Phase engineering of giant second harmonic generation in Bi$_2$O$_2$Se

Two-dimensional (2D) materials with remarkable second-harmonic generation (SHG) hold promise for future on-chip nonlinear optics. Relevant materials with both giant SHG response and environmental stability are long-sought targets. Here, we demonstrate the enormous SHG from the phase engineering of a high-performance semiconductor, Bi$_2$O$_2$Se (BOS), under uniaxial strain. SHG signals captured in strained 20 nm-BOS films exceed those of NbOI$_2$ and NbOCl$_2$ of similar thickness by a factor of 10, and are four orders of magnitude higher than monolayer-MoS$_2$, resulting in a significant second-order nonlinear susceptibility on the order of 1 nm V$^{-1}$. Intriguingly, the strain enables continuous adjustment of the ferroelectric phase transition across room temperature. Consequently, an exceptionally large tunability of SHG, approximately six orders of magnitude, is achieved through strain or thermal modulation. This colossal SHG, originating from the geometric phase of Bloch wave functions and coupled with sensitive tunability through multiple approaches in this air-stable 2D semiconductor, opens new possibilities for designing chip-scale, switchable nonlinear optical devices.