Band-to-band tunnel field-effect-transistors (TFETs) are considered a possible replacement for the conventional metal-oxide-semiconductor field-effect transistors due to their ability to achieve subthreshold swing (SS) below 60 mV/decade. This letter reports a comprehensive study of the SS of TFETs by examining the effects of electrostatics and material parameters of TFETs on their SS through a physics based analytical model. Based on the analysis, an intrinsic SS degradation effect in TFETs is uncovered. Meanwhile, it is also shown that designing a strong onset condition, quantified by an introduced concept - “onset strength”, for TFETs can effectively overcome this degradation at the onset stage, and thereby achieve ultra-sharp switching characteristics. The uncovered physics provides theoretical support to recent experimental results, and forward looking insight into more advanced TFET design.