Science and Application of Nanotubes / Fundamental Materials Research (PDF)

contact geometry, transport can occur in the direction parallel to the nanotube axis, in the case of the nanotube field-effect-transistor (FET),5,9 or perpendicular to it, in the case of the STS measurement.10,11 In the STS measurement, the Fermi-level is found to have shifted to the valence band edge of the semiconducting nanotube.10 Such observed Fermi-level "pinning" has been used to explain the operation of the nanotube FETs with highresistance contacts,5 where the measured two-terminal resistance for metallic nanotube is Recently low resistance contacts with two-terminal resistance as low as have been obtained.9 However, low temperature transport measurements using these low resistance contacts show that the Fermi-level is located between the valence and the conductance band of the semiconducting nanotube, instead of being "pinned" at the valence band edge. This conflict raises the important question of whether the Fermi-level positioning may depend on the contact geometry and the interface coupling. In this paper we present a theory of the scanning tunneling spectroscopy of a singlewall carbon nanotube (SWNT) supported on the Au(111) substrate.

The central idea is that the work function difference between the gold substrate and the nanotube leads to charge transfers across the interface, which induce a local electrostatic potential perturbation on the nanotube side. This atomic-scale interfacial potential perturbation shifts the energy level of the nanotube relative to the gold Fermi-level, and gives rise to the observed Fermi-level shift in the STS current-voltage characteristics. However, for transport in the direction parallel to the nanotube axis, as in the case of nanotube transistors, such local potential perturbation at the interface is not important in determining the Fermi-level position if the coupling between the metal and the nanotube is strong (i. e. , low resistance contact). In this case, the metal-induced gap states (MIGS) model provides a good starting point for determining the Fermi-level position. Based on this model, we expect that any discrepancy between the metal Fermi-level and the nanotube "charge-neutrality level" should be rapidly screened out by the metal-induced gap states in the nanotube side,12–14 leading to the "pinning" of the Fermi-level. Another important feature in our theory is that we have taken into account the localized 5d orbitals of the platinum tip in our treatment of the STS which can have significant effects on the interpretation of the STS data.15 Our discussion is restricted to the low temperature regime, in correspondence with the experimental works.

METHODS

A convenient way of characterizing the band lineup problem at any interface is to find a reference level, the role of which is to put all materials forming the interface on a common absolute energy scale.13,14 If the position of the reference level depends only on the bulk property, then the relative position of the energy bands at the interface can be determined trivially by merely lining up the reference levels. This is the elegant idea of "charge-neutrality level",12 which has been applied with impressive success by Tersoff13,14 to various metal-semiconductor junctions and semiconductor heterojunctions. For metal, the reference level is the Fermi-level while for semiconductor, it is the so called "charge-neutrality level" which can be taken as the energy where the gap states cross over from valence- to conduction-band character.

This approach greatly simplifies the band lineup problem and gives quantitatively accurate prediction of the Schottky barrier height when applied to the metalsemiconductor interface.13 The success of this model relies on the fact that there exists a continuum of gap states around at the semiconductor side of the metalsemiconductor interface due to the tails of the metal wavefunction decaying into the semiconductor, which can have significant amplitude a few atomic layers away from the interface.12 Any deviation from the local charge neutrality condition in the interface region will be screened out rapidly by these metal-induced gap states (MIGS). In this way, the local charge and potential perturbations right at the interface are not important in determining the barrier height observed in the transport characteristics since the range of this local perturbation is only a few atomic layers, and the charge carriers can easily tunnel through this region.