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UBC Theses and Dissertations

A self-consistent numerical model for bipolar transport in carbon nanotube field-effect transistors Clifford, Jason Paul


Carbon nanotube (CNT) field-effect transistors (CNTFETs) utilize a semiconducting CNT channel controlled by an isolated electrostatic gate. The essential physics of these devices is captured in a numerical model that allows calculation of energy band diagrams and currentvoltage (I-V) relationships to describe their behavior. The numerical CNTFET device model is based on a solution to Poisson's equation that links the electrostatic potential everywhere in the device to charge induced in the CNT. This charge is a function of the local electrostatic potential and can be calculated from the carrier distribution and the local density of states for the nanotube. Under equilibrium conditions the carrier distribution within the CNT channel is known precisely. However, under non-equilibrium conditions (when a source-drain bias is present) carrier distributions in the channel are distorted from their equilibrium forms due existence of hot electrons and holes emitted from the source and drain, respectively. Quasi-equilibrium Fermi statistics are used to approximate non-equilibrium carrier distributions using an equilibrium distribution function shifted in energy. Solving Poisson's equation self-consistently for charge and the electrostatic potential provides a profile of potential energy along the length of the CNT channel. Current flow in the device is a function of the ability of carriers to tunnel through or be thermionically emitted over the potential barriers in the channel. The contribution of both electrons and holes is considered when solving Poisson's equation and calculating the drain current. The numerical CNTFET model is a flexible framework for the examination of a wide variety of device geometries and materials parameters. It employs a finite element package to solve Poisson's equation in a two-dimensional projection of a cylindrical model space with azimuthal symmetry. The technique of conformal mapping is used to allow exact electrostatic solutions in unbounded structures without imposing artificial boundary conditions. The geometry and materials parameters of the CNTFET are systematically varied and the effects of these changes are observed in the performance predictions of the model. The model is also used to explore the behavior of more complex experimental architectures, such as partially gated CNTFETs, and provides new insight into their operation.

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