Modeling of ac quantum transport through imperfect carbon nanotube interconnects by means of nonequilibrium Green's functions

Abstract

Because of their long mean free path and superior current-carrying capabilities, carbon nanotubes (CNTs) are considered as an alternative for Cu in future interconnects. To simulate their dynamical properties, a linear equivalent-circuit model is usually invoked containing, among other things, a kinetic inductance and a quantum capacitance. As this equivalent circuit has been derived for perfect CNTs, the effect of imperfections is lacking. Still, imperfections considerably change the CNTs’ characteristics, necessitating the development of novel accurate simulation techniques to aid the electronic interconnect designer. Therefore, in this paper, an ac nonequilibrium Green’s function modeling technique is constructed for CNT interconnects, yielding a fully quantum mechanical first-principles method. The implemented method abandons the often-used small-signal requirement and includes the self-consistent solution with the Poisson equation. Additionally, a new, generally valid approach to partition a CNT into small units is presented. This allows us to rewrite the Hamiltonian into a block tridiagonal form with small submatrices and, subsequently, to employ the recursive Green’s function algorithm in an efficient way. Comparison with the equivalent-circuit model serves as validation of the constructed technique, which is an essential, but challenging, task for periodically driven quantum transport problems. The results show that, in order to accurately model the kinetic inductance, the self-consistent solution with the Poisson equation is a fundamental requirement. The constructed method is used to investigate finite-size effects and vacancies, from which it is argued that local defects can, in the linear equivalent-circuit model, be approximated by means of an additional series resistance as long as the applied bias is small. For a large bias, however, nonlinear effects come into play and the circuit model is no longer valid. Lastly, it is demonstrated, both analytically and numerically, that the even harmonics of the current and the potential are absent within the nearest-neighbor tight-binding approximation for the Hamiltonian of the CNTs.