Comprehensive determination of Burgers vectors of threading dislocations in GaN substrates by combining reflection and transmission synchrotron-radiation x-ray topography

This paper demonstrates that combining reflection and transmission synchrotron radiation x-ray topography enables the comprehensive determination of Burgers vectors for individual threading dislocations, including edge, mixed, and screw types, in acidic ammonothermal-grown GaN substrates.

The Gist

Imagine you are trying to fix a giant, high-tech city made of a special material called Gallium Nitride (GaN). This material is the backbone of next-generation electronics that could save the world a lot of energy. But, like any city under construction, this material has "cracks" and "glitches" inside it called dislocations.

Some of these glitches are harmless, but others are "killer defects" that can cause the electronics to fail, leak electricity, or break down. To fix the city, engineers need to know exactly what these glitches look like and how they are oriented.

This paper is like a detective story where the authors use two different types of "super-vision" to figure out the exact identity of these glitches.

The Problem: The "Invisible" Glitches

The material is thick and heavy (like a dense block of lead). Usually, when you try to look inside a thick block with X-rays, the X-rays get absorbed and stop before they reach the other side. It's like trying to see through a brick wall with a flashlight; the light just gets stuck.

Because of this, scientists usually only look at the surface of the material. But the real troublemakers might be hiding deep inside.

The Solution: Two Super-Vision Modes

The authors combined two powerful techniques to get a complete 3D picture of the glitches. Think of it as using a Flashlight and a X-Ray Scanner together.

1. The Flashlight (Reflection Mode)

First, they shined an X-ray beam at the surface of the material, like a flashlight hitting a wall.

• What they saw: They saw little bright or dark spots where the glitches were.
• The Clue: The size and brightness of these spots told them how "tall" the glitch was (specifically, its vertical component).
• The Limitation: This only told them about the surface. It was like looking at footprints in the snow; you know someone walked there, but you don't know if they were walking north, south, or if they were carrying a heavy backpack.

2. The X-Ray Scanner (Transmission Mode)

Next, they used a special trick called the Borrmann Effect. Imagine a ghost walking through a solid wall because the wall's atoms are arranged in a perfect pattern that lets the ghost pass through without hitting anything.

• The Trick: By tuning the X-rays to a very specific angle and wavelength, the X-rays could pass through the thick block of material without getting absorbed.
• The Clue: When the X-rays passed through, they created a shadow map. By changing the angle of the X-rays, they could see which glitches disappeared (went invisible) and which stayed visible.
• The Magic Rule: There's a rule in physics called the "Invisibility Criterion." If the X-ray beam hits the glitch at a perfect right angle, the glitch becomes invisible. By watching which glitches vanished when they turned the "flashlight" to different angles, they could figure out exactly which direction the glitch was pointing.

Putting the Puzzle Together

By combining the "Flashlight" (surface view) and the "X-Ray Scanner" (deep view), the authors could solve the mystery of every single glitch they found:

1. The "Tall" Glitches: They found some glitches that were purely vertical (like a screw going straight up). They even found a pair of these screws twisting in opposite directions, like a double helix.
2. The "Slanted" Glitches: They found glitches that were leaning (mixed-type). The reflection mode told them how tall they were, and the transmission mode told them which way they were leaning.
3. The "Flat" Glitches: They found glitches that were lying flat. By measuring the width of the shadow the glitch cast (like measuring the width of a shadow to guess the size of the object), they could tell exactly how "heavy" the glitch was.

Why This Matters

Before this study, scientists had to guess what these deep-seated glitches looked like, or they had to cut the material open (which destroys the sample) to look inside with a microscope.

This paper proves that you can look at a thick, valuable piece of Gallium Nitride without cutting it, and figure out the exact 3D shape and direction of every single defect inside.

The Big Takeaway:
It's like having a medical scanner that can not only see a tumor but also tell you exactly how it's growing, which way it's pointing, and how big it is, all without making a single cut. This helps engineers build better, more reliable, and more energy-efficient electronics for the future.

Technical Summary

1. Problem Statement

Gallium Nitride (GaN) is a critical wide-bandgap semiconductor for power devices, but its performance and reliability are severely compromised by threading dislocations (TDs). While screw-type TDs with a Burgers vector ($b$) of $\pm 1c$ are well-known "killer defects," other dislocation types (edge and mixed) with different $b$ vectors can also degrade device performance.

Accurately identifying the full Burgers vector (both magnitude and direction) of individual TDs in thick GaN substrates (typically ~350 $\mu$m) is challenging due to the limitations of existing characterization methods:

• Reflection X-ray Topography (XRT): Limited to surface-near defects. While contrast size relates to $|b|$, the spatial resolution of X-ray films is often insufficient for precise magnitude determination, and contrast shape interpretation is ambiguous.
• Transmission XRT: Historically difficult in thick GaN due to strong X-ray absorption by heavy Ga atoms. While the Borrmann effect (anomalous transmission) allows observation in thick crystals, interpreting dynamical diffraction contrasts for non-screw dislocations remains complex and lacks comprehensive experimental data.
• Gap: No single method currently provides a complete, non-destructive determination of both the direction and magnitude of Burgers vectors for all TD types in thick substrates.

2. Methodology

The authors employed a hybrid approach combining Reflection and Transmission Synchrotron Radiation X-ray Topography (SR-XRT) on an n-type GaN substrate grown via the acidic ammonothermal method (thickness ~350 $\mu$m, TD density $\sim 10^3$ cm$^{-2}$).

A. Reflection SR-XRT (Surface Analysis)

• Setup: Performed at KEK Photon Factory (BL-3C) using a grazing-incidence geometry on the (0001) surface.
• Conditions: Used six equivalent diffraction vectors ($g = 11\bar{2}4$) with a wavelength of 1.40 Å.
• Analysis:
  • Analyzed spot-like contrasts (bright/dark) to constrain possible Burgers vectors based on contrast conditions.
  • Estimated the $c$-axis component ($b_c$) of mixed-type TDs by comparing contrast sizes, leveraging the fact that the $c$-axis lattice constant is larger than the $a$-axis.

B. Transmission SR-XRT (Bulk Analysis)

• Setup: Performed at SPring-8 (BL24XU) utilizing the Super-Borrmann effect (multi-beam diffraction) to overcome X-ray absorption in the thick substrate.
• Conditions:
  • Six-beam diffraction condition (forward-transmitted wave + 5 diffracted waves) to confirm crystal quality.
  • Switched to two-beam diffraction conditions for specific $g$ vectors ($g_1$ to $g_6$) to apply the $g \cdot b = 0$ invisibility criterion.
  • Used a wavelength of 1.24 Å (near the Ga K-edge) to optimize the Borrmann effect.
• Kinematical Contrast Analysis:
  • Deliberately deviated from the exact Bragg condition ($\Delta\omega$) to induce kinematical diffraction contrast.
  • Under these conditions, dislocation lines appear as thin, straight lines where the scattered area is proportional to $|g \cdot b|$.
  • Measured the Full Width at Half Maximum (FWHM) of the dislocation line profiles to determine the magnitude of the $a$-axis component ($b_a$).

3. Key Contributions

1. Hybrid Characterization Protocol: Demonstrated a practical workflow combining reflection and transmission SR-XRT to overcome the individual limitations of each mode.
2. Kinematical Linewidth Analysis in Thick Crystals: Successfully applied the analysis of dislocation linewidths under kinematical contrast (typically used in thin samples) to thick GaN substrates using the Borrmann effect, enabling the determination of the magnitude of the $a$-axis component of $b$.
3. Comprehensive Vector Determination: Established a method to unambiguously determine the full Burgers vector (direction and magnitude) for edge, mixed, and screw-type TDs without destructive sample thinning.

4. Key Results

The study successfully determined the Burgers vectors for specific labeled TDs (E1, E2, E3, M1, M2) and screw-type pairs:

• Edge-Type TDs:
  • E1: Identified as pure edge-type with $b = \frac{1}{3}[2\bar{1}\bar{1}0]$ (magnitude $1a$).
  • E2 & E3: Identified as edge-type. E2 has $b = \frac{1}{3}[\bar{2}110]$ ($1a$). E3 was found to have a larger magnitude, $b = \frac{2}{3}[\bar{2}110]$ ($2a$), confirmed by FWHM ratios.
• Mixed-Type TDs:
  • M1: Identified as mixed-type with $b = \frac{1}{3}[21\bar{1}3]$ (containing both $a$ and $c$ components).
  • M2: Identified as mixed-type with $b = \frac{1}{3}[11\bar{2}3]$ (containing both $a$ and $c$ components). The $c$-component was estimated from reflection contrast size, and the $a$-component direction/magnitude was resolved via transmission linewidth analysis.
• Screw-Type TDs:
  • Observed a pair of screw-type TDs with opposite Burgers vectors ($\pm 1c$) in reflection mode.
  • In transmission mode, these appeared as spot-like contrasts without dislocation lines. This is attributed to the satisfaction of $g \cdot b = 0$ (invisibility of the line) combined with surface relaxation effects (Eshelby twist) creating localized strain spots.
• Crystal Quality: The successful observation of the Super-Borrmann effect (six-beam diffraction) confirmed the high crystalline perfection of acidic ammonothermal-grown GaN substrates.

5. Significance

• Defect Engineering: This methodology provides a non-destructive tool to identify "killer defects" beyond just screw-type dislocations. Understanding the distribution of edge and mixed dislocations with specific Burgers vectors is crucial for optimizing GaN power device reliability and yield.
• Methodological Advancement: The paper validates that transmission SR-XRT using the Borrmann effect is viable for thick substrates (350 $\mu$m), removing the need for destructive thinning (to ~50 $\mu$m) required in previous studies.
• Growth Mechanism Insights: The observation of screw-type TD pairs with opposite vectors suggests a common nucleation mechanism at inclusions for both acidic and basic ammonothermal growth, offering clues for improving crystal growth techniques.
• Future Applications: The established protocol for determining full Burgers vectors can be applied to other wide-bandgap semiconductor substrates, facilitating the development of next-generation high-power electronics.