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Determination of Burgers-vector directions of threading edge dislocations in GaN by phase-contrast microscopy

This paper establishes that the in-plane Burgers-vector direction of threading edge dislocations in GaN can be nondestructively determined using phase-contrast microscopy by analyzing the specific arrangement of bright and dark contrast, a finding validated by X-ray topography and electron microscopy techniques.

Original authors: Yukari Ishikawa, Maki Shimizu, Koji Sato, Kisara Matsumoto, Kazuki Ohnishi, Yongzhao Yao, Ryo Hattori

Published 2026-10-07

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CC BY 4.0

Original authors: Yukari Ishikawa, Maki Shimizu, Koji Sato, Kisara Matsumoto, Kazuki Ohnishi, Yongzhao Yao, Ryo Hattori

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Gallium nitride is a material that powers the bright blue lights in our smartphones and the efficient lasers in modern medical devices. It is also the foundation for the next generation of high-power electronics that could make electric vehicles and renewable energy grids far more efficient. However, the crystals used to make these devices are rarely perfect. Inside them, tiny defects called dislocations exist, which are essentially misalignments in the atomic structure. These defects can weaken the material, shorten the lifespan of a device, or cause it to fail entirely. To build better technology, scientists need to find these defects quickly and understand exactly how they are oriented within the crystal. While some methods can spot these flaws, they often struggle to tell the direction in which the defect is pointing without destroying the sample or taking an impractically long time.

Researchers in Japan have developed a way to solve this specific problem using a standard optical microscope. They discovered that by looking at the pattern of light and dark shadows around a defect, they can determine the direction of the defect's internal stress without cutting or damaging the crystal. This method, known as phase-contrast microscopy, allows for rapid, nondestructive inspection of entire wafers. The team demonstrated that the arrangement of bright and dark areas around a specific type of defect, called a threading edge dislocation, reveals the direction of its "Burgers vector." In simple terms, the Burgers vector is a measurement that describes how the atoms are shifted or displaced around the defect. By understanding this direction, engineers can better predict how the defect will affect the performance of the final device.

To prove this connection, the researchers first studied a high-quality crystal grown using an ammonothermal method, which produces very few defects. Because the defects in this sample were so sparse, the team could use a powerful technique called X-ray topography to map the exact direction of each defect's Burgers vector. They then took images of the same defects using their phase-contrast microscope. They found a consistent pattern: for every defect, the boundary between the dark and bright regions was parallel to the direction of the Burgers vector. More specifically, if one were to draw a line from the darkest part of the shadow to the brightest part and then rotate that line 90 degrees counterclockwise, the resulting direction would point exactly where the Burgers vector was pointing. This rule held true for defects arranged in bundles as well as for isolated, single defects.

To ensure this finding was not just a quirk of the low-defect sample, the team repeated the experiment on a different type of crystal grown by a method called hydride vapor phase epitaxy. This second sample was much more crowded with defects, making it impossible to map them individually using X-rays. Instead, the researchers used the new optical rule to predict the direction of the Burgers vector for several defects. They then selected specific defects, cut tiny slices out of the crystal using a focused ion beam, and examined them under a transmission electron microscope. This advanced imaging technique allowed them to measure the Burgers vector directly. The results confirmed their prediction: the direction derived from the simple light-and-dark pattern in the optical microscope matched the complex measurements from the electron microscope perfectly.

The researchers also investigated why this pattern appears in the first place. They compared their optical observations with theoretical models of how light travels through strained material. Their analysis suggests that the contrast seen in the microscope is caused by the photoelastic effect, where the strain from the defect changes the material's refractive index. Specifically, the brightness and darkness seem to reflect the sum of the strain in the two directions across the surface of the crystal. This explanation aligns with findings from other techniques, such as Raman spectroscopy, which also detects strain in similar ways. However, the team noted that this method works best when the defects are standing nearly straight up relative to the microscope lens. If a defect is tilted at a steep angle, a long, linear streak of light appears that can obscure the circular pattern, making it difficult to determine the direction.

This work establishes a reliable, nondestructive way to map the internal stress directions of defects in gallium nitride crystals using a standard microscope. By simply observing the orientation of bright and dark shadows, scientists can now determine the Burgers vector of threading edge dislocations. This capability is a significant step forward for the semiconductor industry, as it offers a fast and gentle method to inspect entire wafers for defects that could compromise device performance. While the technique has limitations regarding highly tilted defects, its ability to provide immediate, detailed structural information without damaging the sample makes it a powerful tool for improving the quality and reliability of the next generation of electronic and optical devices.

Technical Summary: Determination of Burgers-vector directions of threading edge dislocations in GaN by phase-contrast microscopy

Problem Statement
Gallium nitride (GaN) is a critical wide-bandgap semiconductor for next-generation power devices and light sources, yet its performance is often limited by crystal defects, specifically threading dislocations. While nondestructive optical microscopy techniques, such as polarized-light microscopy and phase-contrast microscopy, allow for rapid, whole-wafer inspection, a significant gap exists in their analytical capabilities. While polarized-light microscopy has established a correlation between dislocation contrast and the in-plane Burgers vector, phase-contrast microscopy—which offers superior spatial resolution for high-density defect environments—has not yet had its contrast mechanisms clarified. Consequently, there is no established method to determine the Burgers vector direction of threading edge dislocations (TEDs) using phase-contrast images alone, limiting the technique to mere defect detection rather than comprehensive classification.

Methodology
To address this, the authors employed a multi-modal approach combining optical microscopy with advanced structural characterization techniques:

Sample Selection: Two distinct GaN samples were utilized:
- A low-dislocation-density ( $3 \times 10^4$ cm $^{-2}$ ) ammonothermal GaN wafer, where individual dislocations could be resolved by X-ray topography (XRT).
- A high-dislocation-density ( $7 \times 10^5$ cm $^{-2}$ ) hydride vapor phase epitaxy (HVPE)-grown GaN wafer, where individual dislocations are difficult to resolve by XRT but represent typical industrial conditions.
Imaging and Correlation: Phase-contrast microscopy was performed using a 405-nm LED source. The arrangement of bright and dark contrast around dislocations in the ammonothermal sample was correlated with Burgers vectors independently determined by XRT using six equivalent $\mathbf{g} = 11\bar{2}4$ reflections.
Verification: The relationship derived from the ammonothermal sample was applied to the HVPE sample. To verify the predictions, specific dislocations in the HVPE sample were identified via etch pits, extracted via focused ion beam (FIB), and analyzed using weak-beam dark-field transmission electron microscopy (TEM) and large-angle convergent-beam electron diffraction (LACBED) to determine their Burgers vectors.
Theoretical Analysis: The authors analyzed the contrast formation mechanism by comparing the observed phase contrast with theoretical models of refractive-index changes induced by strain, utilizing the photoelastic effect and comparing the findings with existing Raman spectroscopy data.

Key Results

Contrast-Burgers Vector Relationship: The study established a definitive rule for determining the in-plane Burgers vector direction of TEDs from phase-contrast images. For a dislocation exhibiting dipole-like contrast (a dark region adjacent to a bright region), the Burgers vector direction coincides with the direction obtained by rotating the vector from the minimum of the dark contrast to the maximum of the bright contrast by 90° counterclockwise.
Validation: This rule was first established using the ammonothermal sample (where XRT provided ground truth) and subsequently verified in the HVPE sample. TEM and LACBED analysis of selected dislocations confirmed that the Burgers vectors predicted by the phase-contrast rule (e.g., $\mathbf{b} = \frac{1}{3}[11\bar{2}0]$ ) matched the experimental TEM results.
Influence of Inclination: The study noted that the clarity of the dipole-like contrast depends on the dislocation line inclination relative to the optical axis. When the inclination is small (nearly parallel to the optical axis), point-like dipole contrast is observed, allowing for easy determination. However, as the inclination increases (e.g., in certain bundles in the ammonothermal sample or mixed dislocations in HVPE), linear contrast superimposes on the dipole pattern, complicating the determination of the Burgers vector direction.
Contrast Mechanism: Theoretical analysis suggests that the phase contrast primarily reflects the sum of the two in-plane normal strain components ( $\varepsilon_{xx} + \varepsilon_{yy}$ ) around the dislocation. This is mediated by the photoelastic effect, which alters the average refractive index. The authors note that this mechanism is analogous to the strain sensitivity observed in Raman mapping of the $E_{2H}$ peak, explaining the similar directional relationships found in both techniques.

Significance and Claims
The paper claims to demonstrate that phase-contrast microscopy can serve as a nondestructive optical method for determining the in-plane Burgers-vector direction of threading edge dislocations in GaN. By establishing a clear relationship between contrast polarity and the Burgers vector, the authors argue that this technique enables comprehensive wafer evaluation using a single inspection tool. This capability is significant for both the growth of low-defect-density crystals and device manufacturing, as it allows for the rapid classification of defects across entire wafers without the need for destructive or time-consuming electron microscopy for every defect. The authors remain modest regarding the quantitative evaluation of the refractive-index change, noting that experimental photoelastic coefficients for GaN are currently unavailable, and acknowledge that absorption changes may also contribute to the contrast, requiring further investigation.

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