Symmetry Adapted Analysis of Screw Dislocation: Electronic Structure and Carrier Recombination Mechanisms in GaN

TL;DR

This work presents a symmetry-adapted analysis of screw dislocations in GaN, restoring the hidden screw symmetry to derive exact constraints on the electronic structure and optical transitions. By constructing a symmetry-adapted basis and block-diagonalizing the Hamiltonian, the authors reveal band connectivity rules and dipole selection rules that organize the symmetry channels for radiative processes. Their GaN case shows sixfold screw symmetry yields a band-flow constraint, strongly polarized infrared radiative channels, and a pronounced suppression of radiative recombination due to piezoelectric-induced electron-hole separation, with nonradiative processes dominating by several orders of magnitude. The framework offers a rigorous foundation for interpreting dislocation-related luminescence and provides a path to quantitatively connect defect structure to optoelectronic performance in wide-bandgap semiconductors.

Abstract

As fundamental one-dimensional defects, screw dislocations profoundly reshape the energy landscape and carrier dynamics of crystalline materials. By restoring the exact algebra of the screw dislocation group, we unveil the latent symmetry constraints that govern the electronic structure, providing a more rigorous physical picture than the conventional treatments. When applied to GaN, the method yields a band-connectivity constraint and rigorous dipole selection rules for polarization-resolved transitions. Combined with computed Hamiltonian matrix, the approach gives symmetry-filtered radiative and dielectric calculations and reveals a piezoelectrical effect at the dislocation core that strongly suppresses radiative recombination. The pronounced dominance of non-radiative capture over radiative recombination highlights the detrimental impact of screw dislocations on the luminous efficiency of GaN, providing a theoretical foundation for optimizing dislocation-limited optoelectronic devices.

Figures (8)

• Figure 1: Structural models of a screw-dislocation GaN nanowire. (a) Cross-sectional structure of the nanowire passivated by fractional H atoms. (b) Schematic illustration of the screw dislocation symmetry. (c, d) Schematic illustration of constructing screw-symmetry-adapted basis functions from localized atomic orbitals. The visualization depicts an $s$-orbital model at $k_z=0$ for the screw representation index $\mu=1$.
• Figure 2: Heatmap of the Hamiltonian matrix in the localized-orbital basis. The color represents the magnitude of the matrix elements. After transformation to the screw-symmetric basis the matrix decomposes into six independent blocks $H_\mu(k)$. This result presents the meaning of the symmetry-adapted basis.
• Figure 3: Calculated band structures of GaN nanowires. (a) The ideal nanowire. (b) The screw-dislocated nanowire, where the dislocation-induced gap states are labeled from $1$ to $6$. The bands are color-coded according to their screw symmetry index $\mu$.
• Figure 4: Six blocks split into two independent band-flow chains: (a)the even chain $(\,0\to2\to4\to0\,)$; (b)the odd chain $(\,1\to3\to5\to1\,)$. This rule is the internal connection between bands from different blocks under screw symmetry.
• Figure 5: Optical properties of screw-dislocated GaN nanowires. (a, b) Optical transition matrix elements in the screw basis for transverse (perpendicular to $c$) and axial (parallel to $c$) polarizations, respectively. (c, d) Imaginary parts of the dielectric function for the corresponding directions, showing the decomposition into different $\Delta \mu$ channels.