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Silicon photonics has emerged as a key platform for next-generation communication and sensing technologies, enabling compact, scalable, and energy-efficient optical systems compatible with large-volume semiconductor manufacturing. When combined with highly nonlinear organic electro-optic materials, silicon photonics gains functionalities unavailable in silicon alone, opening new opportunities for ultrafast modulation and for direct transduction between high-frequency wireless electromagnetic fields and guided optical signals. In this work, we investigate hybrid silicon–organic devices based on patch-array antennas integrated with silicon waveguides for the detection of free-space terahertz waves. A telecom probe beam is routed through the silicon circuitry and converted into a plasmonic slot mode that interacts with the terahertz field accumulated in the nanoscale gap of the antenna. The latter is filled with a poled organic material providing the Pockels nonlinearity required for electro-optic terahertz modulation. We design various patch-antenna geometries and compare them to more conventional bowtie antennas. We show that patch-array antennas provide enhanced sensitivity at selected frequencies through a stronger resonant field concentration, in contrast to bowtie layouts that instead exhibit broadband responses owing to their tapered dipolar design. We further analyze how the detected signal depends on the relative position of the terahertz beam spot with respect to these two types of antenna on the chip, thus reconstructing the spatial coupling behavior of the two configurations. These results clarify the trade-offs between bandwidth, sensitivity, and spatial tolerance in planar antenna-coupled plasmonic terahertz detectors and provide practical design guidelines for integrated optical sampling of terahertz signals.