  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.
