Abstract

This paper reports advances in analyzing the network structure of carbon nanotube (CNT) networks. CNT devices continue to receive attention for a variety of applications. Unfortunately, understanding the characteristics of random networks formed by such tubes has stymied progress. With respect to transistors constructed from CNT networks, electron and hole mobility provide a measure of the rate of current flow as a gate voltage is applied. The higher the mobility, the faster the gate can switch; this leads to faster computation and faster processors, e.g. faster routers, wireless links, computers, etc. Mobility is relatively easy to predict for a single carbon nanotube. Unfortunately, mobility becomes extremely complex for networks of tubes. The performance of pure carbon nanotube networks and networks with impurities has been complicated by their random network structures. A model to predict CNT network device performance based on randomized tube layout and metallic tube characteristics has been needed in order to explore CNT network performance. This report develops a mathematical network model, implemented in Mathematica, based upon the eigenspectrum of the graph laplacian of the network. This technique allows the impact of individual tube characteristics on the entire network structure to be analyzed in detail rather than requiring aggregate and often-inaccurate estimates. The analytically derived values using the eigenspectrum approach are shown to match trends obtained from experimental measurements. Future technical reports will use this model to provide guidance in identifying methods to improve performance based upon such characteristics as distributions of tube angles and tube lengths. Mathematica commands are included in this report to demonstrate the operation of the software tool implementing the analysis as well as the theory behind its operation.