ABSTRACT
A model describing the electromagnetic field propagation along a CNT is indispensable in order to study the interconnection performance of CNT while comparing with traditional metal
Lüttinger liquid theory [44] describes interacting electrons (or other fermions) in a one-dimensional conductor and is necessary since the commonly used Fermi liquid model breaks down in one-dimension. Burke [45,46] regards that electrons are strongly correlated when they transport along the CNT and proposed a transmission line model based on the Lüttinger liquid theory. Another transmission line model was built based on the Boltzmann transport equation (BTE) [47]. Two-dimensional electron gas, where the charged particles are confined to a plane and neutralized by an inert uniform rigid positive plane background was studied by Fetter [48,49]. Based on the work of Fetter [48,49], Maffucci et al. [50] investigated electron transport along the CNT and proposed a third model, fluid model. In these models [48-50], electron-electron correlation, which is significant in CNTs [51-53], has not been considered. The first model is based on quantum dynamics concepts; the second model requires solving the BTE; the third model has been developed within the framework of the classical electrodynamics and is simple on concepts and mathematical modeling.Interacting electrons in two and three-dimensions are well described in terms of an approximate model of weakly interacting quasi-particles, namely Fermi liquid theory. This model has been highly successful in explaining the properties of two and three-dimensional conductors. However, this approximate picture does not hold in one-dimension. Instead, the ground state of an interacting one-dimensional electron gas (1DEG) is a strongly correlated state known as a Lüttinger liquid. Unlike in a Fermi liquid, in a Lüttinger liquid, the low energy excitations are Bosonic sound-like density waves (plasmas). In two-dimensional electron gas model [48-50], electron-electron correlation has not been considered in studying electron transport in CNTs. Although the Lüttinger liquid model using quantum mechanical concept considers this correlation, the result and expression are too complicated to be solved. As quasi one-dimensional system, quantum effects [54] must be considered to characterize CNT interconnects. Therefore, we have made modification to the two-dimensional electron gas model to include electron-electron interactions and built one-dimensional liquid model [55], which is relatively easy to solve and apply in transmission line SWCNT
S parameters and group delays of SWCNT interconnect for RF/ microwave applications. In the following sub-sections, we will first describe the two-dimensional fluid model and our one-dimensional fluid model of SWCNTs.
