from the expansion curve
• Repeat on replicate specimens and report mean values and standard deviation

Applications

CTE test data for underfill adhesives are used throughout the electronics packaging value chain, including the following typical scenarios:

• Qualification of capillary underfills for flip-chip and controlled-collapse chip connection (C4) assemblies
• Material selection and corner/edge bonding adhesives for chip-scale packages (CSP) and wafer-level chip-scale packages (WLCSP)
• No-flow and molded underfill evaluation for 2.5D/3D interposer and stacked-die architectures with fine-pitch microbumps
• Automotive and industrial electronics reliability programs, where extended temperature cycling per IEC 60068-2-14 imposes severe CTE mismatch stress
• Incoming material verification against supplier datasheet specifications
• Failure analysis of solder joint fatigue, delamination, and die cracking to confirm whether CTE drift contributed to the mechanism
• Input material properties for finite element thermomechanical simulation of package deformation and joint stress
• Research and development of new formulations, particularly optimization of silica filler loading to lower α1 while retaining flowability

Accredited third-party laboratories routinely perform these experiments to provide independent data for customer qualification, supplier change notification, and internal engineering correlation studies.

FAQ

What CTE values are considered acceptable for underfill adhesives?

Most reliability specifications call for α1 in the range of 20–45 ppm/°C with a target below approximately 35 ppm/°C, and α2 typically below 100–150 ppm/°C. The exact acceptance limits depend on die size, solder alloy, substrate material, and the end-use temperature range, and should be agreed between packaging engineer and material supplier.

What is the difference between α1 and α2?

α1 is the CTE in the glassy region below Tg, where the polymer network is rigid and expansion is low. α2 is the CTE in the rubbery region above Tg, where segmental mobility increases and expansion rises sharply. Device operation should ideally remain well below the underfill Tg so that the effective CTE stays at the α1 value.

Which standard is most widely used for underfill CTE testing?

Thermomechanical analysis per ASTM E831 or ISO 11359-2 is the dominant method, because a single small specimen yields α1, α2, and Tg. ASTM D696 and GB/T 1036 dilatometry are used less frequently for underfill due to specimen size requirements.

How does the cure schedule affect the measured CTE?

Under-cured material has a lower crosslink density, which lowers Tg and increases α2, and may also shift α1. Verifying complete cure through the recommended time–temperature profile, and confirming the absence of residual exotherm by DSC, is therefore essential before CTE results are accepted.

Can CTE be measured on an actual assembled package instead of a bulk coupon?

Bulk cured coupons are preferred because the measurement reflects the intrinsic material property. Measurements on assembled packages convolute the response of die, solder, substrate, and copper, so they are used mainly for warpage correlation rather than for material specification.

What is the typical temperature range and heating rate of the experiment?

A typical scan runs from −50 °C (or ambient) to 200–250 °C at 5 °C/min under nitrogen, which comfortably spans both the glassy and rubbery regions for commercial underfills with Tg between 90 and 170 °C.

How many specimens are required for a valid test?

At least three replicate specimens should be tested per cure condition. Reported results normally include the mean and standard deviation, and outliers traced to voids or cure non-uniformity are re-tested with corrected specimens.

Why is CTE so strongly linked to solder joint reliability?

During thermal cycling, the CTE mismatch between silicon, underfill, solder, and substrate generates cyclic shear strain in the joints. An underfill with appropriate α1 mechanically couples the die and substrate, reducing this strain by a large factor and extending fatigue life severalfold compared with non-underfilled assemblies.