Modeling of graphene geometrical rectifiers

Ballistic geometric rectifiers represent a novel class of electron devices whose working principle is based on the peculiar properties of ballistic transport. In this regime, charge carriers behave like "billiard balls," and non-linear transport effects can be achieved considering certain shapes of the device. Ballistic transport occurs when the mean free path of the carriers is comparable to the device dimensions. The mean free path is strongly dependent on the temperature and on the scattering mechanisms that could occur in a specify material. For this reason, early prototypes of these rectifiers, typically fabricated on III-V materials, required cryogenic temperatures (around a few K) to operate. However, the discovery of graphene, with its high mean free path at room temperature, has sparked renewed interest, as it enables the fabrication of such devices that function under ambient conditions. Although several experimental and theoretical works have been devoted to understand the working principles of ballistic rectifiers, many aspects remain unexplored. To this end, the aim of this thesis is to investigate how the geometric parameters and the transport conditions (ballistic or with scattering) affect the rectification performance of these devices. For this purpose, a self-consistent Monte Carlo simulator has been developed, coupling the charge transport in the graphene layer with 3-D electrostatics arising from the gate voltage under the oxide substrate where the graphene is placed. This thesis focuses on two types of graphene-based ballistic rectifiers: the two-terminal "Geometric diode" and the four-terminal rectifier. For the geometric diode, we initially studied the impact of electrostatic effects, arising from gate voltage, on the device's non-linear behavior in the ballistic regime. Additionally, the study explores how geometric parameters affect non-linearity, identifying potential optimal configurations. Furthermore, the impact of various scattering mechanisms, typical in graphene on silicon oxide, on non-linearity is also investigated. For the four-terminal rectifier, we developed a model based on a combination of Monte Carlo transport (without self-consistency) and Landauer-Büttiker formalism. This model evaluates how non-linearity is influenced by key geometric parameters, bias voltage, and different scattering mechanisms. Finally, this thesis outlines ongoing modeling work. In particular, the development of a Monte Carlo simulator which uses the numerical solution of Maxwell's equation ( calculated with the FDTD method) to study the behavior of such devices in the time-domain and the development of a self-consistent Monte Carlo simulator to describe the behavior of the four-terminal rectifier.