A cascade model for the defect-driven etching of porous GaN distributed Bragg reflectors

1. Problem Statement

The fabrication of high-reflectivity Distributed Bragg Reflectors (DBRs) in III-nitride semiconductors (specifically GaN) is challenging using conventional compositional alloying (e.g., AlN/GaN) due to poor refractive index contrast and significant lattice mismatch, which leads to cracking and strain issues.

• Current Solution: Porous GaN DBRs offer a solution by creating alternating layers of porous (low refractive index) and non-porous (high refractive index) GaN. This is achieved via selective electrochemical etching of Si-doped layers separated by non-intentionally doped (NID) layers.
• The Gap: While "defect-driven" etching (utilizing threading dislocations as transport channels) allows for lithography-free fabrication, the prevailing understanding of the pore morphology was the "kebab model." This model assumes that every threading dislocation acts as a continuous vertical nanopipe running through the entire stack, with pores emanating radially at each doped layer like a skewer.
• Limitation: Previous studies were largely restricted to 2D cross-sectional imaging or surface-level analysis, which failed to capture the complex 3D connectivity of pores across multiple layers or the behavior of dislocations that might activate or deactivate at different depths.

2. Methodology

The authors employed advanced 3D characterization techniques to visualize the internal structure of porous GaN-on-Si DBRs.

• Sample Preparation: Five-pair porous GaN DBRs were grown on Si(111) substrates via Metal-Organic Chemical Vapour Deposition (MOCVD). The structure consisted of alternating highly Si-doped ($n^+$) and NID GaN layers.
• Electrochemical Etching: Samples were etched in oxalic acid at three distinct voltages: 5 V, 8 V, and 10 V.
• 3D Imaging (Serial-Section Tomography):
  • Used a Focused Ion Beam Scanning Electron Microscope (FIB-SEM) (Zeiss Crossbeam 540).
  • Employed a "slice-and-view" technique: The ion beam milled away thin layers (approx. 5–9 nm) while the electron beam imaged the cross-section.
  • Generated datasets comprising hundreds of aligned cross-sectional images.
• Reconstruction & Analysis:
  • Data was reconstructed into 3D volumetric models using Dragonfly software.
  • Plan-view reconstructions were generated to visualize pore morphology within specific layers.
  • "Onset frames" (images taken just above the porous layers) were used to map the exact positions of dislocation cores before they expanded into pores.
  • Correlative Microscopy: For the 10 V sample, sub-surface Backscattered Electron (BSE) SEM imaging was used to correlate 2D surface features with the 3D tomographic data.

3. Key Contributions

• First 3D Volumetric Characterization: This is the first study to provide full 3D reconstruction of porous GaN DBRs across multiple layers (5 pairs), moving beyond the limitations of 2D cross-sections.
• Proposal of the "Cascade Model": The authors fundamentally challenge the "kebab model." They propose a "cascade model" where etching pathways are not static, continuous vertical pipes. Instead, etching cascades through the material via:
  • Vertical etching down nanopipes.
  • Horizontal etching across pores in doped layers.
  • Dynamic Activation/Deactivation: Dislocations can "switch on" or "switch off" at different layers. A pore from one dislocation can intersect and "undercut" a neighboring dislocation, activating it as a new pathway or deactivating the original one due to depletion zones.
• Statistical Quantification: The study provides the first statistical analysis of dislocation behavior across hundreds of defects, quantifying "active dislocation density" (ADD) and the continuity of etching sequences relative to etching voltage.

4. Key Results

• Morphological Regimes:
  • 5 V: Pores form distinct, fine-tipped "cells" with limited lateral expansion. Many dislocations deactivate after the first layer. No dislocations formed continuous 5-layer "kebab" structures.
  • 8 V & 10 V: Pores become broader and more cavernous. The density of active dislocations increases significantly.
• Dislocation Behavior:
  • Interrupted Sequences: Many dislocations exhibit "interrupted" etching (e.g., active in layer 1, inactive in 2 & 3, active in 4). This contradicts the kebab model.
  • Voltage Dependence: As voltage increases (5 V $\to$ 10 V):
    • The total density of active dislocations increases (from $1.9 \times 10^9$ to $4.4 \times 10^9$ cm$^{-2}$).
    • The probability of a dislocation forming a continuous 5-layer "kebab" structure increases (0% at 5 V $\to$ 37.1% at 10 V).
    • The likelihood of "interrupted" etching sequences decreases.
• Mechanism of the Cascade: The data suggests that etching is probabilistic. A dislocation that etches deeply early on creates a large lateral pore that can intersect a neighboring dislocation. This intersection can either activate the neighbor (if the pore overlaps the core) or deactivate it (if the pore creates a depletion zone that blocks further vertical etching).

5. Significance

• Mechanistic Understanding: The "cascade model" provides a more accurate physical framework for defect-driven etching, explaining phenomena like premature nanopipe termination and the formation of complex pore networks that the kebab model could not.
• Process Optimization: The study demonstrates that etching voltage is a critical control parameter. Higher voltages increase the probability of forming continuous, kebab-like structures, which may be desirable for specific optical properties, while lower voltages result in more fragmented, cascade-like networks.
• Device Engineering: Understanding these 3D pathways allows for better prediction of refractive index contrast and strain management in porous DBRs. This is crucial for designing high-performance optoelectronic devices (e.g., VCSELs, single-photon sources) that require overgrowth on porous substrates.
• Methodological Advance: The workflow established here (FIB-SEM serial-section tomography) sets a new standard for characterizing sub-surface porous multilayer structures, applicable beyond GaN to other porous semiconductor systems.

In conclusion, this paper shifts the paradigm of porous GaN DBR fabrication from a static, defect-centric view to a dynamic, network-based understanding, offering a roadmap for optimizing device performance through controlled electrochemical etching.