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We show that a short channel High Electron Mobility Transistor (HEMT) has a resonance response to electromagnetic radiation at the plasma oscillation frequencies of the two dimensional electrons in the device. This response can be used for new types of detectors, mixers, and multipliers. These devices should operate at much higher frequencies than conventional, transit-time limited devices, since the plasma waves propagate much faster than electrons. The responsivities of such devices may greatly exceed the responsivities of Schottky diodes currently used as detectors and mixers in the terahertz range. A long channel HEMT has a nonresonant response to electromagnetic radiation and can be used as a broadband detector for frequencies up to several tens of terahertz