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The conduction channel of a semiconductor heterostructure high electron mobility transistor (HEMT) can act as a plasma wave resonator for density oscillations in quasi-two-dimensional (2D) electron gas. The plasma wave is an electron density excitation, possible at frequencies significantly higher than the cut-off frequency in a short channel device. The hydrodynamic model predicts a resonance response to electromagnetic radiation at the plasma oscillation frequency, which can be used for detection, mixing, and frequency multiplication in the terahertz range . In particular, the hydrodynamic nonlinearities produce a constant source-to-drain voltage when gate-to-channel voltage has a time-harmonic component. In the Dyakonov-Shur detector a short channel HEMT is used for the resonant tunable detection of terahertz radiation. The non-linear plasma response has been observed in InGaAs [2,3] and GaN [4-6] HEMTs, in the frequency range from 0.2 to 2.5 THz.