Theoretical Modelling of Charge Transport Properties of Individual Single-Wall Carbon Nanotubes

Abstract

Experimental projection of transport properties of semiconductor devices faces a challenge nowadays. As devices scale to nanometre scale range, the classical transport equations used in current device simulators can no longer be applied. Conversely, the use of a more accurate and better non-equilibrium green function (NEGF) is limited by the fact that it requires excessive quantum of memory and computational time, having quasi-separable matrices that are extremely convoluted to solve. This work exploits the Boltzmann Transport Equation (BTE) to assess the transport properties of carbon nanotubes. Previous works on solving the BTE have employed either a stochastic method or an approximate method, both of which do not possess the necessary properties for practical device applications. Therefore, this work represents the first direct theoretical solution of the BTE for one-dimensional carbon nanotubes that can be utilized for practical device applications. The complete spectrum of transport in CNTs extending from ohmic to high-field through ballistic transmission is examined to delineate plethora of transport properties. The transport for arbitrary values of the electric field is based on the BTE applied to experimental data on CNTs. In the limit of low field, the mobility expressions are obtained in terms of the mean free path (mfp) that is distinctly shorter than the length of the sample. The ohmic resistance is quantized a value of 6.453k-ohms consistent with experimental findings with transmission approaching unity as channel length shrinks below the carrier mfp. The emission of a quantum was observed to lower the saturation velocity that is independent of scattering and hence ballistic. Transition to ballistic domain was found to occur when the channel length is scaled below the ballistic limit that is shown to be the extended version of the long-channel mfp modulated by injections from the contacts, yet the mobility degrades. The mobility degradation is shown to be the cause of resistance quantum in the low-channel length limit. These findings are important in predicting the transport properties of low-dimensional CNTs.