Anisotropic Thermal Expansion Testing of Gallium Nitride (GaN) Wafers

Anisotropic thermal expansion testing of gallium nitride (GaN) wafers quantifies the distinct coefficients of thermal expansion along the a-axis and c-axis of this hexagonal semiconductor, delivering critical input data for epitaxial growth control, wafer bow management, and power device packaging design. Accredited third-party laboratories measure orientation-dependent CTE values from room temperature up to 800 °C using thermomechanical analysis, push-rod dilatometry, and high-temperature X-ray diffraction in accordance with ASTM E228, ASTM E831, and ISO 11359 standards. This article explains the technical background, sample requirements, test items, measurement methods, and typical applications of GaN thermal expansion anisotropy characterization.

Technical Overview

Gallium nitride crystallizes in the hexagonal wurtzite structure (space group P63mc). Because the polar [0001] c-axis and the perpendicular a-axes are not symmetry-equivalent, the second-rank thermal expansion tensor of GaN contains only two independent components: the coefficient perpendicular to the c-axis (alpha-a) and the coefficient parallel to the c-axis (alpha-c). Reported literature values at room temperature are approximately 5.3 to 5.6 x 10-6 K-1 for alpha-a and 3.0 to 3.3 x 10-6 K-1 for alpha-c, giving an anisotropy ratio of roughly 1.6 to 1.8. Both coefficients increase nonlinearly with temperature, and alpha-c in particular rises more steeply at elevated temperatures, so the anisotropy ratio decreases as the wafer is heated.

This orientation-dependent behavior has direct engineering consequences. For standard (0001) c-plane wafers, in-plane expansion is governed by alpha-a while out-of-plane expansion is governed by alpha-c. During epitaxial growth cooldown, the mismatch between GaN expansion and that of common substrates, such as silicon at approximately 2.6 x 10-6 K-1 or silicon carbide at approximately 4.0 to 4.5 x 10-6 K-1, generates residual stress that manifests as wafer bow, edge cracking, or film delamination. In packaging, cyclic thermal mismatch between the die, die-attach solder, and heat sink drives fatigue failure. Accurate directional CTE data is therefore essential for strain engineering, finite element thermal-mechanical simulation, and reliability prediction.

Reliable measurement requires orientation-verified specimens and traceable calibration. Accredited third-party laboratories typically perform these measurements according to ASTM E831 and ISO 11359-2 for thermomechanical analysis, ASTM E228 for push-rod dilatometry, ASTM E289 for interferometric dilatometry, and equivalent GB/T and JIS national methods for solid-material expansion testing.

Testing Samples

Free-Standing GaN Wafers and Coupons

Free-standing GaN substrates produced by hydride vapor phase epitaxy (HVPE) or ammonothermal growth are sectioned into rectangular coupons along known crystallographic directions, typically along the [11-20] a-direction and the [10-10] m-direction. Orientation is verified by X-ray diffraction with an accuracy of approximately ±0.5 degrees and is physically marked on each coupon before testing.

Non-Polar and Semi-Polar Oriented Specimens

m-plane (10-10) wafers are especially valuable for anisotropy work: both the [0001] and [11-20] directions lie in the wafer plane, so two orthogonal measurements on a single coupon directly yield alpha-c and alpha-a. Semi-polar orientations, such as (10-12) or (11-22), require tensor transformation to extract the principal coefficients.

GaN Epitaxial Films on Foreign Substrates

For GaN-on-sapphire, GaN-on-Si, and GaN-on-SiC structures, the film is too thin for direct dilatometry. The effective film CTE is instead extracted indirectly through wafer curvature measurements as a function of temperature, combined with the known expansion of the substrate.

• Coupon dimensions: typically 3 to 6 mm length for TMA, 10 to 25 mm for push-rod dilatometry
• Thickness: 0.3 to 2 mm with two parallel faces within ±5 micrometers
• Surfaces lapped or ground to remove saw damage, followed by stress-relief annealing where required
• Two to three replicate coupons per crystallographic direction for statistical validity

Testing Items

Testing programs for GaN thermal expansion anisotropy typically include the following deliverables:

• Coefficient of thermal expansion perpendicular to the c-axis (alpha-a) at specified temperatures
• Coefficient of thermal expansion parallel to the c-axis (alpha-c) at specified temperatures
• In-plane and out-of-plane mean CTE for (0001) c-plane wafers over ranges such as 25 to 200, 25 to 400, and 25 to 600 °C
• Instantaneous (tangent) CTE curves as a function of temperature, alpha(T)
• Fractional length change curves, dL/L0 versus temperature
• Anisotropy ratio alpha-a/alpha-c and its temperature dependence
• Thermal hysteresis and repeatability after multiple heating and cooling cycles
• Effective film CTE for GaN layers on foreign substrates derived from curvature data
• Wafer-level uniformity mapping of directional expansion behavior

Testing Methods

Thermomechanical Analysis (TMA)

TMA per ASTM E831 and ISO 11359-2 measures linear expansion of a coupon under a small static load using a quartz or alumina probe. Heating rates of 5 to 10 °C per minute under nitrogen or argon are standard, with fused silica, sapphire, or tungsten reference materials used for baseline and calibration correction. Displacement resolution is approximately 0.05 micrometers, giving CTE uncertainty on the order of ±0.1 x 10-6 K-1 or ±3 percent. TMA is the preferred routine method for quality-control screening of oriented GaN coupons.

Push-Rod Dilatometry

Dilatometry per ASTM E228 accommodates larger specimens (10 to 25 mm) and temperatures up to 1000 °C. A horizontally or vertically configured alumina push-rod transmits specimen expansion to a displacement sensor, with a blank-run baseline subtraction to remove apparatus expansion. This method is well suited to reference-grade measurements and to evaluating thermal cycling stability over repeated excursions.

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

HT-XRD determines lattice parameters a(T) and c(T) directly from 2theta-theta scans of symmetric reflections such as (0002) and (0004) and asymmetric reflections such as (10-15). The CTE is computed as (1/a)(da/dT) and (1/c)(dc/dT). Because the method is non-contact and lattice-based, it is ideal for small specimens, for coupons where both axes must be measured in-plane, and for detecting strain relief in defective material. Heating stages operate under inert gas or low vacuum; prolonged exposure above approximately 850 °C in vacuum is avoided to prevent surface decomposition of GaN.

Interferometric and Optical Dilatometry

Laser interferometric dilatometry per ASTM E289 offers the highest length-change sensitivity, enabling CTE resolution approaching 0.01 x 10-6 K-1. Non-contact optical dilatometry and digital image correlation techniques provide full-field strain maps of whole wafers, revealing local variations in expansion behavior associated with doping gradients, residual stress, or defect clusters.

Wafer Curvature Method for Thin Films

Laser-scanning curvature measurement tracks wafer bow as a function of temperature. Applying the Stoney equation together with substrate CTE data yields the biaxial stress-temperature response of the GaN film, from which its effective in-plane CTE can be extracted even for layers only a few micrometers thick.

Applications

Directional thermal expansion data for GaN wafers supports a wide range of development, qualification, and production activities across the compound semiconductor industry:

• Epitaxial process optimization, including buffer layer design and MOCVD cooldown schedule tuning to minimize bow and cracking
• Incoming quality control and supplier specification verification for free-standing GaN substrates
• Packaging design for GaN-on-Si power devices, including die-attach material selection and solder fatigue life prediction
• Thermal cycling and reliability qualification, with measured CTE values used as inputs for finite element thermal-mechanical simulation
• Wafer bonding, handle-wafer processing, and laser lift-off process development
• Crystal growth research into the effects of doping (Si, Fe, C, Mg), native defects, and dislocation density on lattice expansion
• Datasheet generation for RF, power electronics, and optoelectronic product qualification packages

FAQ

Why does GaN expand differently along different crystal axes?

GaN has a non-cubic wurtzite lattice in which the bonding environment along the polar [0001] c-axis differs from that in the perpendicular basal plane. This structural anisotropy makes alpha-a roughly 1.7 times larger than alpha-c near room temperature, with both values converging as temperature increases.

What temperature range can be tested?

Standard testing covers room temperature to 600 or 800 °C under inert atmosphere. HT-XRD heating stages can extend to approximately 900 °C, but long dwell times above roughly 850 °C, particularly under vacuum, are avoided because GaN surfaces begin to decompose.

How do I choose between TMA, dilatometry, and HT-XRD?

TMA is the most economical choice for routine QC of oriented coupons. Push-rod dilatometry suits larger specimens and reference-grade data at higher temperatures. HT-XRD is preferred when specimens are small, when lattice-level orientation-specific data is required, or when both principal coefficients must be obtained from a single non-polar coupon.

Can the CTE of a thin GaN film on a substrate be measured?

Yes. Because micrometer-scale films are too thin for direct dilatometry, temperature-dependent wafer curvature measurement combined with the Stoney analysis and known substrate properties is used to extract the effective in-plane CTE of the GaN layer.

How is specimen crystallographic orientation confirmed before testing?

Orientation is verified by X-ray diffraction rocking curves and, where necessary, pole figures. Each coupon is marked with its measurement axis to within approximately ±0.5 degrees, ensuring that reported values correspond to the intended crystallographic direction.

What accuracy and turnaround time can be expected?

Typical CTE uncertainty is ±0.1 x 10-6 K-1 or ±3 percent for TMA, with interferometric methods achieving higher precision. Accredited third-party laboratories generally complete testing, calibration verification, and reporting within five to ten working days after orientation-verified samples are received.