In the quest for the further miniaturization of electronic devices, numerous fabrication techniques have been developed. The semiconductor industry has been able to manifest miniaturization in highly complex and ultra low-power integrated circuits and devices, transforming almost every aspect of our lives. However, we may have come very close to the end of this trend. While advanced machines and techniques may be able to overcome technological barriers, theoretical and fundamental barriers are inherent to the top-down miniaturization approach and cannot be circumvented. As a result, the need for novel and natural alternatives to replace old materials is valued now more than ever. Fortunately, there exists a large group of materials that essentially has low-dimensional (quasi-one- or quasi-two-dimensional) structures. Graphene, a two-dimensional form of carbon, which has attracted a lot of attention in recent years, is a perfect example of a prime material from this group. Niobium tri-selenide (NbSe3), from a family of trichalcogenides, has a highly anisotropic structure and electrical conductivity. At sufficiently low temperatures, NbSe3 also exhibits two independent "sliding charge density waves"– an exciting phenomenon, which could be altered by changing the overall size of the material. In NbSe3 (and Blue Bronze K0.3MoO3 which has a similar structure and electrical behavior), the effect of a periodic potential could be seen in creating a charge density wave (CDW) that is incommensurate to the underlying lattice. The required periodic potential is provided by the crystal ions when ordered in a particular way. The consequence is a peculiar non-linear conductivity behavior, as well as a unique narrow-band noise spectrum. Theoretical and experimental studies have concluded that the dynamic properties of resulting CDW are directly related to the crystal impurity density, and other pinning potentials. Therefore, reducing the overall size of the crystal could potentially alter the CDW behavior in a significant way. Theoretical studies, as well as preliminary experimental results, suggest exceptionally interesting charge carrier behavior, including an energy gap opening and an anisotropic modulation of carrier mobility, in graphene when it is under a periodic potential. The fabrication process to achieve the desired periodic structure, with the required length scale on graphene is a challenging one. Therefore, in this manuscript, the fabrication process and its challenges are discussed. The arrangement of the manuscript is as follows: In Chapter 1, first, I study the theory of charge density waves and their dynamics. Next, I describe the fabrication process for thin NbSe3 and Blue Bronze crystals and devices. Finally, I discuss the device measurement results, and compare them with bulk crystals. In Chapter 2, I focus on the fabrication of periodic potentials on graphene layers. I begin by providing the theoretical background and motivations of the project. Then, the fabrication process is discussed in details. And lastly, I present the fabrication and preliminary electrical measurement results. Chapter 3 is a summary of additional experiments that I performed during the course of my PhD.




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