Numerical simulation of plasma waves in a quasi-2D electron gas based on the Boltzmann transport equation

The calculation of plasma waves in a homogeneous quasi-2D electron gas is usually based on the Euler equation. It yields a dispersion relation with two branches, which are often referred to as Vlasov modes. Dyakonov and Shur were able to show that under certain boundary conditions for a constant current flow in a high electron mobility transistor these two modes can lead to a plasma instability and generation of THz waves. If, on the other hand, the more physics-based Boltzmann transport equation is solved for plasma waves, a multitude of modes is obtained in addition to the two Vlasov modes. In the case of nonequilibrium and high frequencies, it is no longer possible to identify the two Vlasov modes by simple means. This phenomenon is discussed in detail, and a method for the identification of the Vlasov modes is proposed. In addition, it is shown that for strong nonequilibrium the Dyakonov–Shur instability can be evaluated numerically using a method based on the Boltzmann transport equation.