Simulation of plasma waves in III-V devices based on the Boltzmann equation

The need for bandwidth pushes high data rate applications to higher and higher frequencies. At frequencies above 100 GHz the power efficiency of electronic devices degrades very much. Above 10 THz optical devices become available, which are again reasonably power efficient. The frequency range inbetween is called Terahertz gap. To bridge the Terahertz gap generators based on plasma wave instabilities have been suggested by Dyakonov and Shur. In this case electrons move ballistically in the channel of a high electron mobility transistor (HEMT) with a sub-micrometer gate length and if appropriate boundary conditions are applied, the current flow becomes unstable and plasma waves in the THz range are generated. Since the plasma waves are faster than the electrons, the power efficiency of the device increases. On the other hand, the theory by Dyakonov and Shur is based on stringent approximations and it is not clear, whether plasma instabilities can occur in real devices or not. While plasma resonances in HEMTs have been experimentally observed, conclusive measurements for instabilities are still lacking. The purpose of the thesis is to improve the theoretical understanding of this effect by microscopic modeling and to investigate, if plasma instabilities are possible under more realistic conditions. This work presents numerical modeling in the semi-classical framework and microscopic simulations of plasma waves in nanoscale transistors. To this goal a deterministic solver based on a Fourier harmonics expansion of the Boltzmann equation is developed to describe transport in III-V devices, where the Schrödinger equation determines the confinement of electrons in the channel. The solutions of the Boltzmann equation are compared to the results of the modeling approach used by Dyakonov and Shur, which is based on the continuity and Euler equations, which can be derived by projecting the Boltzmann equation onto two moments involving many approximations. The thesis consists of two main parts. First, a homogeneous channel is assumed in accordance with the Dyakonov-Shur approach. To this end, both models are compared in the small signal regime where plane plasma waves are assumed for an arbitrary frequency and wave number. The comparison reveals that the Euler equation fails not only in the case of strong non-equilibrium but also in the linear response regime at equilibrium. While the Dyakonov-Shur model yields only two branches for the dispersion relation of the plasma waves, the Boltzmann equation yields a multitude of branches, but only two of these modes are of interest and they are identified by appropriate means in this work. According to the prediction of Dyakonov and Shur the two plasma waves form a standing wave by superposition, where their amplitudes are enhanced by reflection at the boundaries of the gated channel. Thus the plasma waves can become unstable and generate electromagnetic radiation at THz frequencies. The comparison shows that the Pauli principle, scattering and velocity saturation lead to strong damping of the plasma waves not captured by the Euler equation. Thus, the predictions by the Dyakonov-Shur model are too optimistic. In the second part of the thesis, the simulation is extended to a two-dimensional transistor structure with an inhomogeneous channel for which the Boltzmann, Poisson and Schrödinger equations are solved self-consistently. The small signal high frequency behavior of the transistor is analyzed based on the admittance parameters, which show a resonance behavior in the frequency range from 1 to 10 THz. The spectrum of the resonances depends on the device geometry, voltages and the temperature.The results of the two-dimensional device simulations differ significantly from the results of the Dyakonov-Shur model with its assumption of a homogeneous channel. It turns out that the impact on the damping of the two-dimensional structure is even stronger than the impact of the Pauli principle and scattering rendering plasma instabilities in transistors rather unlikely