Nature of point defects in bulk hexagonal diamond

Abstract: Hexagonal diamond (HD), an exotic carbon allotrope recently synthesized in bulk form, exhibits superior mechanical properties compared to cubic diamond (CD) and holds promise for advanced industrial and quantum applications. Using first-principles calcu-lations, we systematically investigate intrinsic defects, extrinsic dopants, and defect complexes in HD. Our study shows that VC dominates intrinsic conductivity, while Ci is unstable. Among extrinsic dopants, boron acts as a benign acceptor enhancing p-type conductivity, whereas nitrogen and phosphorus serve as effective donors for n-type conductivity. Group II and Group IV dopants, however, introduce high formation energies or neutral charge states with limited impact. Furthermore, VC, MgC and XV defect com-plexes display multiple spin and charge states within the HD band gap, highlighting their potential as color centers for hosting qubits. These results not only clarify the defect physics of HD but also demonstrate its broader implications for conductivity engineering and quantum technologies.

• The paper presents high-precision DFT analyses that identify dominant intrinsic and extrinsic defects in bulk hexagonal diamond.
• It quantifies formation energies and demonstrates that B, N, and P act as effective dopants for p-type and n-type conductivity.
• The study highlights vacancy and complex defects as promising quantum color centers for advanced optoelectronic and quantum applications.

Point Defects and Defect Complexes in Bulk Hexagonal Diamond: A First-Principles Investigation

Introduction

The research comprehensively analyzes the nature of point defects and defect complexes in bulk hexagonal diamond (HD) using first-principles density functional theory (DFT) calculations. Unlike cubic diamond (CD), which has been extensively investigated for both its exceptional mechanical properties and quantum technological applications, HD offers an alternative stacking (lonsdaleite structure), predicted and recently confirmed to have superior mechanical metrics and altered electronic structure. The study systematically examines both intrinsic defects (e.g., vacancies and interstitials) and a wide range of extrinsic dopants across several chemical families, including their complexes, to elucidate their roles in charge and spin physics relevant to conductivity engineering and quantum information science.

Methods

High-accuracy DFT calculations were performed using the VASP code, incorporating structural relaxations via the PBE-GGA functional and refined total energies and transition levels using HSE06 hybrid functional with $x = 0.32$, yielding a theoretical band gap of 4.62 eV, consistent with $GW$ benchmarks. Defect calculations deployed 432-atom HD supercells and included correction schemes for charged defects (FNV). The chemical potential space was rigorously constrained to realistic C-rich conditions, ensuring that all secondary phase formation boundaries were enforced for each dopant.

Intrinsic Defects

The study identifies the C vacancy (Vc) as the dominant intrinsic defect species in HD, exhibiting robust bipolar character with deep donor and acceptor states within the band gap. Vc can manifest in $+1$, neutral, $-1$, and $-2$ charge states, with multiple spin-split levels, underlining its potential as a color center. Intrinsic C interstitials (Ci) are found to be highly unstable (formation energies $\sim$12 eV), leading to negligible equilibrium concentrations and thus insignificant impact on transport properties.

Divacancies (VV) exhibit slightly reduced formation energies compared to interstitials but remain too high to facilitate appreciable concentrations in equilibrium. Their complex spin and charge manifolds may, however, be harnessed in color center engineering. The compensation between donor and acceptor states of Vc pins the Fermi level 1–1.5 eV above the valence band maximum, yielding HD’s signature weak p-type intrinsic conductivity.

Extrinsic Doping: Group-wise Analysis

Group II (Mg, Ca, Sr)

Antisite defects for Mg, Ca, and Sr have very high formation energies and induce significant local lattice distortions as their atomic radii increase from Mg to Sr. They introduce levels within the gap but contribute negligibly to carrier concentration due to their thermodynamic cost. Nonetheless, Mg antisites show rich spin physics similar to Vc, pointing to color center potential rather than carrier engineering.

Group III (B, Al, Ga)

Among all extrinsic dopants, B antisites (Bc) emerge as particularly effective acceptors. Bc is stable, low in formation energy ($<$2 eV), and introduces shallow acceptor levels close to the VBM, making it ideally suited to enhance p-type conductivity in HD. In comparison, Al and Ga, with larger atomic radii, introduce higher energy distortions and higher formation enthalpies (Alc, Gac $\sim$9 eV). Their acceptor activities are less relevant for practical p-type doping.

Group IV (Si, Ge, Sn, Pb)

Si and Ge antisites are isoelectronic, resulting in neutral charge states and negligible perturbation to the band structure due to compatible size and bonding preferences. For heavier congeners (Sn, Pb), the increased ionic radii and diffusive orbitals introduce deep donor levels and severe lattice distortions, leading to high formation energies and weak n-type doping, making them unsuitable for effective carrier engineering in HD.

Group V (N, P, As)

Group V antisites show distinct behavior: N$_\mathrm{C}$ is established as a prime n-type dopant with low formation energy (comparable to Vc) and shallow donor levels, effectively raising the Fermi level towards the conduction band. P$_\mathrm{C}$ similarly acts as an efficient n-type dopant, but As$GW$0, due to its greater atomic size, has much higher formation energy and weak dopant behavior.

Defect Complexes and Color Centers

Extensive investigation of XV complexes—where X is an extrinsic element (Mg, Ca, Sr, B, Al, Ga, Si, Ge, Sn, Pb, N, P, As) coupled to a C vacancy—shows that many such complexes (notably B-Vc, Si-Vc, N-Vc, P-Vc and Mg-Vc) possess multiple spin- and charge-state manifolds within the HD band gap. Structural analyses reveal two main configurations: antisite-like for B and N, and split-vacancy for others. Many of these complexes are stable in negative charge states, reportably functioning as acceptors. The formation energies for key complexes such as B-Vc, Si-Vc, N-Vc, and P-Vc are competitive with Vc, indicating possible equilibrium populations under suitable synthetic conditions.

Notably, the study identifies that Vc, Mgc, and various XV defects in HD can act as promising candidates for solid-state qubits, with implications for color center photonics and quantum information science paralleling, and potentially surpassing, those in cubic diamond.

Discussion and Implications

The results provide an exhaustive map of defect energetics and their associated electronic structure in HD, establishing that:

• Only B is a truly benign, low-barrier p-type dopant.
• N and P are effective n-type dopants, with corresponding shallow donor levels.
• Group II and most Group IV dopants introduce large local strain and high energy cost with little utility for carrier density control.
• The rich suite of spinful centers among vacancy and complexed defects earmarks HD as a versatile host for quantum applications, leveraging its lower symmetry relative to CD for new optical and spin properties.

These findings recast HD as a promising material for both robust industrial applications in extreme environments and advanced quantum technologies. The clarified defect landscape offers guidance for experimental doping strategies and quantum emitter engineering, essential for the continued development of HD-based devices.

Conclusion

Through systematic, high-precision DFT calculations, the study illuminates the defect physics of bulk hexagonal diamond, identifying dominant intrinsic and extrinsic point defects, their impact on carrier type and concentration, and outlining the potential of various defect complexes as quantum color centers. These results provide a theoretical foundation for exploiting HD in electronic, optoelectronic, and quantum information applications, and inform future experimental defect engineering strategies aiming at both conductivity optimization and spin-photonics platforms (2604.22393).