Towards Multi-Scale Modeling of Carbon Nanotube Transistors

Multiscale simulation approaches are needed in order to address scientific and technological questions in the rapidly developing field of carbon nanotube electronics. In this paper, we describe an effort underway to develop a comprehensive capability for multiscale simulation of carbon nanotube electronics. We focus in this paper on one element of that hierarchy, the simulation of ballistic CNTFETs by self-consistently solving the Poisson and Schrödinger equations using the non-equilibrium Green's function (NEGF) formalism. The NEGF transport equation is solved at two levels: i) a semi-empirical atomistic level using the p z 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. Simulation examples show that these approaches describe quantum transport effects in nanotube transistors. The paper concludes with a brief discussion of how these semi-empirical device level simulations can be connected to ab initio, continuum, and circuit level simulations in the multi-scale hierarchy. 2 12/1/03 1. Introduction Carbon nanotubes show promise for applications in future electronic systems, and the performance of carbon nanotube transistors, in particular, has been rapidly advancing [Win02, Jav03]. From a scientific perspective, carbon nanotube electronics offers a model system in which to explore and understand the effects of detailed microstructure of contacts, interfaces, and defects. It is also an opportunity to develop the theory and computational techniques for the atomistic simulation of small electronic devices in general. A detailed treatment of carbon nanotube electronics requires an atomistic description of the nanotube along with a quantum mechanical treatment of electron transport, both ballistic and with the effects of dissipative scattering included. As shown in Fig. 1, even for this simple system, multi-scale methods are essential. Metal/nanotube contacts, nanotube/dielectric interfaces, and defects require a rigorous, ab initio treatment, but to treat an entire device, simpler, p z orbital descriptions must be used. Techniques connect different descriptions used for different regions of the device will need to be developed (e.g. the ab initio basis functions for the metal/nanotube contacts must be connected to the semi-empirical basis functions for the device itself). For extensive device optimization, continuum, effective mass level models may be necessary, and methods to relate the phenomenological parameters in those approaches to the atomistic models must be developed. For circuit simulation, even simpler, analytical models are needed, and efficient techniques for extracting …