NON-LINEAR PLASMA OSCILLATIONS IN SEMICONDUCTOR AND GRAPHENE CHANNELS AND APPLICATION TO THE DETECTION OF TERAHERTZ SIGNALS

Abstract

The conduction channel of a semiconductor Field Effect Transistor (FET) or a heterostructure High Electron Mobility Transistor (HEMT) can act as a plasma wave resonator for density oscillations in electron gas, at frequencies significantly higher than the transistor cut-off frequency in a short channel device. The hydrodynamic model predicts a resonance response to electromagnetic radiation at the plasma oscillation frequency. 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. Starting with the quasi-classical Boltzmann equation for a semiconductor and graphene channels, we derived the viscous hydrodynamic model with temperature dependent transport coefficients in both cases. We evaluated the detector response function and in the case of semiconductor channel we also obtained the temperature dependence of the quality factor of the plasma resonance. The present treatment extends the theory of Dyakonov-Shur plasma resonator and detector to account for the temperature dependence of viscosity. In the case of semiconductor channels the treatment here also includes the energy balance equation into the analysis. The numerical results are given in cases of GaAs and GaN channels. We showed that in high mobility semiconductor channels at low temperature the quality of the resonance is strongly limited by the viscosity of the electron fluid. In the case of graphene channel the hydrodynamic model derived here accounts both for electrons and holes, and includes the related diffusion currents. When the gate voltage is a few volts, the Fermi temperature of the electron-hole liquid is considerably higher than the room temperature. In such cases the diffusion currents can be ignored, and from the simplified hydrodynamic equations we evaluated the non-linear response of the plasma in graphene channel to the external perturbation. The results are of interest in potential application to graphene based detectors due to potential of obtaining a channel with the room temperature mobility considerably higher than the mobility in semiconductor channels.