Numerical Simulation of Semiconductor Devices and Circuits for THz Applications

Electromagnetic waves with a frequency in the range from 0.1 to 10 THz are referred to as THz waves. They are difficult to generate, because their frequencies are on the one hand too high for efficient operation of state of the art solid-state devices and on the other too low for optical generators. Current generators extract the third harmonic of an oscillator, leading to extremely low power efficiency. This led to the proposal of a new kind of solid-state devices based on plasma waves in quasi 2D electron gases, where the THz signal is generated directly within the device. Since the dispersion relation of the plasma waves, their instabilities and the gain of the device depend on the structure, permittivity of the materials, dimensionality of the electron gas and its density, boundary conditions etc., it gives the device designer a lot of freedom and various device concepts have been proposed but yet not been realized. For accurate prediction of the device performance simulation engines employing an approach beyond the 1D transmission line models are required. The standard electron/hole transport models based on the Euler equation are to be generalized to describe transport in THz regimes, e.g. by a convective term or moments of higher order (e.g. hydrodynamic model). This requires novel numerical algorithms ranging from generalizations of the Scharfetter-Gummel stabilization, numerical integration techniques for THz oscillations, e.g. trigonometric spline-wavelet methods, to iterative linear and nonlinear solvers for huge systems of equations. The device behavior must be simulated within a circuit environment, since the signal power which can be decoupled depends on the termination of the device`s ports and each individual configuration has to be simulated since the circuit behavior is nonlinear. Thus, a coupled device/circuit simulator is required to investigate nonlinear effects.

In this project we strived to develop a general solver framework based on extended drift-diffusion models to investigate plasma instabilities for efficient generation of THz waves and the general impact of plasma oscillations on THz circuits. Since the classical drift-diffusion equation is parabolic we need to consider extended, hyperbolic models to simulate oscillations. In spite of fundamental, unforeseen problems, we developed a device simulator based on an extended drift-diffusion model. The investigation of various promising approaches led to new insights into the simulation of THz oscillations, and we were able to develop an efficient scheme, which we used to simulate a passive mixer circuit for THz wave detection. A simulation scheme for the two-dimensional problem is currently under development. Parallel to this development we investigated plasma waves using the Boltzmann equation and higher-order transport models derived from it. An unexpected result of these investigations were that even the Boltzmann equation discretized by the usual even/odd splitting fails under the quasi-ballistic conditions necessary for the Dyakonov-Shur instability. We were able to reuse our first method for the extended drift-diffusion model to discretize the Boltzmann equation directly in the phase space similar to Godunov's approach. This new scheme is stable even in the ballistic case, works with realistic boundary conditions, is efficient and permits more complex band structures and scattering models. We obtained first transient large-signal simulation results for a nanowire transistor. We will investigate if our stabilization scheme for the 2D drift-diffusion model can be applied to the Boltzmann equation. An important result was that the Dyakonov-Shur plasma instability seems to be an artifact of transport and contact modeling. If the fundamental Boltzmann equation is solved together with realistic boundary conditions, the Dyakonov-Shur instability vanishes. Thus, the impact of plasma resonances on the behavior of THz devices is much weaker than previously thought, and the generation of THz waves might not be feasible with the proposed devices. The classical drift-diffusion model stabilized by the Scharfetter-Gummel scheme yields only positive densities. This should be a fundamental property of all transport models. In order to better understand this property, we re-investigated the classical drift-diffusion model and were able to confirm this even in the transient case. First results for the new discretization of Boltzmann's equation suggest that it also exhibits this property which usually results in an improved numerical robustness. An interface for the coupling of a device/field simulator and a circuit simulator has been developed, which besides the actual simulation also handles the determination of initial values and the output of results. Using this interface, novel THz devices embedded in a larger circuit environment could be successfully tested.