The coefficient of thermal expansion (CTE) is a decisive design parameter for PET ceramic substrates used in electronic packaging, thick-film circuits, LED modules, and power electronics. The push-rod dilatometer method, standardized in ASTM E228, ISO 17562, and GB/T 16535, provides accurate and reproducible measurement of linear thermal expansion over a wide temperature range. This article explains the principle, sample requirements, test procedure, data reduction, and typical applications of CTE testing for PET ceramic substrates.
Technical Overview
The coefficient of thermal expansion (CTE) quantifies the fractional dimensional change of a material per unit temperature change, expressed in units of 10⁻⁶/K (ppm/K). For PET ceramic substrates, which combine a rigid ceramic body with polymer-based (PET) dielectric or bonding layers, an accurate CTE value is essential for predicting thermomechanical behavior during soldering, wire bonding, and long-term thermal cycling. A CTE mismatch between the substrate, conductive traces, semiconductor dies, and encapsulants generates interfacial stresses that cause warpage, solder-joint fatigue, film cracking, and delamination.
The push-rod method (dilatometry) is the internationally recognized technique for measuring the linear thermal expansion of rigid solids. The specimen is placed inside a temperature-controlled furnace between a fixed platform and a low-expansion push rod. The rod, pressed against the specimen by a small, constant force, transmits every change in specimen length to a high-resolution displacement transducer, typically a linear variable differential transformer (LVDT). Because the measuring system itself expands during heating, a correction run with a certified reference material, such as sapphire or fused silica, is subtracted from the raw signal. The mean CTE is calculated as the ratio of the corrected length change to the product of the initial length and the temperature interval.
Relevant standards for this test include ASTM E228 (push-rod dilatometry of solid materials), ISO 17562 (monolithic fine ceramics by the push-rod technique), GB/T 16535 (fine ceramics, linear thermal expansion by push-rod dilatometry), and ISO 7991 (glass), ensuring cross-laboratory comparability of results.
Testing Samples
Rigid Ceramic Substrates
Bare ceramic bodies such as 96% and 99.6% alumina, aluminum nitride, silicon nitride, zirconia-toughened alumina, and fired LTCC tapes are tested as rectangular bars or cylindrical rods. These samples exhibit well-defined, nearly linear expansion behavior, with reference CTE values of approximately 6.2 to 7.5 ppm/K for alumina and 4.2 to 5.0 ppm/K for aluminum nitride between room temperature and 300 °C.
PET-Laminated and Composite Substrates
Samples consisting of a ceramic core laminated with PET dielectric films, adhesive layers, or ceramic-filled PET composites are tested to determine the effective (apparent) CTE of the composite stack. Because PET exhibits a glass transition near 75 to 80 °C and melts near 255 °C, the maximum test temperature for these laminates is normally limited to 200 to 300 °C, and orientation (machine direction versus transverse direction of the PET film) must be recorded.
Sample Preparation and Dimensional Requirements
- Specimen length of 20 to 50 mm (minimum 10 mm on short-travel instruments); cross-section of 3 to 10 mm square or round.
- End faces ground flat and parallel within 0.01 mm over the contact area, free of burrs, chips, and loose particles.
- Ceramic-only specimens pre-dried at 110 °C for 2 hours; PET-containing specimens conditioned at 23 °C and 50% relative humidity for at least 24 hours.
- Initial length L₀ measured at 23 ± 0.5 °C with a calibrated micrometer or measuring microscope to within ±2.5 µm.
Testing Items
Testing Items:
- Mean linear CTE over specified intervals, for example 25–100 °C, 25–200 °C, and 25–300 °C.
- Instantaneous (differential) CTE as a continuous function of temperature.
- Total percent linear expansion (ΔL/L₀) curves from room temperature to the maximum test temperature.
- Anisotropic expansion: in-plane (X and Y) versus through-thickness (Z) CTE for laminated and tape-cast substrates.
- Glass-transition and softening onsets of the PET constituent, detected as slope changes in the expansion curve.
- Thermal hysteresis and residual dimensional change after a heating–cooling cycle.
Testing Methods
A horizontal or vertical push-rod dilatometer equipped with a fused-silica or high-purity alumina measuring system is used. The push rod applies a small dead load, typically 0.15 to 0.30 N, which maintains contact without inducing measurable creep in polymer-containing laminates. The displacement transducer provides a resolution of 0.05 to 0.1 µm, and a thermocouple positioned immediately adjacent to the specimen records the temperature with an accuracy of ±1 to 2 °C.
Calibration and System Correction
Temperature calibration is verified using the melting points of pure metals such as indium, tin, and zinc. Expansion calibration and blank correction are performed with a certified reference material, for example NIST SRM 732 sapphire or SRM 739 fused silica, using a specimen of the same length as the test sample. The blank run is repeated whenever the furnace program, atmosphere, or holder is changed.
Test Procedure
- Mount the specimen between the platform and the push rod, verify axial alignment, and allow a stable baseline for 10 to 15 minutes.
- Purge the furnace with high-purity nitrogen or dry air at approximately 50 mL/min to prevent oxidation of metallization and moisture effects.
- Heat from room temperature to the target temperature at a controlled rate of 3 to 5 K/min, with an optional 10-minute hold at 100 °C to remove absorbed moisture.
- Record length change and temperature continuously, with data points taken at intervals of no more than 10 seconds or 1 K.
- For hysteresis evaluation, cool at the same rate and record the return curve; report any residual permanent dimensional change.
Data Reduction and Reporting
The mean CTE is calculated from αₘ = (L₂ − L₁) / [L₀ × (T₂ − T₁)], where L₁ and L₂ are the corrected specimen lengths at temperatures T₁ and T₂. The instantaneous CTE is obtained from the first derivative of the expansion curve. The test report must state the temperature interval, heating rate, atmosphere, specimen orientation, calibration reference, and the corrected expansion curve. Typical repeatability is 0.05 to 0.1 × 10⁻⁶/K, with an overall measurement uncertainty of approximately ±3% or ±0.15 × 10⁻⁶/K, whichever is greater.
Applications
- Thick-film and thin-film hybrid circuits: matching substrate CTE with resistor, conductor, and dielectric pastes to prevent firing cracks.
- Power electronics and IGBT modules: verifying that substrate expansion matches copper baseplates and silicon dies for reliable thermal cycling from −40 °C to +150 °C.
- LED packaging: selecting substrates whose CTE limits solder-joint and phosphor-layer stress during junction temperature swings.
- Flexible and hybrid electronics: qualifying PET-laminated ceramic carriers where the effective CTE controls registration and warpage of printed traces.
- Finite-element simulation of packaging: supplying temperature-dependent CTE curves for warpage and stress prediction.
- Incoming quality control and failure analysis: batch-to-batch consistency checks and root-cause investigation of delamination and cracking.
FAQ
Which standards apply to push-rod CTE testing of ceramic substrates?
ASTM E228 covers the general push-rod dilatometer method for solid materials, ISO 17562 and GB/T 16535 address monolithic fine ceramics specifically, and ISO 7991 applies to glass and glass-ceramic substrates. Testing laboratories typically report against ASTM E228 or ISO 17562 with full traceability.
What is the minimum sample size, and can thin substrates be tested?
The preferred specimen length is 20 to 50 mm. Thin sheets below the minimum length may be stacked in the same orientation with polished interfaces, provided the interfaces are flat and dry; alternatively, a thermomechanical analyzer (TMA) in expansion mode can be used for sub-millimeter specimens, accepting a slightly higher measurement uncertainty.
Can PET-containing substrates be heated above 300 °C?
No. PET softens above its glass transition at roughly 75 to 80 °C and melts near 255 °C. Testing beyond 250 to 300 °C risks creep under the rod force and irreversible damage; the recommended upper limit for PET ceramic laminates is 200 to 250 °C with the minimum contact force.
How is the glass transition of the PET layer identified in the results?
The glass transition appears as a distinct inflection in the expansion curve, where the CTE steps up from roughly 20–40 ppm/K to 60–80 ppm/K. The onset and midpoint are determined by the tangent-intersection method and are reported together with the mean CTE values.
How does push-rod dilatometry differ from TMA?
Push-rod dilatometers use longer specimens, larger furnaces, and larger displacement ranges, delivering better CTE accuracy for rigid ceramics over wide temperature spans. TMA excels at small or soft samples, low forces, and transition detection such as Tg. Both methods share the same basic expansion equation and require identical blank-correction logic.
How can measurement accuracy be improved?
Use a reference specimen of the same length as the sample, maintain a slow and constant heating rate, ensure perfectly parallel end faces, perform a blank run before every test series, and condition polymer-containing samples in a controlled humidity environment. Following these practices keeps reproducibility within approximately ±0.1 × 10⁻⁶/K.