Quantum-transport simulations of current-voltage characteristics are performed in ultra-small double-gate and gate-all-around metal-oxide-semiconductor field-effect-transistors (MOSFETs) with a single attractive ion in the channel region. The ion induces a threshold voltage shift, whose origin is attributed to an ion-induced barrier lowering (IIBL). An analytical expression for the IIBL in ultra-small MOSFETs is derived. The analytical expression for the IIBL consists of two terms: a term related to the potential curvature at the potential top and a correction term due to the screening effects. The analytical model reproduces reasonably well the stimulated IIBL in the subthreshold region.