This work presents a comprehensive analysis of indium phosphide (InP) triple-barrier resonant tunneling diodes (TB-RTDs) operating as direct terahertz (THz) detectors at zero bias. Through analytical derivation, the influence of device dimensions and of current-voltage curvature on voltage responsivity and noise equivalent power (NEP) is explored, and theoretical expressions for diode sensitivity are derived. On-wafer measurements of two scaled TB-RTDs with top contact areas of 0.5 mu m(2 )and 1 mu m(2) are conducted, followed by a comparative analysis, including harmonic-balance simulation results based on a self-developed TB-RTD nonlinear model. The measurements reveal that the responsivity scales with device area, as predicted by the theory, with a peak responsivity of 2123V/W at 340GHz for the TB-RTD, and above 1200V/W across the entire WR2 band (330-500GHz) for the smaller 0.5 mu m(2) area device. The NEP values do not exceed 3.5 pW/Hz and 2pW/Hz for the 1 mu m(2) and 0.5 mu m(2) devices, respectively, with the lowest measured NEP being 1.15pW/Hz for the 0.5 mu m2 device. These sensitivity values place the TB-RTD at a level comparable with the state-of-the-art THz direct detectors operating at room temperature. The investigation offers a clear picture of the intrinsic performance of TB-RTD operating at zero bias, with a detailed overview of the on-wafer measurement setup, power characterization method, and detector figures of merit, highlighting the potential of TB-RTDs as compact, power-efficient, and ultra-sensitive direct THz detectors.