Coefficient of Thermal Expansion Determination Testing for Gallium Nitride on Alumina Substrates

The coefficient of thermal expansion (CTE) determination experiment for gallium nitride (GaN) on alumina (Al2O3) substrates is a critical reliability test that quantifies the thermal mismatch between the epitaxial semiconductor layer and its ceramic carrier. Accurate CTE data, measured according to recognized standards such as ASTM E831 and ASTM E228, are essential for predicting wafer bow, film stress, and delamination risk in LEDs, RF transistors, and power electronic devices.

Technical Overview

Gallium nitride epitaxial layers grown on alumina substrates form the material foundation of a wide range of optoelectronic and electronic products, including LED chips, RF HEMT transistors, and emerging power switching devices. Because the coefficient of thermal expansion (CTE) of GaN differs from that of the alumina substrate, significant thermal strain accumulates during cooling from the growth temperature of approximately 1000 °C, during subsequent die thinning and soldering operations, and throughout long-term device operation. A controlled CTE determination experiment therefore provides the quantitative basis for predicting wafer bow, residual film stress, micro-cracking, and interfacial delamination, and it supplies essential input data for finite-element thermal stress simulations used in package design and qualification programs aligned with standards such as IEC 60068-2-14 for temperature-change testing.

• GaN (wurtzite structure): approximately 5.59 × 10⁻⁶/K in the a-axis (in-plane) direction and approximately 3.17 × 10⁻⁶/K in the c-axis (out-of-plane) direction near room temperature, increasing at elevated temperature.
• Single-crystal sapphire (α-Al2O3): approximately 5.0–5.6 × 10⁻⁶/K perpendicular to the c-axis and 7.4–8.8 × 10⁻⁶/K parallel to the c-axis over the range of 25 °C to 1000 °C.
• Polycrystalline alumina ceramic substrates (96–99.5 percent purity): typically 6.5–7.7 × 10⁻⁶/K between room temperature and 400 °C.
• The resulting mismatch strain accumulated from the growth temperature to room temperature is commonly on the order of 0.1–0.3 percent, which is sufficient to generate stresses approaching the fracture strength of the GaN film if the layer exceeds critical thickness.

Reported values vary with material purity, crystallographic orientation, dopant concentration, temperature interval, and measurement method, which is precisely why a standardized, repeatable determination experiment performed by accredited third-party laboratories is required for engineering-critical data.

Testing Samples

GaN-on-Alumina Epitaxial Wafer Coupons

Samples are typically prepared from two-inch to eight-inch wafers consisting of c-plane sapphire or polycrystalline alumina substrates carrying GaN epitaxial layers with thicknesses ranging from approximately 1 micrometer for buffer-layer studies to more than 10 micrometers for thick HVPE-grown films. Coupons are laser- or diamond-scribed into pieces of 3 to 10 mm in length with two faces ground and polished parallel to within the flatness tolerance demanded by the selected measurement standard, then ultrasonically cleaned and conditioned in a standard laboratory atmosphere of 23 ± 2 °C before testing.

Bare Alumina Reference Substrates

Uncoated substrate coupons from the same wafer lot are measured in parallel to establish the substrate baseline CTE. Subtracting the substrate contribution from the composite wafer response allows the effective thermal expansion behavior of the GaN film and the GaN-to-alumina interface to be isolated, which is essential when the epitaxial layer is too thin for direct bulk measurement.

Thinned Dies and Assembled Test Vehicles

Processed dies, thinned wafers, and die-on-substrate assemblies may also be characterized to evaluate the net CTE of the finished stack. These samples are particularly relevant for packaging studies in which solder reflow, silver sintering, or molding compound curing temperatures introduce additional thermal excursions that compound the intrinsic GaN-to-alumina mismatch.

Testing Items

The determination experiment is structured to deliver a complete thermal expansion characterization of the GaN-on-alumina material system. Core deliverables include:

• Average (mean) linear CTE over specified temperature intervals, for example 25–200 °C, 25–300 °C, and 25–500 °C, calculated as α = (L2 − L1) / (L0 × (T2 − T1)).
• Instantaneous (differential) CTE as a continuous function of temperature, obtained from the first derivative of the expansion curve.
• Full thermal strain and dimensional change curves (ΔL/L0 versus temperature) covering heating and cooling segments to reveal hysteresis and residual strain.
• Anisotropic CTE characterization distinguishing in-plane and out-of-plane expansion for the hexagonal GaN lattice and the anisotropic sapphire crystal.
• Identification of inflection points or discontinuities in the expansion curve that indicate stress relaxation, crack initiation, or interfacial sliding events.

Testing Methods

Thermomechanical Analysis (TMA) per ASTM E831

Thermomechanical analysis is the primary method for composite wafer coupons in the practical engineering temperature range. A low-expansion fused-silica probe applies a small static force to the sample while a precision linear variable displacement transducer records length change during heating at a controlled rate of 3–5 °C/min under an inert nitrogen or argon purge. Typical sample lengths of 3–10 mm provide repeatability on the order of ±0.1 × 10⁻⁶/K after baseline correction and calibration against certified reference materials such as synthetic sapphire.

Push-Rod Dilatometry per ASTM E228

For bare alumina substrates and thick GaN bulk layers, horizontal or vertical push-rod dilatometry extends the measurable range from room temperature up to 1000 °C or higher, which is necessary to approach the actual epitaxial growth temperature. The instrument is calibrated with a certified reference expansion standard, a zero-run baseline is recorded with the empty holder, and the mean CTE is extracted from the corrected expansion curve. This method is well suited to establishing the substrate reference values referenced in fine-ceramic test practice, including approaches described in ISO 11359-2 for thermomechanical analysis and corresponding national fine-ceramic standards such as GB/T 16535.

High-Temperature X-Ray Diffraction (HT-XRD)

When the GaN layer is only a few micrometers thick, its lattice parameters rather than bulk dimensions are tracked as a function of temperature using in-situ high-temperature X-ray diffraction in symmetric or grazing-incidence geometry. By recording the temperature dependence of the (0002) and (10-12) reflections for GaN and the (0006) reflection for sapphire, the anisotropic CTE of both film and substrate can be derived independently, free of the substrate-dominated response that limits mechanical methods on thin layers.

Laser Interferometry per ASTM E289

Absolute laser interferometry offers the highest accuracy, with displacement resolution in the nanometer range, and is appropriate when CTE values below approximately 2 × 10⁻⁶/K must be resolved or when a laboratory reference-grade determination is needed to validate dilatometer and TMA results.

General Test Procedure

• Specimen inspection, dimensional metrology, and parallelism verification under an optical microscope or surface profiler.
• Instrument baseline acquisition and calibration using a certified reference material traceable to national metrology requirements.
• Programmed thermal profile, typically a hold at 23 °C followed by heating at 3–5 °C/min to the target temperature, then controlled cooling, with at least two cycles to assess repeatability and hysteresis.
• Data reduction to mean CTE per temperature interval, instantaneous CTE curves, and uncertainty budgets covering calibration, baseline drift, and temperature uniformity.
• Test report including the applicable standard, sample orientation, atmosphere, heating rate, and raw expansion curves alongside the calculated coefficients.

Applications

CTE determination results for GaN-on-alumina systems directly support design and manufacturing decisions across the compound semiconductor value chain:

• LED chip design, where expansion mismatch governs wafer bow, chip warpage after singulation, and phosphor or encapsulant delamination.
• RF GaN HEMT development on sapphire substrates for telecommunication amplifiers, where thermally induced stress affects gate leakage and device lifetime.
• Power electronics packaging, where measured CTE values guide the selection of die-attach solders, sintered silver, direct-bonded copper, and active metal brazing layers to minimize joint fatigue.
• Substrate supplier qualification, comparing sapphire against polycrystalline alumina, aluminum nitride, and silicon alternatives during material selection.
• Thermal cycling and thermal shock qualification programs conducted per IEC 60068-2-14 and related environmental test standards, where known CTE values enable lifetime prediction from simulated stress profiles.
• Wafer thinning and handling process optimization, since grind-induced and thermally induced stresses superimpose during high-temperature carrier de-bonding steps.

FAQ

Why is CTE mismatch between GaN and alumina so important?

Because GaN films are grown at approximately 1000 °C and operate from −40 °C to more than 150 °C, every thermal excursion converts the expansion difference between film and substrate into mechanical stress. This stress drives wafer bow during processing, crack initiation in the epitaxial layer, and interfacial delamination during device operation, all of which can be quantitatively predicted only with reliable measured CTE data.

What temperature range should the experiment cover?

A practical engineering evaluation typically spans room temperature to 300–500 °C, which covers die attach, reflow, and junction operating conditions. For growth-related stress analysis, push-rod dilatometry can extend the measurement to 800–1000 °C to approximate the epitaxial deposition temperature, while cryogenic start temperatures down to −55 °C support automotive and aerospace qualification requirements.

Can a thin GaN film be measured directly by dilatometry?

Not reliably. When the GaN layer is only a few micrometers thick, the bulk specimen response is dominated by the substrate. In such cases, high-temperature X-ray diffraction is used to track the GaN lattice parameters directly, or wafer-curvature measurements combined with the substrate CTE are used to extract the effective film stress and mismatch behavior.

What accuracy can be expected from the determination experiment?

Repeatability of ±0.05 × 10⁻⁶/K to ±0.1 × 10⁻⁶/K is typical for a well-maintained TMA or dilatometer on samples of adequate length, provided that baseline correction, certified reference calibration, and parallel-faced specimens are used. Interferometric methods can improve resolution further, at the cost of longer setup and alignment times.

How should the results be reported?

A compliant report states the governing standard, specimen geometry and orientation, temperature program, purge atmosphere, calibration reference, and heating and cooling expansion curves, together with the mean CTE for each specified temperature interval and associated measurement uncertainty. Reporting both the composite wafer values and the bare substrate baseline is strongly recommended so that downstream users can reconstruct the film-level behavior.