In this paper, we present a novel Pocket-SGO iTFET design with overlapping gate on source, Schottky contact to drain, and doping-less SiGe pocket. The aim is to achieve steep subthreshold swing (S.S) and high ION current. By optimizing the gate and source overlap, the tunneling efficiency is significantly enhanced, while the ambipolar effect is suppressed. The use of a Schottky contact at the drain, instead of ion implantation drain, reduces leakage current and thermal budget. Additionally, the tunneling region is replaced by a pocket SiGe with a narrower bandgap, which increases the probability of band-to-band tunneling and enhances the ION current. Our experiments are based on the feasibility of the actual process, thorough Sentaurus TCAD simulations demonstrate that the Pocket-SGO iTFET exhibits an average and minimum subthreshold swing of S.Savg = 16.2 mV / dec and S.Smin = 4.62 mV / dec, respectively. At VD = 0.2 V, the ION current is 1.81 × 10-6 A / μm, and the ION / IOFF ratio is 1.34 × 109. Furthermore, when considering interface traps, the device still achieves S.Savg = 31.9 mV / dec and ION / IOFF = 1.76 × 107. The Pocket-SGO iTFET design shows great potential for low-power devices that are required for the Internet of Things (IoT) and AI applications.