Quantum computing and communication technologies require robust and well-characterized qubits. Silicon, with its well-established semiconductor industry and relatively long coherence times, is a promising material for hosting such qubits. Point defects in silicon, which exhibit unique optical and spin properties, have emerged as promising candidates. This research focuses on the CO2 defect in silicon, also known as the C-center, a recently identified defect whose potential for quantum applications is yet to be fully explored. This study aims to comprehensively characterize the electronic structure, spin properties, and optical transitions of this defect, paving the way for its potential implementation in quantum technologies. Understanding the precise electronic structure, spin dynamics, and optical characteristics of the C-center is essential for its potential application in quantum information processing. This detailed analysis would bridge the gap between experimental observations and theoretical understanding, thus enabling the realization of the C-center's potential as a solid-state quantum bit. The importance of this research lies in expanding the range of available quantum defects in silicon, which can offer diverse functionalities and potentially overcome the limitations of existing systems.

Previous research has explored various point defects in silicon for quantum applications, including the G-, T-, and W-centers. These centers have demonstrated promising properties, but each has its own limitations. The G- and T-centers emit in the telecommunication O-band, while the W-center emits near its short wavelength edge. The Er³⁺ ion emits in the C-band. The C-center, however, exhibits a ZPL in the more favorable L-band, which is advantageous for optical fiber transmission. However, these previous defects exhibit varying radiative lifetimes and require further investigation for potential enhancements in their efficiency. This literature review highlights the ongoing search for ideal quantum defects in silicon, emphasizing the need for comprehensive characterization and optimization strategies to achieve superior performance in quantum technologies. The comparative analysis of the C-center's properties with those of existing defects serves as a crucial foundation for evaluating its potential advantages and limitations. This thorough literature review is essential for understanding the context and significance of the current research in developing quantum technologies based on silicon point defects.

The research employed density functional theory (DFT) calculations to investigate the atomic structure and electronic properties of the CO2 defect in silicon. The Heyd-Scuseria-Ernzerhof (HSE06) functional was used within the VASP plane-wave code, with projector augmented wave (PAW) pseudopotentials for core electrons. A 512-atom silicon supercell was utilized to model the defect. The calculations included spin-polarized calculations to determine the ground state and excited state energy levels and wavefunctions. The charge transition levels were calculated to characterize the defect's electronic behavior. Further calculations incorporated spin-spin interactions (using a Hamiltonian incorporating axial D and rhombic E parameters), spin-orbit coupling (using a Hamiltonian expressed in terms of one-particle spin-orbitals and DFT-calculated matrix elements), and hyperfine interactions (for ¹³C, ¹⁷O, and ²⁹Si isotopes). The zero-phonon line (ZPL) energy was computed, with corrections applied to account for excitonic effects. The simulated photoluminescence (PL) spectrum was calculated using the Franck-Condon principle, enabling a comparison with experimental data. Additionally, the authors employed the GOWO and Bethe-Salpeter-equation (GOWO+BSE) methods, using the HSE06 relaxed atomic positions, to validate the HSE06 DFT results. This comparative approach ensured the reliability and accuracy of the calculated data.

The calculated electronic structure of the CO2 defect reveals a deep donor level induced by the carbon impurity dangling bond. The calculated (+/0) charge transition level of EVBM + 408 meV showed good agreement with experimental data (360 meV). The calculations yielded a ZPL energy of 750 meV after correction for finite size effects. The triplet state was found to be 2.8 meV below the singlet excited state, consistent with experimental activation energy for the reverse intersystem crossing (rISC) process. The axial and rhombic zero-field splitting (ZFS) parameters (D and E) were calculated to be -771 MHz and 94 MHz, respectively. Spin-orbit coupling calculations revealed significant mixing of singlet and triplet states, particularly for the ms = 0 sublevel, modifying the ZFS parameter to 5.7 GHz (in good agreement with experimental data). Hyperfine interaction calculations provided values for ¹³C, ¹⁷O, and ²⁹Si nuclei, showing agreement with experimentally reported values for the Si-G15 EPR center and aiding in understanding nuclear spin control for quantum applications. The simulated PL spectrum showed a sideband structure with local vibrational modes (LVMs) at energies consistent with experimental observations. The Huang-Rhys factor was calculated to be 2.1. The calculations also predict weak phosphorescence transitions, with radiative lifetimes exceeding 10 ms, that are attributable to the triplet states. The intensity ratio of the triplet phosphorescence for the ms = 0 state was found to be 1%, matching experimental findings and suggesting it as an initialisation route for quantum protocols.

The findings of this study provide a comprehensive characterization of the CO2 defect in silicon, showcasing its potential for quantum technology applications. The detailed analysis of the electronic structure, spin interactions, and optical transitions confirms the suitability of this defect as a single-photon emitter for quantum communication, particularly in the L-band region. The ability to optically initialize and read out the spin state within the triplet excited state opens exciting avenues for implementing quantum protocols. The calculated hyperfine interactions with nearby nuclei suggest potential for using the C-center as a quantum register. These results significantly advance the understanding of the C-center and position it as a strong contender among other silicon-based quantum defects for quantum information processing and sensing. The good agreement between theoretical calculations and experimental data validates the methodologies used and lends credence to the predictions made regarding the C-center’s potential in quantum technologies.

This research provides a comprehensive theoretical investigation of the CO2 defect in silicon, highlighting its potential for single-photon emission and quantum computing. The detailed analysis of its electronic structure, spin properties, and optical transitions, supported by strong agreement with experimental data, positions the C-center as a promising candidate for various quantum technologies. Future research should focus on experimental verification of the predicted quantum protocols, exploring methods to enhance the PL and phosphorescence intensities, for example, through integration into optical resonators. Further investigation into the coherence times of both electron and nuclear spins is necessary to fully assess the viability of this defect for quantum information processing.

The study relies primarily on theoretical calculations, and experimental validation of the predicted properties and quantum protocols is crucial. The supercell size used in the DFT calculations may introduce some limitations, although efforts were made to mitigate finite-size effects. While the calculations provide a comprehensive picture, uncertainties inherent to DFT calculations remain. Future studies could incorporate more advanced methods to further refine the accuracy of the theoretical predictions. The investigation focuses on individual defects; the impact of defect interactions in higher concentrations is not considered here.