The coefficient of thermal expansion (CTE) of an IC substrate directly governs solder joint reliability, package warpage, and long-term device performance in advanced semiconductor packaging. This article explains the experimental methods used to measure the X, Y, and Z-axis thermal expansion of IC package substrates, covering specimen preparation, TMA and dilatometry procedures, data analysis, and the relevant IPC and ASTM standards.
Technical Overview
The coefficient of thermal expansion (CTE) defines the fractional dimensional change of a material per unit temperature change, conventionally expressed in parts per million per degree Celsius (ppm/°C). For integrated circuit (IC) substrates, CTE is a first-order reliability parameter because the substrate mechanically bridges a silicon die with a CTE of approximately 2.6 ppm/°C and a system-level printed circuit board with a CTE of roughly 14 to 17 ppm/°C. Every thermal excursion during reflow soldering, power cycling, and accelerated life testing converts this CTE mismatch into shear strain in solder joints, tensile stress in low-expansion layers, and out-of-plane stress in plated through-holes and microvias.
Organic IC substrates are anisotropic laminates composed of resin, glass fabric or build-up films, and patterned copper. The in-plane (X and Y) CTE is constrained by the glass reinforcement and copper balance and typically falls between 10 and 17 ppm/°C below the glass transition temperature (Tg), whereas the out-of-plane (Z-axis) CTE, dominated by the resin phase, commonly ranges from 30 to 70 ppm/°C below Tg and can exceed 200 ppm/°C above Tg. Because Z-axis expansion stresses plated interconnects while in-plane mismatch drives solder joint shear, a complete characterization must quantify all three axes under controlled laboratory conditions.
Polymer expansion behavior changes abruptly at Tg, so CTE results are reported in two segments: alpha 1 below Tg, which represents normal operating conditions, and alpha 2 above Tg, which represents reflow and thermal excursion conditions. A full experimental study also yields Tg itself and the total expansion percentage up to peak reflow temperature, all of which feed warpage simulation, solder fatigue modeling, and material qualification decisions.
Testing Samples
Rigid Organic Core Substrates
Bismaleimide triazine (BT) and epoxy-glass core substrates represent the most widely tested sample class. Specimens are cut from production panels or dedicated qualification coupons, and both copper-clad and copper-etched conditions are evaluated to separate full composite behavior from pure dielectric behavior. Core thickness, glass cloth style, and resin content must be recorded because each variable measurably shifts the in-plane CTE.
Build-Up Film Substrates
Epoxy or polyphenylene-ether based build-up films, such as Ajinomoto build-up film (ABF), form the sequential layers of high-density substrates. These films may be tested as laminated stackups or as free-standing films with thicknesses of 15 to 60 micrometers. Free-standing film measurement requires special low-force TMA film fixtures to avoid probe penetration and slack errors at such small gauge lengths.
Flexible and Rigid-Flex Substrates
Polyimide-based flexible layers exhibit in-plane CTE values typically between 15 and 30 ppm/°C and absorb measurable moisture, which elevates apparent expansion. Specimens must be conditioned consistently, and the machine direction versus transverse direction must be marked, since film drawing during manufacture introduces directional anisotropy.
Ceramic and Glass-Core Substrates
Alumina (6 to 7 ppm/°C), low-temperature co-fired ceramic, and emerging glass cores (3 to 9 ppm/°C) are used for low-warpage packaging. Their low expansion values demand high-resolution instruments, because an absolute uncertainty of even 0.5 ppm/°C represents a large relative error. Push-rod dilatometers or interferometric methods are preferred for these materials.
Specimen Geometry and Conditioning
Z-axis TMA specimens are typically 6 to 10 millimeter squares or discs with flat, parallel faces and thicknesses between 0.3 and 4.0 millimeters. In-plane specimens are strips of 10 to 25 millimeters for TMA fixtures or 25 to 50 millimeters for dilatometers and strain gauges. Unless an as-received moisture condition is explicitly required, all specimens are baked at 105 ± 5 °C for 1 to 2 hours and cooled in a desiccator. A minimum of three specimens per condition is tested, with orientation, thickness, and copper state documented for every sample.
Testing Items
- Alpha 1 CTE below Tg in the X, Y, and Z axes for operating-condition characterization.
- Alpha 2 CTE above Tg for reflow and excursion-condition characterization.
- Glass transition temperature determined by the TMA tangent-intersection method.
- Total expansion percentage from room temperature to 260 °C in the Z axis, which correlates with reflow survivability of plated holes and microvias.
- CTE measured before and after copper etching to distinguish composite versus pure dielectric expansion.
- Free-standing build-up film CTE for sequential build-up layer modeling.
- Dry versus moisture-conditioned CTE comparison for humidity-sensitive materials.
Testing Methods
Thermomechanical Analysis (TMA)
TMA is the primary industrial method, standardized in ASTM E831 and IPC-TM-650 method 2.4.24. A quartz probe rests on the specimen under a small static force, typically 0.01 to 0.05 N, while a linear variable differential transformer records length change and a furnace heats the specimen at 5 °C/min under a nitrogen purge of 20 to 50 mL/min. Temperature is calibrated with an indium melting standard, and expansion calibration is verified with fused silica and certified aluminum references.
In Z-axis expansion mode, alpha 1 is computed by linear regression over a defined sub-Tg window, commonly 50 to 120 °C or 30 to 100 °C depending on the governing specification, while alpha 2 is taken from the steeper slope between approximately Tg plus 20 °C and the maximum test temperature. Tg is identified at the intersection of extrapolated tangents to the two segments. In-plane mode uses a horizontal quartz fixture that supports strip specimens so that expansion is measured along the strip axis, with longer specimens improving signal-to-noise.
Push-Rod Dilatometry
Push-rod dilatometry per ASTM E228 measures longer specimens, typically 25 to 50 millimeters, inside a fused-silica dilatometer tube at heating rates of 3 to 5 °C/min. The longer gauge length improves resolution, making the method well suited to verifying TMA results and to characterizing ceramic and glass cores whose low CTE values challenge TMA sensitivity.
Strain Gauge Method
The strain gauge technique, standardized as IPC-TM-650 method 2.4.24.2, bonds precision foil gauges to large substrate coupons that are cycled in a thermal chamber. Changes in gauge resistance are converted to strain and differentiated against temperature. Self-temperature-compensated gauges, combined with a reference material of known CTE such as fused silica or titanium silicate, correct for apparent strain. The method is particularly valuable because it measures true in-plane X and Y expansion on production-format coupons.
Optical and Non-Contact Methods
Laser interferometry per ASTM E289 provides the highest precision for thin or very low expansion specimens. Digital image correlation and hot-stage microscopy map full-field strain, revealing local anisotropy near pad arrays, via structures, and copper balance zones. Bimetallic curvature techniques, which extract thin-film CTE from wafer bow measurements using Stoney-type analysis, serve as a complementary approach for very thin dielectric films.
Data Reduction and Calculation
The instantaneous CTE is calculated as alpha equals one over the initial length L0 multiplied by the slope of the expansion curve, that is, alpha = (1/L0) × (ΔL/ΔT), obtained by linear regression over the specified temperature window. The secant or mean CTE over an interval is computed as (L2 − L1) divided by L0 multiplied by (T2 − T1). Total expansion percentage equals 100 × ΔL/L0 at the peak temperature. Each report should state the regression windows, correlation quality, specimen orientation, thickness, copper condition, conditioning history, heating rate, and calibration standards.
Quality Control and Reporting
- Report individual specimen values, the arithmetic mean, and the standard deviation for every axis and condition.
- Reject runs exhibiting probe penetration artifacts, visible softening above Tg under excessive force, or baseline drift.
- Verify instrument performance periodically using certified reference materials traceable to national standards.
- Confirm reproducibility with replicate specimens and cross-check in-plane results between TMA, dilatometry, and strain gauge methods when feasible.
Applications
Material qualification uses measured CTE values to verify incoming core and build-up materials against supplier datasheets and IPC-4101-class base material specifications before production release. Warpage engineering feeds the measured X, Y, and Z CTE values into finite-element models for ball grid array, flip-chip, and chip-first packages, allowing designers to tune copper balance, core selection, and build-up layer architecture. Solder joint reliability studies combine substrate CTE with die and board values to compute mismatch strain for Coffin-Manson fatigue life estimation and temperature-cycle test planning.
Additional applications include statistical process control of lamination and cure through CTE trending, detection of under-cure or resin degradation in failure analysis by comparing shifted CTE and Tg values against baseline data, and supplier comparison studies during new package development. In every case, the experimental CTE dataset forms the quantitative foundation upon which thermomechanical design decisions are made.
FAQ
What is the target CTE range for an IC substrate?
Most rigid organic substrates target an in-plane CTE of 10 to 17 ppm/°C below Tg, positioning the substrate between silicon and the printed circuit board to minimize mismatch strain on both interfaces. Low-warpage designs increasingly use cores or glass fabrics engineered toward 8 to 12 ppm/°C.
Why are alpha 1 and alpha 2 measured separately?
Alpha 1 below Tg governs dimensional stability during normal operation and temperature cycling, while alpha 2 above Tg governs behavior during reflow, where the resin softens and expansion can triple or more. Reporting both segments plus Tg gives designers the complete expansion profile needed for both operating and processing conditions.
Which standards govern CTE testing of IC substrates?
The principal standards are ASTM E831 for TMA-based linear expansion, ASTM E228 for push-rod dilatometry, ASTM E289 for interferometry, and IPC-TM-650 methods 2.4.24 and 2.4.24.2, which define TMA and strain gauge procedures specifically for printed board and substrate materials.
Should copper be etched away before testing?
It depends on the objective. Copper-clad specimens give the composite CTE that the package actually experiences, while etched specimens reveal the pure dielectric CTE used for material specifications and laminate design. Many qualification plans require both measurements to quantify the reinforcing contribution of the copper.
What temperature program is typically used for TMA testing?
A common program heats from room temperature to 260 °C at 5 °C/min under nitrogen purge with a probe force near 0.05 N. Alpha 1 is extracted from a sub-Tg window such as 50 to 120 °C, and the run continues far enough above Tg to establish a clean alpha 2 slope.
How does absorbed moisture affect CTE results?
Moisture plasticizes the resin and can raise apparent expansion and depress Tg, particularly for polyimide and epoxy systems. Standard practice bakes specimens at 105 °C for 1 to 2 hours before testing, and dedicated studies compare baked and humidity-conditioned states when moisture sensitivity is a concern.
When should dilatometry be used instead of TMA?
Dilatometry is preferred for low-expansion materials such as ceramic and glass cores, for long specimens where the greater gauge length improves resolution, and for independent verification of TMA data. TMA remains the fastest and most common method for routine organic substrate qualification.
How many specimens are required for a valid result?
A minimum of three specimens per axis and condition is standard, with five preferred for qualification programs. The report should include individual values, the mean, and the standard deviation so that lot-to-lot variation can be statistically assessed.