Determination of the Linear Thermal Expansion Coefficient of Substrate Glass: Standards, Methods, an

The linear thermal expansion coefficient (CTE) of substrate glass is a critical parameter that governs dimensional stability, warpage behavior, and film adhesion in flat-panel displays, semiconductor packaging, and photovoltaic products. Accurate determination of this coefficient requires standardized dilatometric testing performed under controlled thermal profiles in accredited third-party laboratories. This article explains the testing principles, applicable standards such as ISO 7991, ASTM E228, ASTM E831, and GB/T 16920, sample requirements, and typical applications of substrate glass CTE measurement.

Technical Overview

The linear thermal expansion coefficient, commonly abbreviated as CTE or alpha, quantifies the fractional change in length of a glass specimen per unit change in temperature. For a reference temperature t0 and an upper temperature t1, the mean linear CTE is defined as the length change divided by the initial length and by the temperature interval, and it is conventionally expressed in units of 10⁻⁶ K⁻¹. For substrate glasses used in electronics, the most frequently reported value is the mean CTE between 20 °C and 300 °C, because this range covers most downstream processing and service conditions.

Substrate glass serves as the mechanical and thermal foundation for thin-film transistor (TFT) arrays, OLED device stacks, touch sensors, through-glass-via interposers, and thin-film photovoltaic cells. During manufacturing, these assemblies are repeatedly heated and cooled in deposition, annealing, crystallization, and encapsulation steps. Any mismatch between the CTE of the glass substrate and that of silicon, metals, ceramics, or polymer layers generates residual stress that can cause substrate bow, overlay misalignment, film cracking, or delamination. Consequently, CTE determination is a routine incoming-inspection, lot-release, and R&D qualification test performed by accredited third-party laboratories.

Typical mean CTE values relevant to substrate engineering include approximately 3.0–4.0 ×10⁻⁶ K⁻¹ for alkali-free aluminoborosilicate display glass, about 3.3 ×10⁻⁶ K⁻¹ for borosilicate glass, roughly 8.5–9.5 ×10⁻⁶ K⁻¹ for soda-lime glass, and about 2.6 ×10⁻⁶ K⁻¹ for single-crystal silicon, which is the matching target for many advanced packaging designs. Because the differences that matter are on the order of tenths of a unit of 10⁻⁶ K⁻¹, measurement precision and traceable calibration are essential.

• Primary measurand: mean linear CTE between defined temperatures, most commonly 20–300 °C
• Supporting measurands: instantaneous (tangent) CTE, dilatometric transition temperature, and dilatometric softening behavior
• Governing standards: ISO 7991, ASTM E228, ASTM E831, GB/T 16920, and JIS R3102

Testing Samples

Alkali-Free Display Substrate Glass

Coupons cut from Generation-size mother sheets of alkali-free aluminoborosilicate glass, with thicknesses typically ranging from 0.1 mm ultra-thin glass to 1.1 mm standard TFT substrates, are the most common specimens. Coupons are usually prepared as rectangular bars with ground, parallel end faces and a length suited to the dilatometer, commonly 25–50 mm. The specimen orientation relative to the original sheet is recorded so that any in-plane anisotropy introduced by the forming process can be evaluated.

Soda-Lime, Borosilicate, and Specialty Glass Sheets

Standard commercial glass families, including soda-lime float glass, borosilicate glass, and alkali-containing display or cover glass, are tested with the same specimen geometry. Before testing, specimens are annealed to relieve residual stress where required by the specification, because frozen-in stresses can bias the apparent expansion curve.

Glass Wafers and Semiconductor Packaging Substrates

Glass wafers and panels intended for wafer-level packaging, fan-out processing, and through-glass-via interposers are sampled along defined diameters or diagonals. CTE matching to silicon across the expected processing window is verified, and both radial and tangential orientations may be compared.

Cover Glass and Chemically Strengthened Glass

Chemically strengthened cover glass can be tested either before or after ion exchange. Because the ion-exchanged layer is thin relative to the bulk, the measured CTE primarily reflects the substrate composition, but the conditioning state is always documented in the report.

Thin and Flexible Glass

For glass of 0.2 mm thickness or less, stacked multi-layer specimens, miniaturized TMA specimens, or non-contact optical dilatometry may be used to maintain adequate sensitivity and mechanical stability during measurement.

Testing Items

• Mean linear CTE over standard intervals such as 20–100 °C, 20–200 °C, and 20–300 °C, or over custom intervals specified by the customer
• Instantaneous (tangent) CTE as a function of temperature below the transition range
• Dilatometric transition temperature, determined from the intersection of the extrapolated expansion curves of the glassy and rubbery regimes
• Dilatometric softening point and transformation-range behavior for process-limit assessment
• In-plane CTE anisotropy comparison between machine direction and cross direction of formed sheets
• Expansion stability across repeated thermal cycles, evaluated from heating and cooling curve hysteresis

Testing Methods

Push-Rod Dilatometry (ISO 7991, ASTM E228, GB/T 16920)

A ground specimen is placed in a horizontal or vertical dilatometer and contacted by a low-force push rod. The furnace heats the specimen at a controlled rate, typically 3–5 K/min, while a displacement sensor records the length change and a thermocouple records the specimen temperature. The apparatus expansion baseline is characterized using certified reference materials such as fused silica and sapphire, and the correction is applied to all results. The mean CTE is calculated from the slope of the corrected length-change curve between the specified temperature limits. Testing is performed in a dry inert gas atmosphere to prevent surface hydration effects.

Thermomechanical Analysis, TMA (ASTM E831)

TMA uses a miniaturized specimen, often 2–10 mm in length, resting on a quartz stage with a probe applying a static force on the order of 0.05–0.1 N. The method is well suited to thin substrate coupons, limited material availability, and screening studies. The tangent CTE is derived from the displacement-versus-temperature curve over user-defined temperature intervals, and the transition region is avoided unless explicitly part of the test plan.

Optical and Laser Dilatometry

Non-contact interferometric or laser-scanning dilatometers measure expansion without mechanical loading, which benefits ultra-thin, flexible, or low-modulus specimens near the transformation range. These absolute methods also serve as high-accuracy cross-checks for push-rod systems.

Data Reduction and Reporting

Results are reported as the mean CTE in 10⁻⁶ K⁻¹ for each defined interval, together with the heating rate, atmosphere, specimen orientation, annealing condition, and the transition temperature where applicable. Repeatability of a well-controlled push-rod measurement is typically better than 0.1 ×10⁻⁶ K⁻¹, and measurement uncertainty is quoted with traceability to certified reference materials.

Applications

• Display manufacturing: verifying substrate CTE for TFT-LCD and OLED process windows, overlay accuracy, and color-filter stack compatibility
• Semiconductor packaging: matching glass wafers and interposers to silicon and copper for warpage control in fan-out and 2.5D/3D architectures
• Photovoltaics: aligning cover and barrier glass expansion with silicon cells, metallization, and encapsulants to limit thermal-cycling stress
• Touch and lamination: ensuring compatibility between cover glass, optically clear adhesives, and sensor films during curing and service
• Quality control: incoming inspection, supplier lot release, and statistical process monitoring of glass production
• Research and development: composition screening and CTE tuning of new alkali-free, high-strain-point, and glass-ceramic substrate families

FAQ

What specimen size is required for CTE testing of substrate glass? Standard push-rod dilatometry generally needs a bar of approximately 25–50 mm in length with ground parallel ends, while TMA accepts specimens of only a few millimeters, making it suitable for small coupons and thin glass.

What temperature range is covered? The default interval is 20–300 °C per ISO 7991 practice, but custom ranges up to the transformation region, for example 20–500 °C, can be specified to evaluate behavior across specific processing steps.

What is the difference between mean and instantaneous CTE? The mean CTE is a single averaged slope between two temperatures and is the value cited in glass data sheets, whereas the instantaneous CTE describes the local slope at a given temperature and reveals how expansion accelerates near the transition range.

How accurate are the results? With certified reference material calibration and controlled heating rates, repeatability better than 0.1 ×10⁻⁶ K⁻¹ and uncertainties on the order of 1–3 percent of the measured value are routinely achievable in accredited laboratories.

Can ultra-thin glass be tested? Yes. Stacked specimens, TMA mini-specimens, and non-contact optical dilatometry allow reliable measurement of glass thinner than 0.3 mm.

Which standards govern the test? The principal methods are ISO 7991 and GB/T 16920 for push-rod dilatometry of glass, ASTM E228 for push-rod dilatometry of solids, ASTM E831 for TMA, and JIS R3102 for linear thermal expansion testing of glass.