Elimination of the internal electrostatic field in two-dimensional GaN-based semiconductors

Gallium nitride (GaN)-based semiconductors are known for their desirable properties: tunable and direct band gap, high thermal conductivity, and good chemical stability, leading to applications in light-emitting diodes (LEDs), photodetectors, and laser diodes. However, the growth of these materials along the c-axis [0001] presents a significant limitation due to the wurtzite crystal structure. The wurtzite structure, characterized by a c/a ratio less than that of an ideal hexagonal close-packed structure and lacking inversion symmetry, results in a spontaneous dipole moment along the [0001] direction. This dipole moment generates polarization charges on the surfaces, leading to a strong internal electrostatic field (IEF). The IEF spatially separates electrons and holes, causing the quantum confined Stark effect (QCSE), and reducing the emission efficiency and causing a redshift in light-emitting devices. Previous attempts to mitigate this IEF, such as doping, have proven ineffective due to the extremely high doping concentrations required. Other approaches, including using semi-polar or non-polar materials and the zinc-blende phase, have faced challenges due to material quality and substrate limitations. The discovery of various two-dimensional (2D) GaN-based semiconductors, including hexagonal, haeckelite (48), and tetragonal structures, offers a promising avenue to address this problem. These 2D structures are often non-polarized, suggesting a potential solution to eliminate the IEF. Recent successes in synthesizing 2D GaN and AlN via metal organic chemical vapor deposition (MOCVD) with graphene encapsulation have further propelled this research area. The haeckelite (48) structure in particular, predicted to be a stable reconstruction of few-layer GaN, displays a unique 48 motif in its interlayer bonding along the c-axis. This configuration is expected to significantly reduce or eliminate the IEF.

The literature extensively documents the challenges posed by the internal electrostatic field in GaN-based semiconductors and the efforts to overcome these challenges. Early attempts focused on doping techniques to screen the field but required impractically high doping concentrations. The development of semi-polar or non-polar GaN growth techniques showed some promise, but the resulting materials often suffered from low quality due to high stacking fault densities. Investigations into alternative crystal structures, such as the zinc-blende phase, were also explored, but the inherent thermodynamic metastability and lack of suitable substrates hindered the production of high-quality materials. The emergence of two-dimensional (2D) GaN-based materials offered new possibilities. Theoretical and experimental studies reported on various 2D structures, including hexagonal and tetragonal configurations, many of which exhibited non-polar characteristics. However, experimental methods such as molecular beam epitaxy (MBE) faced limitations in cost and sample quality, hindering large-scale applications. Recent advancements in MOCVD with graphene encapsulation enabled the successful synthesis of high-quality 2D GaN and AlN, bringing the prospect of practical applications closer. Previous theoretical predictions indicated that thin layers of GaN might spontaneously reconstruct into the more stable haeckelite structure, which could resolve the IEF issue. This study builds upon these previous findings and explores the stability, optoelectronic properties, and the influence of substrate interactions on the different structural phases of 2D GaN-based materials.

The research employed first-principles calculations using the Vienna Ab initio Simulation Package (VASP) with the generalized gradient approximation (PBE) and projector-augmented wave method. A dispersion correction (DFT-D3) was incorporated to account for van der Waals interactions. Calculations were performed on supercells of wurtzite, haeckelite (48), and hexagonal structures of AlN, GaN, and InN. The stability of the bulk 48 configurations was verified by phonon spectrum calculations. To mitigate the underestimation of band gaps from PBE, the hybrid Heyd-Scuseria-Ernzerhof (HSE06) functional was used for accurate band structure calculations, with mixing parameters optimized to match experimental wurtzite band gaps. Absorption spectra were calculated using the PWmat code. The climbing image nudged elastic band method was used to determine the energy barriers for phase transitions. Density functional perturbation theory, implemented in VASP, was used to calculate force constants for phonon dispersion curves, which were obtained using the PHONOPY package. Ab initio molecular dynamics (AIMD) simulations were conducted using the CP2K package with the hybrid Gaussian and plane wave method to evaluate the temperature effects on structural transitions at 1000 K. The surface energy (γ) was calculated to assess the stability of 2D slabs using the formula: γ = (Ebulk - Eslab)/2N, where Ebulk and Eslab are the total energies of bulk and slab materials respectively, and N is the number of formula units on the surface. Carrier effective mass (m*) was calculated from the band edge using the equation: m* = ħ²(∂²ε(k)/∂k²), where ħ is the reduced Planck constant, ε(k) is the band edge eigenvalue, and k is the wavevector. The study also investigated the influence of substrates (graphene and SiC) on the stability of 4-layer GaN slabs, employing AIMD simulations at 1000 K to consider temperature effects.

The study's key findings demonstrate that the haeckelite (48) configuration becomes energetically more favorable than the wurtzite configuration in GaN-based semiconductors when the material's thickness is reduced to the nanoscale (several nanometers). This phase transition is driven by the significantly lower surface energy of the 48 structure compared to the wurtzite structure, which compensates for the energetic penalty associated with structural distortions. The transition follows a pathway of wurtzite → 48 → hexagonal as the thickness decreases. Importantly, the 48 configuration exhibits nearly zero internal electrostatic field (IEF), eliminating the detrimental quantum confined Stark effect (QCSE) observed in the wurtzite structure. The optoelectronic properties of the 48 configuration are comparable to, or even better than, those of the wurtzite configuration, making it a viable replacement. Analysis of band structures shows that the 48 and wurtzite configurations possess very similar band gaps. However, the reduction in thickness leads to a direct-to-indirect band gap transition for AlN and GaN, but not for InN in the hexagonal configuration. Notably, the in-plane hole mobility of the 48 and hexagonal structures is significantly improved compared to the wurtzite structure. The choice of substrate significantly affects the stability of the 2D GaN structures. Using graphene as a substrate, the 48 structure remains stable, while the wurtzite structure transforms into the 48 configuration. In contrast, on a SiC substrate, both wurtzite and 48 configurations retain their initial structures due to stronger interactions and surface structure matching. Ab initio molecular dynamics (AIMD) simulations at 1000 K confirmed the stability of the 48 configuration and indicated that this temperature is sufficient to overcome the energy barriers for the wurtzite-to-48 phase transition. The results suggest that the 48 configuration can be experimentally realized by using weakly interacting substrates such as graphene and carefully controlling the film thickness via a "thickness-controlled" vdW epitaxy method.

The findings of this study provide a crucial theoretical foundation for overcoming the long-standing challenge of the strong IEF in GaN-based semiconductors. The prediction of the stable 48 configuration in 2D GaN, which exhibits negligible IEF and comparable or superior optoelectronic properties, opens exciting possibilities for enhancing the performance of optoelectronic devices. The demonstrated pathway from wurtzite to 48 to hexagonal with decreasing thickness offers a new approach for materials engineering, suggesting that manipulating the dimensions of the material can fundamentally alter its properties. The identification of the substrate effect as a critical factor highlights the importance of choosing appropriate substrates for experimental realization of the 48 structure. The use of weakly interacting substrates, such as graphene, combined with precise thickness control, offers a feasible path towards synthesizing the desired 48 phase. These findings are relevant to diverse areas of optoelectronics, particularly in the development of highly efficient LEDs and other lighting devices. The improved in-plane hole mobility in the 48 and hexagonal structures also suggests potential benefits for horizontal-structure devices.

This research theoretically demonstrates a method for eliminating the internal electrostatic field in GaN-based semiconductors by reducing material dimensionality to two dimensions. The haeckelite (48) structure emerges as a stable configuration in thin films, exhibiting near-zero IEF while maintaining or surpassing the optoelectronic performance of the wurtzite configuration. This study proposes a "thickness-controlled" vdW epitaxy scheme using substrates such as graphene for experimental realization. Future research could focus on experimental verification of these findings, exploring different substrate materials, and investigating the detailed device physics of optoelectronic devices based on the 48 configuration.

The study is primarily based on theoretical calculations. While the computational methods employed are robust, experimental verification is necessary to confirm the predicted stability and properties of the 48 configuration. The investigation of substrate effects is limited to graphene and SiC. Exploring a wider range of substrates is essential for a more comprehensive understanding of the growth conditions and phase stability. Furthermore, the study primarily focuses on the electronic and structural properties. A more complete analysis encompassing optical properties and device performance will be needed to fully assess the potential of the 48 configuration for practical applications.