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In recent years, significant progress in understanding device physics and in identifying potential applications of carbon nanotube electronic devices has occurred. In a nanotube, low bias transport can be nearly ballistic across distances of several hundred nanometers. Deposition of high-K gate insulators does not degrade the carrier mobility. Carbon nanotube field-effect transistors (CNTFETs) with near ballistic operation and excellent device performance have been recently demonstrated. Developing physical simulation capabilities are important for understanding experiments and exploring device design issues. In this work ballistic CNTFETs was simulated by self-consistently solving the Poisson and Schrodinger equations using the non-equilibrium Green's function (NEGF) formalism. The NEGF transport equation is solved at two levels: i) an atomistic real space approach using the pz orbitals of carbon atoms as the basis, and ii) an atomistic mode space approach, which only treats a few subbands in the tube's circumferential direction while retaining an atomistic grid along the carrier transport direction. The real space approach resolves the nanotube channel in an atomistic scale along both transport and circumference directions.