Investigation of moments-based transport models applied to plasma waves and the Dyakonov–Shur instability

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 drift-diffusion 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.