This work introduces an innovative Source-All-Around Vertical Tunnel Field-Effect Transistor (SAA-VTFET) design based on III-V semiconductors. The unique combination of a GaSb/InSb heterojunction, a wider tunneling space, and an n+ source pocket significantly enhances band-to-band tunneling (BTBT), leading to exceptional on-current levels. The device architecture utilizes InSb in the source pocket and channel, materials chosen for their properties that enable efficient carrier transport, ultimately boosting overall device performance. Through meticulous optimization, the SAA-VTFET achieves an I60 (Ids at SS = 60mV/dec) of 2.73 × 10−4 A/μm, an exceptionally low off-current of 1.7 × 10−17 A/μm, a low threshold voltage of 0.16 V, an outstanding ION/IOFF Ratio of 1.64 × 1013, and an attractive subthreshold swing (point SS of 4 mV/dec, average SS of 7 mV/dec). These remarkable achievements underscore the SAA-VTFET's potential to surpass conventional TFETs, paving the way for advanced low-power, high-speed electronics.