Carbon nanotube field-effect transistor

A carbon nanotube field-effect transistor (CNTFET) refers to a field-effect transistor that utilizes a single carbon nanotube or an array of carbon nanotubes as the channel material instead of bulk silicon in the traditional MOSFET structure. First demonstrated in 1998, there have been major developments in CNTFETs since.

According to Moore's law, the dimensions of individual devices in an integrated circuit have been decreased by a factor of approximately two every two years. This scaling down of devices has been the driving force in technological advances since the late 20th century. However, as noted by ITRS 2009 edition, further scaling down has faced serious limits related to fabrication technology and device performances as the critical dimension shrunk down to sub-22 nm range. The limits involve electron tunneling through short channels and thin insulator films, the associated leakage currents, passive power dissipation, short channel effects, and variations in device structure and doping. These limits can be overcome to some extent and facilitate further scaling down of device dimensions by modifying the channel material in the traditional bulk MOSFET structure with a single carbon nanotube or an array of carbon nanotubes.

The exceptional electrical properties of carbon nanotubes arise from the unique electronic structure of graphene itself that can roll up and form a hollow cylinder. The circumference of such carbon nanotube can be expressed in terms of a chiral vector: Ĉ_h=nâ₁+mâ₂ which connects two crystallographically equivalent sites of the two-dimensional graphene sheet. Here n and m are integers and â₁ and â₂ are the unit vectors of the hexagonal honeycomb lattice. Therefore, the structure of any carbon nanotube can be described by an index with a pair of integers (n,m) that define its chiral vector.

In terms of the integers (n,m), the nanotube diameter d_t and the chiral angle θ are given by:

The differences in the chiral angle and the diameter cause the differences in the properties of the various carbon nanotubes. For example, it can be shown that an (n,m) carbon nanotube is metallic when n = m, has a small gap (i.e. semi-metallic) when n – m = 3i, where i is an integer, and is semiconducting when n – m ≠ 3i. This is due to the fact that the periodic boundary conditions for the one-dimensional carbon nanotubes permit only a few wave vectors to exist around the circumference of carbon nanotubes. Metallic conduction occurs when one of these wave vectors passes through the K-point of graphene’s 2D hexagonal Brillouin zone, where the valence and conduction bands are degenerate. For the semiconducting carbon nanotubes, there is a diameter dependency on bandgap. For example, according to a single-particle tight-binding description of the electronic structure, ${\displaystyle E_{g}=\gamma \left({\frac {2a}{d_{t}}}\right)}$ where γ is the hopping matrix element, and a is the carbon–carbon bond distance.

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