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Graphene Nanoribbons: from chemistry to circuits

The Y-chart is a powerful tool for understanding the relationship between various views (behavioral, structural, physical) of a system, at different levels of abstraction, from high-level, architecture and circuits, to low-level, devices and materials. We thus use the Y-chart adapted for graphene to guide the chapter and explore the relationship among the various views and levels of abstraction. We start with the innermost level, namely, the structural and chemical view. The edge chemistry of patterned graphene nanoribbons (GNR) lies intermediate between graphene and benzene, and the corresponding strain lifts the degeneracy that otherwise promotes metallicity in bulk graphene. At the same time, roughness at the edges washes out chiral signatures, making the nanoribbon width the principal arbiter of metallicity. The width-dependent conductivity allows the design of a monolithically patterned wide-narrow-wide all graphene interconnect-channel heterostructure. In a three-terminal incarnation, this geometry exhibits superior electrostatics, a correspondingly benign short-channel effect and a reduction in the contact Schottky barrier through covalent bonding. However, the small bandgaps make the devices transparent to band-to-band tunneling. Increasing the gap with width confinement (or other ways to break the sublattice symmetry) is projected to reduce the mobility even for very pure samples, through a fundamental asymptotic constraint on the bandstructure. An analogous trade-off, ultimately between error rate (reliability) and delay (switching speed) can be projected to persist for all graphitic derivatives. Proceeding thus to a higher level, a compact model is presented to capture the complex nanoribbon circuits, culminating in inverter characteristics, design metrics and layout diagrams.