Compressive-Sensing-Enhanced First-Principles Calculation of Photoluminescence Spectra in Color Centers: A Comparison between Theory and Experiment for the G Center in Silicon

Photoluminescence (PL) spectra are a versatile tool for exploring the electronic and optical properties of quantum defect systems. In this work, we investigate the PL spectra of the G center in silicon by combining first-principles computations with a machine-learned compressive-sensing technique and experiment. We show that the compressive-sensing technique provides a speed up of approximately 20 times compared with the finite-displacement method with similar numerical accuracy. We compare theory and experiment and show good agreement for the historically proposed configuration B of the G center. In particular, we attribute the experimentally observed E-line of the G center to a local vibration mode mainly involving two substitutional C atoms and one interstitial Si atom. Our theoretical results also well reproduce and explain the experimental E-line energy shifts originating from the carbon isotopic effect. In addition, our results demonstrate that some highly anharmonic modes that are apparent in computed spectra could be absent experimentally because of their short lifetime. Our work not only provides a deeper understanding of the G-center defect but also paves the way to accelerate the calculation of PL spectra for color centers.