Re-examining the M-center in silicon

Silicon is a key material in quantum technologies, forming the foundation for both integrated photonic platforms and spin qubit systems. In this study, we systematically investigate the formation, structure, and stability of carbon-related defect clusters in silicon, focusing on the CsCi, CsCiHi, and CsCiCsHi defects using density functional theory. The CsCi defect exhibits a high formation energy and weak binding energy, indicating a less stable and energetically costly defect. The incorporation of hydrogen to form the CsCiHi cluster significantly lowers the formation energy, demonstrating that hydrogen facilitates defect formation and reduces the binding energy due to structural relaxation and charge redistribution. The more complex CsCiCsHi cluster, which includes an additional substitutional carbon atom, shows the lowest formation energy, suggesting that it forms easily; whereas its negative binding energy reveals that it is more stable than its isolated components. We show that increasing defect complexity does not increase the zero-phonon line (ZPL) energy, but the electronic coupling and symmetry of the defect can play a more decisive role. The ZPL values for both configurations are well outside the telecom O-band reducing their immediate applicability in quantum communications.