We demonstrate that geometric deformation of flux-surface induced by a magnetic island can trigger the bifurcation to an electron internal transport barrier (eITB) through a novel positive feedback loop arising from the nonlinear coupling between the neoclassical tearing mode (NTM) and collisionless trapped electron mode (CTEM). The magnetic island-induced deformation enhances the precession drift frequency of trapped electrons, resulting in suppression of the CTEM turbulence. The consequent reduction in turbulent heat transport steepens the electron temperature gradient, which in turn amplifies the magnetic island via an increase in bootstrap current, thereby closing and reinforcing the feedback loop. The key features of this NTM-triggered eITB theory are qualitatively consistent with the experimental observations from J-TEXT (Mao etal 2025 Nucl. Fusion65 066018).