The underfill adhesive linear expansion test determines the coefficient of thermal expansion (CTE) of underfill materials, a critical parameter governing solder joint reliability in flip-chip, BGA, and wafer-level packaging. Using thermomechanical analysis (TMA) in accordance with ASTM E831 and ISO 11359-2, accredited third-party laboratories measure both the sub-Tg and supra-Tg expansion behavior of cured adhesives. This article explains the test principle, sample requirements, methodology, typical acceptance values, and application scenarios for underfill CTE characterization.
Technical Overview
Underfill adhesives are thermosetting polymer materials, typically epoxy-based and heavily filled with silica, that are dispensed beneath flip-chip devices, ball grid arrays (BGAs), and chip-scale packages (CSPs) to mechanically reinforce solder interconnects. During thermal cycling, the package experiences repeated expansion and contraction driven by the mismatch between the coefficient of thermal expansion (CTE) of silicon (approximately 2.8 ppm/°C), copper and solder (20–25 ppm/°C), and the organic substrate or printed circuit board (14–17 ppm/°C). A properly formulated underfill acts as a compliant, low-expansion coupling layer that redistributes thermomechanical strain away from the solder joints and can extend fatigue life by an order of magnitude.
The linear expansion experiment quantifies how the cured adhesive expands per degree of temperature change, expressed in microstrain per degree Celsius (µm/m·°C, commonly written as ppm/°C). Because epoxy networks pass through a glass transition, two distinct expansion regions are characterized: α1 (CTE below the glass transition temperature, Tg) and α2 (CTE above Tg). Typical underfill specifications call for α1 of 25–45 ppm/°C, α2 below 100–150 ppm/°C, and Tg of 100–150 °C or higher. Excessive CTE, particularly above Tg, produces high shear strain on solder bumps and dramatically reduces assembly reliability, making the linear expansion test a mandatory item in material qualification and incoming inspection.
Testing Samples
Capillary Underfill Adhesives
Cured bulk specimens of conventional capillary-flow underfills, prepared by casting the resin into molds or by curing a free-standing film. The material must be fully cured according to the supplier's recommended schedule (for example, 150 °C for 60 minutes) before testing, since incomplete cure depresses Tg and distorts the measured expansion curve.
No-Flow and Wafer-Applied Underfills
No-flow underfill formulations, wafer-level underfill films, and pre-applied underfill coatings, all of which cure during the solder reflow process. Specimens are conditioned and cured with a reflow-simulating thermal profile to replicate the actual material state inside the finished package.
Molded Underfill and Corner-Bond Materials
Silica-filled epoxy molding compounds used as molded underfill (MU) and corner-bond or edge-bond adhesives for BGA corner reinforcement. These highly filled systems generally exhibit the lowest α1 values and are tested to verify lot-to-lot consistency of filler loading.
Specimen Geometry Requirements
- Flat, parallel top and bottom surfaces, free of bubbles, voids, and unmixed resin streaks.
- Thickness of 2–4 mm (up to 10 mm acceptable) for TMA expansion mode, with a minimum lateral dimension exceeding the probe tip diameter.
- Dried and conditioned at 23 ± 2 °C and 50 ± 5% relative humidity for at least 24 hours before measurement.
- A minimum of three replicate specimens per material lot is recommended to assess homogeneity.
Testing Items
- Coefficient of linear thermal expansion below Tg (α1), reported in ppm/°C.
- Coefficient of linear thermal expansion above Tg (α2), reported in ppm/°C.
- Glass transition temperature (Tg) determined from the inflection point of the dimension-versus-temperature curve.
- Total dimensional change and instantaneous expansion rate over the specified temperature window.
- Optional comparison testing of α1 before and after moisture conditioning, thermal aging, or reflow exposure to evaluate stability.
Testing Methods
Thermomechanical Analysis (TMA) — Primary Method
The dominant technique follows ASTM E831 and ISO 11359-2. A quartz or Invar expansion probe applies a small static force (typically 0.05 N or less) to the cured specimen while a programmed furnace heats it at a controlled rate of 3–5 °C/min under nitrogen purge. The instrument records specimen thickness as a function of temperature, commonly from room temperature to 200–250 °C, which covers the Tg region of most underfills. The CTE is calculated by linear regression of the dimensional change over defined temperature intervals (for example, 40–80 °C for α1 and 160–200 °C for α2), and Tg is taken as the midpoint of the transition between the two slopes. Calibration is verified before each session with certified reference materials such as fused silica and high-purity aluminum.
Push-Rod Dilatometry
For larger specimens or lower-temperature studies, dilatometry per ASTM E228 provides equivalent linear expansion data. A cylindrical sample 25–50 mm long is heated in a furnace while a sensing system tracks the displacement of a refractory push rod. The method offers excellent precision for α1 but requires careful correction for the expansion of the sample holder and rod.
Industry-Specific Screening Procedures
Electronics manufacturing standards bodies such as IPC publish test methods in the IPC-TM-650 series for z-axis expansion of packaging materials, and JIS-based procedures (for example, JIS K 7197 for plastics expansion by TMA) are frequently referenced in Asian supply chains. For space and high-reliability applications, the same CTE data feed ECSS-style derating and stress models. All measurements should be performed by accredited third-party laboratories with ISO/IEC 17025-compliant quality systems.
Data Interpretation Criteria
- The correlation coefficient of each regression window should exceed 0.999 to confirm linearity.
- α2 should remain below approximately twice α1; a larger ratio signals an under-cured or degraded network.
- Tg measured by TMA should agree within 10–15 °C with DSC and DMA results; large discrepancies indicate residual stress or incomplete cure.
- Reported results must state the temperature windows, heating rate, specimen cure history, and the test standard applied.
Applications
- Material qualification of new underfill formulations for flip-chip and micro-bump packaging, where α1 must closely match the solder and substrate CTE to minimize shear strain.
- Incoming lot inspection at EMS and OSAT facilities to detect filler settling, resin aging, or cure-schedule deviations before production use.
- Finite-element reliability modeling of package warpage and solder joint fatigue life during temperature cycling (for example, −40 °C to 125 °C, per JESD22-A104).
- Failure analysis of interconnect cracks and delamination, where a verified CTE mismatch is compared against the failure location and crack morphology.
- Automotive electronics under IATF-aligned quality programs and consumer electronics for AI processor, memory stacking, and wafer-level fan-out packages.
- Adhesion and compatibility studies, since CTE data are prerequisites for calculating thermal stress at the underfill–passivation and underfill–solder interfaces.
FAQ
What is a typical CTE target for underfill adhesive?
Most commercial capillary underfills specify α1 between 25 and 45 ppm/°C, chosen to fall between the CTE of eutopic or lead-free solder (about 21–23 ppm/°C) and the FR-4 substrate (about 14–17 ppm/°C). α2 is typically required to stay below 100–150 ppm/°C because the material softens above Tg.
Why does the test report two CTE values?
Epoxy networks change from a glassy, rigid state to a rubbery state at the glass transition. Below Tg the polymer chain mobility is low and expansion is restrained by the silica filler; above Tg the free volume increases sharply and expansion roughly doubles or triples. Reporting both α1 and α2, along with Tg, fully characterizes the expansion behavior across the operating temperature range.
Which heating rate and atmosphere should be used?
ASTM E831 recommends heating rates of 3–5 °C/min under an inert nitrogen purge to avoid thermal lag and oxidative degradation. Higher rates shift the apparent Tg upward and bias both CTE values, so the heating rate must always be disclosed in the report.
Can the test be performed on an actual assembled package instead of a bulk specimen?
Yes. TMA can measure the effective z-axis expansion of a diced cross-section or whole package, and embedded techniques can evaluate the underfill within a real device. However, composite values reflect the combined expansion of silicon, solder, copper, and adhesive, so bulk-specimen testing remains necessary for pure material characterization.
How does CTE relate to solder joint lifetime?
Solder joint shear strain is approximately proportional to the CTE mismatch multiplied by the die-substrate distance and the temperature swing. Reducing the effective mismatch through a well-matched underfill lowers the plastic strain per cycle, which by Coffin–Manson fatigue relationships translates directly into longer temperature-cycling life and lower field failure rates.