Viscous hydrodynamic model of non-linear plasma oscillations in two-dimensional gated conduction channels and application to the detection of terahertz signals

We study the non-linear plasma oscillations in a semiconductor conduction channel controlled by a gate. The analysis is based on the hydrodynamic equations derived from the Boltzmann equation, and includes the effects of viscosity, finite mobility, and temperature gradients in the channel. The conduction channel of a heterostructure High Electron Mobility Transistor (HEMT) can act as a plasma wave resonator for charge density oscillations at frequencies significantly higher than the transistor cut-off frequency in a short channel device. In the Dyakonov-Shur detector a short channel HEMT is used for the resonant tunable detection of electromagnetic radiation in the low terahertz range. Within the hydrodynamic approximation we evaluated the resonant nonlinear response to a small signal, and obtained the temperature dependence of the quality factor Q of the plasma resonance. We find that in high mobility gated semiconductor conduction channels the quality of the resonance is limited by the temperature dependent viscosity of the electron fluid.