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

The study addresses the long-standing issue of strong internal electrostatic fields (IEF) along [0001] in wurtzite III-nitrides (AlN, GaN, InN). Due to the lack of inversion symmetry and ionic bonding, wurtzite structures exhibit spontaneous polarization that induces opposite surface charges and large IEF, causing spatial separation of carriers and band tilting (quantum confined Stark effect), which lowers emission efficiency and redshifts emission in devices. Prior approaches (heavy doping, nonpolar/semi-polar growth on special substrates, and stabilizing zinc-blende phases) have faced major challenges including high defect densities, thermodynamic metastability, and lack of suitable substrates. The paper hypothesizes that reducing thickness to the two-dimensional limit can drive a structural transformation from polar wurtzite to nonpolar configurations (notably the haeckelite 4|8 structure), thereby eliminating IEF while preserving desirable optoelectronic properties, and explores the conditions and substrate interactions that enable such phases.

The authors summarize efforts to mitigate IEF in GaN-based devices: (1) electrostatic screening via heavy doping is impractical due to required concentrations on the order of 1e19 cm^-3; (2) growth of nonpolar/semi-polar GaN on substrates like LiAlO2 and r-plane sapphire achieved flat surfaces but suffered from high stacking fault densities; (3) zinc-blende III-nitrides offer nonpolar behavior but are thermodynamically metastable with insufficient substrate lattice matching for device-quality films. They highlight emerging two-dimensional III-nitrides: hexagonal, haeckelite (4|8), and tetragonal phases predicted or realized via MBE on Ag(111), Si(111), and more recently via MOCVD with graphene encapsulation. Prior theory indicated few-layer graphitic/wurtzite GaN is unstable and reconstructs to haeckelite with neutral surfaces, suggesting reduced or eliminated IEF in 2D forms. These works set the stage for a thickness-driven phase transition pathway to nonpolar structures with potentially improved device performance.

First-principles DFT calculations were performed using VASP with the PBE GGA functional and PAW method, including DFT-D3 dispersion corrections for long-range vdW interactions. A rectangular 8-atom unit cell was used for the 4|8 structure; comparable supercells were adopted for hexagonal and wurtzite to ensure consistency. Vacuum spacing >20 Å avoided spurious interactions. Plane-wave cutoff was 500 eV; Monkhorst-Pack k-grids of 5×8×1 were used for SCF, and 51 k-points along high-symmetry paths for band structures. Convergence thresholds: forces <0.01 eV Å^-1 and total energy 1e-5 eV. Bulk 4|8 phases were verified dynamically stable via phonon spectra. To correct PBE band-gap underestimation, HSE06 hybrid functional was employed (α = 33% for AlN and 31% for GaN/InN) to reproduce reference wurtzite gaps (AlN 5.98 eV, GaN 3.24 eV, InN 0.69 eV). Optical absorption was computed at the HSE06 level within the random phase approximation using PWmat. Structural transformation barriers were obtained by climbing-image nudged elastic band (CI-NEB) with eight images and force convergence 0.01 eV Å^-1. Phonon dispersions were computed using DFPT in VASP and post-processed with PHONOPY. Temperature effects and interfacial stability were assessed via ab initio molecular dynamics (AIMD) using CP2K (Quickstep) with PBE, GTH pseudopotentials, DZVP-MOLOPT-SR-GTH basis sets, and an auxiliary plane-wave cutoff of 300 Ry. Simulations used 3×3 supercells (>300 atoms), NVT ensemble with Nosé–Hoover thermostat at 1000 K, timestep 1 fs, total 3–4 ps. Surface energy per formula unit was defined as γ_m^c = (E_bulk − E_slab)/(2N), where E_slab and E_bulk are total energies of the slab (with two surfaces) and bulk with the same number of atoms, and N is the number of molecular formula units on one surface; larger γ implies poorer surface stability. Carrier effective masses were extracted by fitting band curvature near band edges along Γ–X, Γ–Y, and Γ–Z using m* = ħ^2 / (∂^2ε(k)/∂k^2).

- Thickness-driven phase stability: Although bulk wurtzite is lower in energy than bulk 4|8 by 78 meV (AlN), 110 meV (GaN), and 48 meV (InN) per formula unit, surface energies strongly favor 4|8 in thin slabs. Computed surface energies (eV per f.u.) indicate 4|8 surfaces are much more stable than wurtzite: for wurtzite γ_AlN ≈ 2.02, γ_GaN ≈ 1.72, γ_InN ≈ 0.91; for 4|8 γ_AlN ≈ 0.93, γ_GaN ≈ 0.74, γ_InN ≈ 0.46. Consequently, 4|8 slabs are more stable than wurtzite for certain layer-number windows: AlN 4 < n ≤ 28, GaN 2 < n ≤ 18, InN 4 < n ≤ 14. For thicker films (beyond these windows), wurtzite becomes favorable. - Ultra-thin limit: As thickness further decreases, 4|8 transforms to planar hexagonal structures (graphene-like). Hexagonal phases exhibit quasi-bonded interlayer coupling with short interlayer distances (AlN 2.14 Å, GaN 2.65 Å, InN 2.47 Å), and are stable up to at most two layers for GaN and InN, and four layers for AlN. - Elimination of internal electrostatic field (IEF): Ten-layer wurtzite slabs show strong IEFs (from metal to N surface) of ~22 MV cm^-1 (AlN), ~16 MV cm^-1 (GaN), and ~7 MV cm^-1 (InN) based on macroscopic-average electrostatic potential slopes (without H-passivation: ~16, 10, 6 MV cm^-1, respectively). In contrast, 4|8 and hexagonal configurations exhibit essentially zero IEF due to stacking of neutral layers, eliminating charge accumulation along c-axis. - Electronic structure: HSE06 band gaps for bulk wurtzite are 5.98 eV (AlN), 3.24 eV (GaN), 0.69 eV (InN), consistent with experiment. Bulk 4|8 gaps are similar: 5.57 eV (AlN), 3.24 eV (GaN), 0.76 eV (InN), indicating band-edge states are largely preserved across the wurtzite→4|8 transition. For monolayer hexagonal structures, band gaps are 4.32 eV (AlN), 3.53 eV (GaN), and 1.72 eV (InN), with indirect gaps for AlN and GaN (VBM at Q between Γ and Y; CBM at Γ), and direct gap retained for InN. - Band-edge character: CBM is dominated by N-s orbitals in both wurtzite and 4|8. VBM remains mainly N-p but changes component across phases (e.g., w-AlN: pz; 4|8-AlN: px; w-GaN: py; 4|8-GaN: pz; w-InN: px; 4|8-InN: py). Hexagonal VBM is at Q (N-pz), CBM is hybridized N-s with cation sp for AlN/GaN; for InN both VBM and CBM arise from N-s / In-sp bonding/antibonding. - Carrier effective masses and mobility: 4|8 and hexagonal phases significantly reduce in-plane hole effective masses compared to wurtzite, implying higher in-plane mobility. Examples (m0 units): w-GaN holes (mx,my,mz) ≈ (9.29, 2.08, 2.11) vs 4|8-GaN ≈ (1.87, 1.99, 0.35); w-AlN ≈ (4.24, 4.28, 0.25) vs 4|8-AlN ≈ (0.64, 2.58, 3.27); w-InN ≈ (2.19, 2.19, 2.14) vs 4|8-InN ≈ (0.09, 0.07, 2.12). Electron masses remain comparable (e.g., w-GaN ~0.18–0.16 vs 4|8-GaN ~0.18–0.19). This favors horizontal optoelectronic device architectures. - Substrate effects and epitaxy strategy: On graphene (van der Waals epitaxy), four-layer w-GaN relaxes into 4|8-GaN, while 4|8-GaN remains stable; charge transfer at the interface is negligible, and at 1000 K AIMD the weak interaction breaks while 4|8-GaN persists and w-GaN transitions to 4|8-GaN. On SiC, strong interfacial bonding and structural matching favor wurtzite; both w-GaN and 4|8-GaN maintain their initial states upon relaxation, but AIMD at 1000 K drives 4|8-GaN→wurtzite. Wurtzite is energetically favored over 4|8 on SiC by ~63.9 meV Å^-2. Calculated w→4|8 barriers for freestanding slabs are modest (AlN 0.30 eV/f.u., GaN 0.31 eV/f.u., InN 0.28 eV/f.u.). - Proposed growth route: A "thickness-controlled" vdW epitaxy on weakly interacting substrates (e.g., graphene) is proposed to experimentally realize 4|8 phases within the stability thickness windows, whereas conventional growth on SiC/Si tends to yield wurtzite under high-temperature conditions (~1000 K).

The work demonstrates that reducing III-nitride thickness to the 2D regime can trigger a wurtzite→haeckelite (4|8) transformation that eliminates the internal electrostatic field responsible for the quantum confined Stark effect, without degrading band-edge characteristics or band gaps. The nearly zero IEF in 4|8 directly addresses carrier separation and band tilting in polar wurtzite, promising improved radiative recombination and reduced spectral redshift in emitters. Comparable band structures and reduced in-plane hole masses further suggest potential gains in device efficiency, particularly for lateral transport geometries. The stability window for 4|8 depends on material and thickness, governed by a competition between bulk distortion energy and markedly lower surface energies of 4|8 neutral surfaces. Substrate selection is critical: weakly interacting, lattice-agnostic graphene allows the 4|8 phase to form, while strongly interacting, structurally matched SiC stabilizes wurtzite. Thermal activation at typical growth temperatures can overcome w→4|8 barriers in vdW contexts but drives the reverse on SiC. The results thus provide a clear physical rationale for past experimental observations and a practical route—thickness-controlled vdW epitaxy—to realize IEF-free III-nitride layers for optoelectronics.

The study identifies a practical pathway to eliminate the detrimental internal electrostatic field in GaN-based semiconductors by exploiting a thickness-driven phase transition from polar wurtzite to nonpolar haeckelite (4|8) configurations. 4|8 phases are energetically favored over wurtzite within material-specific thickness ranges and exhibit nearly zero IEF with band structures comparable to wurtzite. In-plane hole effective masses are significantly reduced in 4|8 and hexagonal phases, indicating enhanced lateral transport. Substrate interactions determine phase outcomes: weakly bonded vdW substrates (e.g., graphene) enable stabilization and growth of 4|8 via thickness-controlled epitaxy, while strong, matched substrates like SiC favor wurtzite. Future research should experimentally realize and characterize 4|8 III-nitride layers grown on vdW substrates, quantify device-level performance gains (e.g., reduced QCSE, increased EQE), explore alloyed systems (InGaN, AlGaN) within the 4|8 framework, and assess thermal, environmental, and defect stability under operating conditions.

The findings are based on first-principles calculations with finite-temperature AIMD over short timescales; long-term kinetic effects and defect-mediated pathways in experimental growth are not fully captured. HSE06 with chosen mixing parameters reproduces bulk gaps but excitonic effects and many-body interactions beyond RPA are not included. The 4|8 stability is limited to specific thickness windows and is sensitive to substrate interactions; strong-bonding substrates (e.g., SiC, Si) and high temperatures can stabilize wurtzite or induce 4|8→wurtzite transitions. Hexagonal phases are only stable up to a few layers (≤2 for GaN and InN, ≤4 for AlN), constraining their practical use. Experimental demonstration of device-quality 4|8 layers remains pending.