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Simulation studies of carbon nanotube field-effect transistors John, David Llewellyn

Abstract

Simulation studies of carbon nanotube field-effect transistors (CNFETs) are presented using models of increasing rigour and versatility that have been systematically developed. Firstly, it is demonstrated how one may compute the standard tight-binding band structure. From this foundation, a self-consistent solution for computing the equilibrium energy band diagram of devices with Schottky-barrier source and drain contacts is developed. While this does provide insight into the likely behaviour of CNFETs, a non-equilibrium model is required in order to predict the current-voltage relation. To this end, the effective-mass approximation is utilized, where a parabolic fit to the band structure is used in order to develop a Schrödinger-Poisson solver. This model is employed to predict both DC behaviour and switching times for CNFETs, and was one of the first models that captured quantum effects, such as tunneling [i.e. tunnelling] and resonance, in these devices. In addition, this model has been used in order to validate compact models that incorporated tunneling via the WKB approximation. A modified WKB derivation is provided in order to account for the non-zero reflection of carriers above a potential energy step. In order to allow for greater flexibility in the CNFET geometries, and to lift the effective-mass approximation, a non-equilibrium Green’s function method is finally developed, which uses an atomistic tight-binding Hamiltonian to model doped-contact, as opposed to Schottky-barrier-contact, devices. This approach benefits by being able to account for both inter- and intra-band tunneling, and by utilizing a quadratic matrix equation in order to improve the computation time for the required self-energy matrices. Within this technique, an expression for the local inter-atomic current is derived in order to provide more detailed information than the usual compact expression for the terminal current. With this final model, an investigation is presented into the effects of geometrical variations, contact thicknesses, and azimuthal variation in the surface potential of the nanotube.

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