Machine-learning-decoupled absorption spectroscopy reveals bandgap shrinkage competition in Si-doped β-Ga₂O₃

β-Ga₂O₃ is promising for power and solar-blind UV photodetection due to its wide bandgap, high critical field, and ease of n-type doping with Si. However, a doping limit arises at high Si concentrations, attributed to band-gap narrowing and renormalization caused by dopants and defects. Dopant ionization (via the Franz-Keldysh effect) and defects (via the Urbach effect) both induce band-gap narrowing and alter the absorption coefficient, yet their individual contributions are difficult to decouple from absorption spectra near the bandgap (4.5-5 eV). This study extends analysis to 2-5 eV using machine learning, enabling the separation of each effect's contribution. The resulting metric directly reflects changes induced by doping. This unreported finding clarifies the intrinsic band-gap narrowing mechanism in Si-doped β-Ga₂O₃ and offers valuable guidance for other n-type doping studies.