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We have demonstrated Schottky diodes using semiconducting single-walled nanotubes (s-SWNTs) with titanium Schottky and platinum Ohmic contacts for high-frequency applications. The diodes are fabricated using angled evaporation of dissimilar metal contacts over an s-SWNT. The devices demonstrate rectifying behavior with large reverse bias breakdown voltages of greater than -15 V. To decrease the series resistance, multiple SWNTs are grown in parallel in a single device, and the metallic tubes are burnt-out selectively. At low biases these diodes showed ideality factors in the range of 1.5 to 1.9. Modeling of these diodes as direct detectors at room temperature at 2.5 terahertz (THz) frequency indicates noise equivalent powers (NEP) potentially comparable to that of the state-of-the-art gallium arsenide solid-state Schottky diodes, in the range of 10(-13) W/ radical Hz.