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In short-channel fully-depleted (FD) silicon-on-insulator (SOI) MOSFETs, the drain leakage current is enhanced by the parasitic bipolar transistor. The parasitic bipolar effect is induced by band-to-band tunneling and floating-body effects. It strongly depends on film thickness and back-gate voltage. We show experimentally the possibility to reduce the parasitic bipolar effect by biasing the back gate (ground plane). Based on devices simulations, we discuss the origin of the bipolar action, its suppression and the possible applications.