Simulation of scanning tunneling spectroscopy of supported carbon nanotubes

The angle and energy dependent transmission of wave packets was calculated through a jellium potential model of a scanning tunneling microscope (STM) junction containing different arrangements of carbon nanotubes. The total tunnel current as a function of STM bias was calculated by statistical averaging over a distribution of wave packets in the allowed energy window. Three tunneling situations were studied: (i) a STM tunnel junction with no nanotube present, (ii) one single wall nanotube in the STM junction, and (iii) a nanotube “raft.” The effects of point contacts at the STM tip/nanotube, at the nanotube/substrate, and at both interfaces were also investigated. The theory allowed us to identify components of pure geometrical origin responsible for the asymmetry in the scanning tunneling spectroscopy (STS) spectrum of the carbon nanotubes with respect to bias voltage polarity. The calculations show that for tip negative bias the angular dependence of the transmission is determined by the tip shape. The particular tip shape introduces an asymmetry on the negative side of the STS spectrum. For tip positive bias the angular dependence of the transmission depends strongly on the nature of the nanosystem in the STM gap. While the transmission of the STM tunnel junction with no nanotube present can be well represented by a one dimensional model, all other geometries cause a large normal-transverse momentum mixing of the wave packet. A diffraction-grating-like behavior is seen in the angular dependence of the transmission of the nanotube raft. Point contacts between the nanotube and the substrate cause an asymmetry in the positive side of the STS spectrum. Calculated STS spectra are compared to experimental ones.