The Electronic Structures and Energies of the Lowest Excited States of the Ns0, Ns+, Ns− and Ns-H Defects in Diamond

At a Glance

Metadata	Details
Publication Date	2023-02-28
Journal	Materials
Authors	Alexander Platonenko, W. C. Mackrodt, Roberto Dovesi
Institutions	University of Turin, University of Latvia
Citations	1
Analysis	Full AI Review Included

The Electronic Structures and Energies of Nitrogen Defects in Diamond

This analysis summarizes the theoretical investigation of the lowest excited states of mono-substituted nitrogen defects (N_s⁰, N_s⁺, N_s^-, and N_s-H) in diamond, focusing on the origin of key optical absorption features and the mechanism of semi-conductivity.

Executive Summary

Strong UV Absorption Source: The strong optical absorption at 270 nm (4.59 eV) is confirmed to originate from multiple nitrogen defects: N_s⁰, N_s⁺, and N_s^-. This supports the hypothesis that N_s⁺ is a significant contributor, especially in CVD diamond where N_s⁰ concentrations may be low.
Visible Absorption Source: The weak visible absorption peak at 520 nm (2.38 eV) is specifically attributed to the N_s⁺ defect.
Semi-conductivity Mechanism: The activation energy for semi-conductivity (~1.7 eV, onset ~500 K) in N-doped diamond is predicted to result from a spin-flip thermal excitation of a CN hybrid orbital within the N_s⁰ donor band, mediated by multiple inelastic phonon scattering events.
Methodology: Direct A-SCF (Augmented Self-Consistent Field) calculations were used, providing fully relaxed excited state energies and detailed charge/spin redistribution maps, which are unavailable through standard virtual spectra methods.
Defect Structure: The self-trapped exciton near N_s⁰ is confirmed to be a highly localized defect, involving only the N atom and its four nearest neighbor (nn) C atoms, with the surrounding host lattice remaining pristine diamond.

Technical Specifications

Parameter	Value	Unit	Context
Strong Optical Absorption Peak	4.59 (270)	eV (nm)	Attributed to N_s⁰, N_s⁺, and N_s^- defects.
Weak Optical Absorption Peak 1	3.44 (360)	eV (nm)	Attributed to N_s-H or other impurities.
Weak Optical Absorption Peak 2	2.38 (520)	eV (nm)	Attributed primarily to the N_s⁺ defect.
N_s⁰ Semi-conductivity Activation Energy	~1.7	eV	Thermal transition energy (onset ~500 K).
N_s⁰ Donor Band Excitation (α → β)	1.96	eV	Γ-point energy for the spin-flip transition.
N_s⁰ Absorption Edge (α → β)	1.43	eV	Lowest energy absorption edge for semi-conductivity.
N_s⁺ Excitation (C*(3s,2py,3py))	2.51	eV	Direct A-SCF energy candidate for the 2.38 eV peak.
N_s⁰ Nearest Neighbor N-C* Distance	2.05 (+27%)	A (% diff)	Ground state structure (C_3v symmetry).
N_s⁺ Nearest Neighbor N-C Distance	1.57 (+0.8%)	A (% diff)	Ground state structure (T_d symmetry).
Diamond Host Calculated Indirect Band Gap (E_g)	5.76	eV	B3LYP/6-21G calculation.

Key Methodologies

The study utilized advanced computational methods to model defect behavior, focusing on the direct calculation of excited state properties:

Direct A-SCF Method: The core technique is the direct Augmented Self-Consistent Field (A-SCF) method, implemented in the CRYSTAL code. This approach calculates the ground and excited states separately and identically.
Excited State Definition: Electronic excitation is modeled as the removal of an electron from the ground state to a locally excited state (point defect model). The total energy difference between the fully relaxed ground state and the fully relaxed excited state yields the excitation energy (∆SCF).
Functional and Basis Sets:
- The hybrid B3LYP functional was used, demonstrated to be superior to PBE0, HSE06, and GGA for direct A-SCF studies of low-lying excited states.
- Modified Pople 6-21G basis sets were used for Carbon (C) and Nitrogen (N).
Supercell Simulation: Defective systems were simulated using large supercells containing 64 or 128 atoms to minimize defect-defect interactions.
Hybrid Orbitals: C, N, and CN hybrid orbitals (sp³ type) were constructed and used directly in the A-SCF procedure to accurately describe the covalent bonding and calculate 1-electron excited state wavefunctions.
Charge and Spin Analysis: Mulliken partition analysis was applied to the excited state wavefunctions to quantify the redistribution of charge and spin (e.g., charge transfer from N to C* or nn C atoms) resulting from the optical transitions.

Commercial Applications

The detailed understanding of nitrogen defect states and their optical signatures is critical for the production and characterization of high-quality diamond materials for advanced applications:

Quantum Sensing and Computing: Precise control over the concentration and charge state of N_s defects is essential, as N_s defects are precursors or competitors to the formation of NV (Nitrogen-Vacancy) centers, the primary qubit in diamond quantum technology.
UV/Visible Optics and Detectors: Identifying the specific defects responsible for UV (270 nm) and visible (520 nm) absorption allows manufacturers to tailor growth conditions (e.g., CVD temperature, gas composition) to minimize or maximize specific defects, optimizing diamond for use as UV detectors or high-power optical windows.
High-Temperature Electronics: The confirmed mechanism for semi-conductivity in N-doped diamond (thermal spin-flip excitation of N_s⁰) informs the design of diamond-based electronic devices intended for high-power or high-temperature operation.
Material Characterization: The correlation between specific optical peaks (270 nm, 520 nm) and defect charge states (N_s⁰, N_s⁺) provides a non-destructive, rapid optical method for assessing defect concentration and charge balance in synthetic diamond, complementing slower EPR techniques.

View Original Abstract

This paper reports the energies and charge and spin distributions of the mono-substituted N defects, N0s, N+s, N−s and Ns-H in diamonds from direct Δ-SCF calculations based on Gaussian orbitals within the B3LYP function. These predict that (i) Ns0, Ns+ and Ns− all absorb in the region of the strong optical absorption at 270 nm (4.59 eV) reported by Khan et al., with the individual contributions dependent on the experimental conditions; (ii) Ns-H, or some other impurity, is responsible for the weak optical peak at 360 nm (3.44 eV); and that Ns+ is the source of the 520 nm (2.38 eV) absorption. All excitations below the absorption edge of the diamond host are predicted to be excitonic, with substantial re-distributions of charge and spin. The present calculations support the suggestion by Jones et al. that Ns+ contributes to, and in the absence of Ns0 is responsible for, the 4.59 eV optical absorption in N-doped diamonds. The semi-conductivity of the N-doped diamond is predicted to rise from a spin-flip thermal excitation of a CN hybrid orbital of the donor band resulting from multiple in-elastic phonon scattering. Calculations of the self-trapped exciton in the vicinity of Ns0 indicate that it is essentially a local defect consisting of an N and four nn C atoms, and that beyond these the host lattice is essential a pristine diamond as predicted by Ferrari et al. from the calculated EPR hyperfine constants.

Tech Support

Original Source

DOI: https://doi.org/10.3390/ma16051979

References

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