Graphene Field Effect Devices and Circuits

Electronics today permeate our life and existence. It has become nearly impossible to evade any dependence on electronic devices that surround us every day - computers, phones, televisions. But also other objects become increasingly "smart" - watches, cars, coffee machines, even entire buildings. Without necessarily being aware of it, every person in our modern world is the owner of billions, probably tens of billions of transistors. These elementary switches are the primitive units, of which all electronic devices are made, much like biological cells constitute our bodies. Decades of technological progress at an incredible pace have been fueled by the constant improvement of semiconductor device technology. The original combination of silicon, silicon dioxide and aluminum required to build a transistor, has been complemented by a myriad of other materials. One of the last remainders of the original technology, the silicon channel, is now about to be replaced as well. While a short term remedy for the next performance bottleneck might be found in III-V compounds a more compelling alternative could be found in 2D materials. Graphene was not only the first 2D material to be discovered and isolated in 2004, but also has the most extraordinary electric properties, owing to the high symmetry of its lattice. The content of this thesis presents a broad examination of the graphene field effect device reaching from the fabrication over electrical characterization to data analysis, device modeling and finally simulation of a small circuit. In this thesis, we present practical considerations regarding the experimental examination of graphene field-effect devices. A fabrication flow tailored for top-gated graphene devices was developed, taking into account the particular requirements and sensitivities of the material. We also describe a set of versatile software tools that were developed for the design of devices, chips and wafers, their automated electric characterization and finally for browsing and visualizing the measurement results. The data analysis was performed with a very effective conductance-based model, which is based on semi-empirical models commonly used to describe graphene devices. We provide an overview of these models, the phenomena which they take into account and the steps that can be taken to improve their accuracy to obtain the model we finally utilized. A environment was created to use our model in a \textsc{Spice}-like circuit simulator in order to study possible topologies in which graphene devices could constitute an elementary circuit block. We focus our study on devices that operate as a differential pair, resembling the configuration that also enables very high-speed source-coupled and emitter-coupled logic circuits based on standard silicon transistors. Using analytical calculations we determine tuning parameters and their optimum values to maximize the transfer characteristics of our graphene-based differential circuit block. In order to achieve more accurate simulation and as a means to verify the empirical model, we worked on a more rigorous approach. Based on first principles, we construct a model building on the specific carrier statistics in graphene. These deviate from the usual Boltzmann statistics and lead to a an equation describing the device's charge-voltage relation, which is transcendental and cannot ordinarily be solved. By using asymptotic approximations, we obtain closed-form expressions for the device current as a function of bias conditions. Unlike many other models, we can discriminate both between electron and hole currents as well as between drift and diffusion currents, making the model well-suited for implementation as a compact model.