This paper describes two types of terahertz-wave detector modules implementing a zero-biased InGaAsP Schottky barrier diode (SBD). A SBD was monolithically integrated with a short-stub resonant matching circuit for increasing the detection sensitivity, and assembled in a compact J-band (WR-3) rectangular-waveguide-input module. The module could detect signals at frequencies from 200 to 500 GHz, and its sensitivity peaked at 1460 V/W around 350 GHz, which is a record value for the InP-based zero-biased SBD. A polarization-sensitive sub-terahertz-wave detector was also developed by integrating a SBD and an extended bowtie antenna. The fabricated quasi-optical module could detect signals at frequencies ranging from 30 GHz to 1 THz at zero bias. The principal-polarization-axis angle for signal detection was stable within ±1.5° at frequencies from 80 to 600 GHz, while the degree of polarization was more than 95%.