SOLPS modeling including full cross-filed drifts is used, for the first time, to reproduce the step-like detachment onset observed in the DIII-D tokamak previously simulated with UEDGE (Jaervinen et al 2018 Phys. Rev. Lett. 121 075001), and to further investigate the underlying physics processes. The SOLPS analysis reveals a strong interplay between the E × B drift-driven flows and carbon radiation in DIII-D. The modeling shows that the high confinement H-mode facilitates the formation of such a detachment cliff due to the narrow SOL width and hence steep radial gradients near the separatrix, which enhances the poloidal E × B drift. Furthermore, the SOLPS modeling indicates that carbon radiation also plays a key role in the formation of the detachment cliff in DIII-D without additional impurity seeding. These findings may have significant implications for the control and maintenance of divertor detachment for the steady-state operation of high power fusion devices.