Finite-Difference Time-Domain Method And Its Application In Simulation Of Carbon-Based Interconnects

With the rapid development of integrated circuit technology, serious challenges will emerge in the design of devices and interconnects in future nano-scale integrated circuits. Considering the bottlenecks in the conventional copper interconnects, it is very important to develop novel interconnect technologies for nano-scale applications. As a good candidate of future nano-scale interconnects, carbon nanotube interconnects have attracted a great deal of research interest in recent years. For modeling and simulation of nano-scale interconnects, more efficient algorithms in computational electromagnetics will be needed, especially for fast modeling of objects with fine structure. Finite-difference time-domain (FDTD) is a popular numerical method in simulation and transient analysis of integrated circuit interconnects. However, its efficiency is limited by the numerical stability condition and numerical dispersion error. Hence it is quite important to improve the numerical stability and the computational efficiency of FDTD method for application in nanometer electronics.The work in this dissertation focuses on the development of novel unconditionally stable FDTD methods as well as modeling and analysis of nano-scale integrated circuit interconnects based on multiwall carbon nanotubes (MWCNTs). Several efficient FDTD methods with both unconditional stability and high accuracy are proposed, including the derivations of the updating formulae, the demonstrations of the validities, and performance comparisons. The FDTD method is then used to analyze the performance of MWCNT interconnects by virtue of the equivalent circuit model of transmission line. The signal delay and crosstalk, inserting of repeaters, and self-heating effects in future MWCNT interconnects have been investigated.The main innovative contributions of this dissertation include(1) An unconditionally stable Laguerre-FDTD algorithm for solution of wave equation is proposed, and then the implementation of perfectly matched layer (PML) absorbing boundary conditions in this novel method is presented. The novel method is very efficient since decoupled wave equation instead of Maxwell equations is used in this method, which leads to an observable reduction of the number of unknows.(2) A mixed method named Laguerre-PSTD (Pseudo-Spectral Time-Domain) method is proposed, which integrates the advantages of both Laguerre-FDTD and PSTD. This integrated method is not only unconditionally stable, but also memory efficient.(3) Based on the implicit spatial difference scheme of the fourth-order, a higher-order locally one-dimensional FDTD (LOD-FDTD) method is proposed to improve the numerical accuracy. Then this method is further improved with a parameter optimization processing which remarkably reduce the numerical error.(4) A simple absorbing boundary condition for the three dimensional (3-D) LOD-FDTD method is presented. Then a novel 3-D LOD-FDTD method with improved numerical accuracy is proposed. By virtue of introduction of three controlling parameters in the update scheme, the numerical error in this novel method is observably reduced, involving little additional computation time.(5) Closed-form formulae for estimation of the time delay and the number of repeaters needed in a single MWCNT interconnect are presented. The validities of these analytical formulae are demonstrated with comparison to the results of FDTD simulation of the equivalent circuit model.(6) The time delay and crosstalk in future MWCNT interconnect system are studied by FDTD circuit simulation. Compared to their copper counterparts, MWCNT interconnects can observably benefit from time delay.(7) The heat conduction equation in MWCNT interconnects is constructed and then solved with the finite difference method together with electric transport equations. The temperature profiles along a set of individual MWCNT interconnects with different lengths are derived and the self-heating effects are carefully discussed.