Sub-10nm wide graphene nanoribbon field-effect transistors (GNRFETs) are studied systematically. All sub-10nm GNRs afforded semiconducting FETs without exception, with I on /I off ratio up to 10 6 and on-state current density as high as ~2000μA/μm. We estimated carrier mobility ~200cm 2 /Vs and scattering mean free path ~10nm in sub-10nm GNRs. Scattering mechanisms by edges, acoustic phonon and defects are discussed. The sub-10nm GNRFETs are comparable to small diameter (d≤~1.2nm) carbon nanotube FETs with Pd contacts in on-state current density and I on /I off ratio, but have the advantage of producing allsemiconducting devices.

The performance limits of monolayer transition metal dichalcogenide transistors are examined with a ballistic MOSFET model. Using ab-initio theory, we calculate the band structures of two-dimensional (2D) transition metal dichalco-genide (MX 2 ). We find the lattice structures of monolayer MX 2 remain the same as the bulk MX 2 . Within the ballistic regime, the performances of monolayer MX 2 transistors are better compared to the silicon transistors if thin high-κ gate insulator is used. This makes monolayer MX 2 promising 2D materials for future nanoelectronic device applications.

Abstract. We present a novel framework, namely AADMM, for acceleration of linearized alternating direction method of multipliers (ADMM). The basic idea of AADMM is to incorporate a multi-step acceleration scheme into linearized ADMM. We demonstrate that for solving a class of convex composite optimization with linear constraints, the rate of convergence of AADMM is better than that of linearized ADMM, in terms of their dependence on the Lipschitz constant of the smooth component. Moreover, AADMM is capable to deal with the situation when the feasible region is unbounded, as long as the corresponding saddle point problem has a solution. A backtracking algorithm is also proposed for practical performance.

We investigated the chlorine plasma reaction with graphene and graphene nanoribbons and compared it with the hydrogen and fluorine plasma reactions. Unlike the rapid destruction of graphene by hydrogen and fluorine plasmas, much slower reaction kinetics between the chlorine plasma and graphene were observed, allowing for controlled chlorination. Electrical measurements on graphene sheets, graphene nanoribbons, and large graphene films grown by chemical vapor deposition showed p-type doping accompanied by a conductance increase, suggesting nondestructive doping via chlorination. Ab initio simulations were performed to rationalize the differences in fluorine, hydrogen, and chlorine functionalization of graphene.

We investigate the thermoelectric properties of graphene nanoribbons (GNRs) by solving atomistic electron and phonon transport equations in the nonequilibrium Green’s function formalism. The dependence of thermopower on temperature and chemical potential is compared to that of graphene, which shows the important role of quasi-one-dimensional geometry in determining the thermoelectric properties of a GNR. The edge roughness and lattice vacancy are found to increase the thermopower but decrease the thermoelectric ZT factor because the decrease in the electronic conductance outweighs the decrease in the thermal conductance and the increase in the thermopower.

Graphene nanoribbons with perfect edges are predicted to exhibit interesting electronic and spintronic properties, notably quantum-confined bandgaps and magnetic edge states. However, so far, graphene nanoribbons produced by lithography have had rough edges, as well as low-temperature transport characteristics dominated by defects (mainly variable range hopping between localized states in a transport gap near the Dirac point). Here, we report that one- and two-layer nanoribbon quantum dots made by unzipping carbon nanotubes exhibit well-defined quantum transport phenomena, including Coulomb blockade, the Kondo effect, clear excited states up to ∼20 meV, and inelastic co-tunnelling. Together with the signatures of intrinsic quantum-confined bandgaps and high conductivities, our data indicate that the nanoribbons behave as clean quantum wires at low temperatures, and are not dominated by defects.

We present a novel accelerated primal-dual (APD) method for solving a class of deterministic and stochastic saddle point problems (SPP). The basic idea of this algorithm is to incorporate a multi-step acceleration scheme into the primaldual method without smoothing the objective function. For deterministic SPP, the APD method achieves the same optimal rate of convergence as Nesterov's smoothing technique. Our stochastic APD method exhibits an optimal rate of convergence for stochastic SPP not only in terms of its dependence on the number of the iteration, but also on a variety of problem parameters. To the best of our knowledge, this is the first time that such an optimal algorithm has been developed for stochastic SPP in the literature. Furthermore, for both deterministic and stochastic SPP, the developed APD algorithms can deal with the situation when the feasible region is unbounded, as long as a saddle point exists. In the unbounded case, we incorporate the modified termination criterion introduced by Monteiro and Svaiter in solving SPP problem posed as monotone inclusion, and demonstrate that the rate of convergence of the APD method depends on the distance from the initial point to the set of optimal solutions.

We propose a novel method, namely the accelerated mirror-prox (AMP) method, for computing the weak solutions of a class of deterministic and stochastic monotone variational inequalities (VI). The main idea of this algorithm is to incorporate a multi-step acceleration scheme into the mirror-prox method. For both deterministic and stochastic VIs, the developed AMP method computes the weak solutions with optimal rate of convergence. In particular, if the monotone operator in VI consists of the gradient of a smooth function, the rate of convergence of the AMP method can be accelerated in terms of its dependence on the Lipschitz constant of the smooth function. For VIs with bounded feasible sets, the estimate of the rate of convergence of the AMP method depends on the diameter of the feasible set. For unbounded VIs, we adopt the modified gap function introduced by Monteiro and Svaiter for solving monotone inclusion, and demonstrate that the rate of convergence of the AMP method depends on the distance from the initial point to the set of strong solutions.