Propagation-mediated amplification of \{11\={2}0\}-biased inversion domain boundary alignment in polarity-mixed GaN lateral overgrowth

Abstract

GaN polarity inversion and the associated inversion domain boundaries (IDBs) are frequently observed during lateral overgrowth and are often discussed in terms of the small energetic spread among competing IDB structures predicted by first-principles calculations. In circular mask openings, \(\{11\bar{2}0\}\)-aligned IDBs have previously been explained by geometric closure of a single-polarity hexagonal domain at the circular boundary. Here we examine an experimentally distinct regime in which opposite-polarity domains already coexist within the opening before the later development of long, straight IDB traces. In this mixed-polarity regime, the final trace orientation cannot be attributed solely to the macroscopic circular boundary. Nevertheless, plan-view SEM line-trace statistics show that IDB orientations remain biased toward the \(\{11\bar{2}0\}\) family. To quantify how this bias develops during propagation, we perform distance-resolved, length-weighted orientation analysis in concentric annular regions defined from the opening center. The resulting metrics show that \(\{11\bar{2}0\}\)-biased alignment is progressively amplified with propagation distance, while the orientation distribution becomes narrower, indicating systematic sharpening of the preferred alignment state. We further apply the same ring-resolved statistical operators to minimal two-domain propagation simulations in a circular opening and find that a propagation-mediated anisotropy reproduces the observed radial amplification under fixed circular geometry. Together, these results establish a quantitative phenomenology of \(\{11\bar{2}0\}\)-biased IDB alignment in polarity-mixed GaN lateral overgrowth on patterned sapphire and indicate that, although mask-boundary-imposed selection may describe single-polarity closure cases, the present mixed-polarity regime is better explained by propagation-mediated amplification.

Figures (5)

• Figure 1: (a) Large-area plan-view SEM image of GaN grown on a SiO$_2$-patterned sapphire substrate, showing IDB-like line traces across many circular openings. (b) Pre-KOH-etching SEM image of a representative GaN domain grown from a single circular opening. (c) Post-KOH-etching SEM image of the same GaN domain. The KOH etch reveals polarity-dependent surface morphologies, i.e., heavily etched N-polar GaN versus nominally inert Ga-polar GaN. Direct comparison before and after etching shows that the pre-etch line traces coincide with the boundary between differently etched Ga- and N-polar regions, thereby confirming that the analyzed traces correspond to inversion domain boundaries (IDBs). The larger-area view further indicates that the qualitative tendency toward preferentially aligned straight IDB traces is reproduced across many openings in the patterned array.
• Figure 2: (a) Representative SEM image of a GaN domain grown on a SiO$_2$-patterned $c$-plane sapphire substrate, shown here as the starting point for the detailed ring-resolved orientation analysis. (b) Ring-resolved IDB skeleton extracted from the SEM image in panel (a), including the center-only region and successive concentric rings. The center-only region is defined by the innermost circle, whereas Rings 1--4 correspond to the annular regions between adjacent concentric circles. (c)--(g) Normalized projected orientation distributions, $P(x)$, for the center-only region and Rings 1--4, plotted as a function of the reduced orientation coordinate $x$. Here, $x=+1$ and $x=-1$ correspond to $\{11\bar{2}0\}$ and $\{1\bar{1}00\}$ alignment, respectively, and higher ring indices denote larger radial distances from the opening center. The orientation-alignment parameter $\kappa$ is shown in each panel. (h) Radial evolution of $\kappa$. C denotes the center-only region, and R1--R4 denote the first through fourth radial rings.
• Figure 3: Summary metrics for distance-resolved IDB alignment in the SEM image. (a) Orientation branch fractions $P_{+}$, $P_{-}$, and $P_{0}$, where $P_{+}$ and $P_{-}$ denote the integrated probability on the $x>0$ and $x<0$ sides, corresponding to the $\{11\bar{2}0\}$- and $\{1\bar{1}00\}$-biased branches, respectively, and $P_{0}$ denotes the weight at the central bin. (b) Strongly aligned tail fractions $P(x \ge 0.8)$ and $P(x \le -0.8)$, which quantify the probability concentrated near the $\{11\bar{2}0\}$- and $\{1\bar{1}00\}$-proximate limits, respectively. (c) Distribution width $\sigma_x(r)$, where smaller $\sigma_x$ indicates a narrower distribution and therefore stronger peak sharpening. All quantities in (a)--(c) are evaluated from length-weighted orientation histograms normalized such that $\sum_i P(x_i)=1$ within each region.
• Figure 4: (a) Representative simulated morphology for IDB propagation following random nucleation of opposite-polarity domains within a circular opening. (b) Ring-resolved IDB skeleton extracted from the simulated structure, including the center-only region and successive concentric rings. The center-only region is defined by the innermost circle, whereas Rings 1--3 correspond to the annular regions between adjacent concentric circles. (c)--(f) Normalized projected orientation distributions, $P(x)$, for the center-only region and Rings 1--3, plotted as a function of the reduced orientation coordinate $x$. Here, $x=+1$ and $x=-1$ correspond to $\{11\bar{2}0\}$ and $\{1\bar{1}00\}$ alignment, respectively, and higher ring indices denote larger radial distances from the opening center. The orientation-alignment parameter $\kappa$ is shown in each panel. (g) Radial evolution of $\kappa$. The same analysis procedure used for the SEM data is applied to the simulated IDB skeleton in order to compare the radial evolution of orientation alignment on an equal footing.
• Figure 5: Distance-resolved summary metrics for the simulated IDB structure (center-only and Rings 1--3), evaluated using the same statistical definitions as for the experimental data. (a) Orientation branch fractions $P_{+}$, $P_{-}$, and $P_{0}$. (b) Strongly aligned tail fractions $P(x \ge 0.8)$ and $P(x \le -0.8)$. (c) Distribution width $\sigma_x(r)$. All metrics in (a)--(c) are derived from length-weighted orientation histograms that are normalized independently within each region such that $\sum_i P(x_i)=1$.