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We compute the growth rate of the Dyakonov-Shur plasma instability of a quasi-2D electron gas by numerical simulations based on the Boltzmann transport equation. We present a method to solve the characteristic equation by a Newton approach to find the two Vlasov modes. A deterministic solver using Fourier harmonics in the 2D k-space is applied to carrier transport in the framework of the Dyakonov-Shur model. We investigate the suppression of the plasma growth rate due to the Pauli principle and temperature.

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Transport models based on balance equations with different degrees of numerical complexity can be derived from the Boltzmann transport equation (BTE). In this paper two different driftdiffusion models based on the first two moments of the BTE as well as two hydrodynamic models based on four moments are derived and analyzed for their accuracy in the THz frequency range with emphasis on the generation of plasma waves. To this end, they are compared to the BTE in the small-signal regime under homogeneous bulk conditions where harmonic waves were assumed, which reveals that the hydrodynamic models provide a higher accuracy. It is also shown that the anisotropy of the distribution function must be taken into account in the closure relations. This leads to convective derivatives in the balance equations, which are very difficult to treat by numerical means in the case of semiconductor devices and are neglected in commercial TCAD suites. But without them a meaningful simulation of the Dyakonov-Shur plasma instability will not be possible.