Thermal Expansion Testing of Underfill Adhesives: CTE Determination Methods, Standards, and Best Pra

Thermal expansion testing of underfill adhesives determines the coefficient of thermal expansion (CTE) below and above the glass transition temperature, a critical parameter governing solder joint reliability in flip-chip, BGA, and wafer-level packages. This article explains the measurement principles, specimen preparation, test conditions, and applicable international standards such as ISO 11359-2 and ASTM E831 used by accredited third-party laboratories for underfill CTE characterization.

Technical Overview

Underfill adhesives are thermosetting polymer materials, typically epoxy-based and often loaded with silica filler, that are dispensed into the gap between a silicon die and its organic or ceramic substrate. Once cured, the underfill forms a rigid composite that mechanically couples the die to the substrate, redistributes thermomechanical strain away from the solder interconnects, and dramatically extends fatigue life in temperature-cycling environments. Among all material properties that determine underfill performance, the coefficient of thermal expansion (CTE) is one of the most decisive.

The coefficient of thermal expansion quantifies the fractional change in length of a material per unit change in temperature. It is typically expressed in ppm/°C (micrometers per meter per degree Celsius). In the electronics assembly being protected, the silicon die expands at approximately 3 ppm/°C, the organic laminate substrate at roughly 14 to 18 ppm/°C, and Sn-Ag-Cu solder joints at around 21 to 23 ppm/°C. The underfill must possess a CTE that sits close to the solder value so that, together with sufficient modulus, it constrains the differential displacement of the joint during thermal excursions.

Because underfills are amorphous or semi-amorphous crosslinked polymers, their expansion behavior is not linear across the entire service range. Below the glass transition temperature (Tg), the cured network is glassy and expansion is modest, typically 25 to 45 ppm/°C. Above Tg, segmental mobility increases sharply and the expansion rate can jump to between 100 and 200 ppm/°C. Accurate measurement of both the sub-Tg CTE (commonly designated alpha-1) and the above-Tg CTE (alpha-2), together with the Tg itself, is therefore essential for material qualification, process qualification, and failure analysis.

• Alpha-1 (CTE below Tg): the governing value for normal device operation and for most reliability specifications.
• Alpha-2 (CTE above Tg): indicates dimensional stability risk during reflow, burn-in, or high-temperature processing.
• Tg by TMA: the inflection point of the expansion curve, which marks the transition between the two expansion regimes.

Testing Samples

Cast Bulk Specimens

The preferred specimen for thermal expansion measurement is a cured bulk plaque prepared from the liquid underfill. The material is degassed, cast into a mold with flat, parallel surfaces, and cured following the manufacturer's recommended schedule, for example a snap cure at 150 to 165 °C for 30 to 90 minutes or a conventional cure at 100 to 125 °C for one to several hours. Specimens are then cut or machined to the required geometry with the top and bottom faces ground parallel, because surface parallelism directly affects the accuracy of the expansion measurement.

Specimens Extracted from Assemblies

For failure analysis or verification of cure in production hardware, small cylindrical or rectangular specimens can be extracted from the cured fillet or from the underfill layer within a populated assembly using precision cutting tools. These specimens are more heterogeneous and may contain filler settling gradients or substrate contamination, so results should be interpreted as representative of the as-built condition rather than of the intrinsic material property.

Specimen Geometry and Conditioning

For thermomechanical analysis, specimens are typically 3 to 5 mm in thickness with a cross-section of 3 to 10 mm, and the thickness is measured to within one micrometer at multiple points. For dilatometry, longer specimens of 10 to 50 mm may be used to improve resolution. Prior to testing, specimens are conditioned in accordance with the material specification, commonly 23 ± 2 °C and 50 ± 5 % relative humidity for at least 24 hours, or stored in a desiccator when moisture-sensitive epoxy systems are being evaluated.

Testing Items

A complete thermal expansion characterization of an underfill adhesive typically includes the following reported quantities, all determined from a single controlled heating run:

• Coefficient of thermal expansion below Tg (alpha-1), in ppm/°C, evaluated over a specified temperature interval below the transition region.
• Coefficient of thermal expansion above Tg (alpha-2), in ppm/°C, evaluated over a specified interval above the transition region but below the onset of degradation.
• Glass transition temperature by TMA, defined as the inflection point of the expansion curve where the slope changes most rapidly.
• Total linear expansion percentage over the full test range, useful for gap-height and fillet-stress modeling.
• Secant (mean) CTE between two reference temperatures, frequently requested for finite-element simulation inputs.

Typical acceptance criteria in electronics industry specifications call for alpha-1 of 45 ppm/°C or less, with alpha-2 reported for information, and Tg of at least 110 to 130 °C depending on the application and the maximum operating temperature of the device.

Testing Methods

Thermomechanical Analysis (TMA)

The primary method for measuring underfill thermal expansion is thermomechanical analysis. A flat-tipped silica or quartz expansion probe rests on the specimen under a very small static force, typically 0.01 to 0.05 N, while the furnace subjects the specimen to a linear temperature program. As the specimen expands, the probe is displaced upward and the displacement is measured with a high-resolution linear variable differential transformer. Because the applied force is negligible and the probe material has a well-characterized, near-zero expansion of its own, the recorded displacement maps directly onto the specimen length change.

Reference Standards

Accredited third-party laboratories perform underfill CTE testing in accordance with internationally recognized standards, including:

• ISO 11359-2, which specifies the determination of the coefficient of linear thermal expansion and the glass transition temperature of plastics by TMA, with a standard heating rate of 5 K/min under nitrogen.
• ASTM E831, the standard test method for linear thermal expansion of solid materials by thermomechanical analysis, covering the typical temperature range of -120 to 600 °C.
• ASTM D696, the vitreous silica dilatometer method for plastics between -30 and 30 °C, occasionally used for near-ambient expansion verification.
• JIS K 7197, the Japanese industrial standard for linear thermal expansion of plastics by thermomechanical analysis.
• Chinese national standards (GB/T) that adopt or are technically aligned with ISO 11359-2 for plastics TMA expansion measurement.

Test Procedure

A representative test sequence conducted in accordance with these standards proceeds as follows:

• The instrument is calibrated for temperature using the melting points of pure metals such as indium and zinc, and for length change using certified reference materials of known expansion such as fused silica, sapphire, or aluminum.
• The specimen is measured for initial length at ambient temperature with a micrometer or calibrated thickness gauge and centered on the platform beneath the expansion probe.
• The furnace is purged with nitrogen at 20 to 50 mL/min to prevent oxidative degradation during heating.
• The specimen is equilibrated at the starting temperature, commonly 20 to 25 °C or -50 °C for sub-ambient characterization, and then heated at a constant rate of 5 °C/min to a final temperature between 200 and 250 °C.
• Where thermal history from curing must be erased, a preliminary heating run is performed and the CTE values are reported from the second heating run.
• Dimensional change is recorded continuously, and the expansion curve is differentiated to obtain CTE as a function of temperature.

Data Evaluation

The mean CTE over a temperature interval is calculated as the change in length divided by the initial length multiplied by the temperature interval, expressed in ppm/°C. Alpha-1 is determined from the regression slope of the linear region between ambient temperature and approximately 20 °C below the transition, and alpha-2 from the linear region above the transition. The Tg by TMA is taken as the midpoint or inflection of the sigmoidal change in slope between the two regions. Differential CTE curves should be reviewed carefully near Tg, where the probe force may begin to penetrate a softening specimen and produce an apparent expansion artifact.

Method Considerations and Precision

Key sources of variability include specimen surface parallelism, probe force selection, heating rate, moisture content of the epoxy, and the degree of cure achieved before testing. Repeatability of alpha-1 within the same laboratory is typically a few percent relative, while between-laboratory reproducibility is improved by strict adherence to identical curing schedules, conditioning protocols, and heating rates. Filler settling during cure can produce anisotropic expansion, so laboratories may measure specimens along more than one axis when anisotropy is suspected.

Applications

Thermal expansion data for underfill adhesives underpin design, qualification, and troubleshooting across essentially every advanced packaging platform:

• Flip-chip on laminate: selecting an underfill whose alpha-1 approximates the solder CTE to minimize joint shear strain during power cycling and temperature cycling qualification.
• Ball grid array and chip-scale package corner and edge bonding: verifying that adhesive expansion will not detach the bond or crack the die during reflow excursions above Tg.
• Wafer-level and panel-level packaging: providing CTE inputs for warpage simulation of molded and capillary underfill films before commit to production tooling.
• Three-dimensional stacked and through-silicon via assemblies: evaluating thin-film underfills where alpha-2 governs stability during stacking reflow steps.
• Automotive and high-reliability electronics: demonstrating compliance with customer-specific CTE windows over extended temperature ranges down to -40 °C and up to 150 °C or beyond.
• Failure analysis: comparing the measured CTE of field-returned underfill against datasheet values to detect under-cure, moisture uptake, or material substitution.
• Incoming material inspection and supplier change qualification: confirming lot-to-lot consistency of expansion behavior in accredited third-party laboratories.

FAQ

What is a typical CTE value for a cured underfill adhesive?

Most commercial capillary and no-flow underfills exhibit alpha-1 between 25 and 45 ppm/°C and alpha-2 between 100 and 200 ppm/°C. Filled capillary underfills trend toward the lower end of these ranges, while unfilled no-flow materials sit at the higher end.

Why does the expansion rate increase above the glass transition temperature?

Below Tg the crosslinked network is in a glassy state and expansion arises mainly from interatomic bond vibrations. Above Tg, free volume increases and polymer chain segments gain mobility, producing a significantly higher rate of dimensional change per degree of heating.

What temperature range is used for the measurement?

A common program runs from ambient temperature to 250 °C at 5 °C/min under nitrogen. For automotive and outdoor applications, testing may start at -40 or -50 °C to capture sub-ambient behavior relevant to cold-start and thermal-shock conditions.

How does TMA differ from dilatometry for this measurement?

TMA uses small specimens, low probe forces, and modest heating rates, and it conveniently captures both CTE and Tg in a single run, which is why ISO 11359-2 and ASTM E831 dominate underfill qualification. Push-rod dilatometry uses longer specimens and can offer excellent precision, but it requires more material and is less convenient for small cured plaques.

How does underfill CTE affect solder joint reliability?

When the underfill CTE closely matches the solder CTE and the modulus is adequate, the underfill mechanically couples the die and substrate so that differential expansion is carried by the composite rather than by the joints. A poorly matched CTE transfers excessive strain to the solder, accelerating fatigue cracking during temperature cycling.

Can the CTE of an underfill be measured inside an actual device?

Bulk plaque measurement remains the standard approach because geometry and probe access must be controlled. However, extracted specimens from cured assemblies can be tested for comparative purposes, and the results are widely used in failure analysis when interpreted alongside cure-state indicators such as Tg and degree-of-conversion data.