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 t unnel current as a function of STM bias was calculated by statistical avera ging over a distribution of wave packets in the allowed energy window. Thre e tunneling situations were studied: (i) a STM tunnel junction with no nano tube 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, a t the nanotube/substrate, and at both interfaces were also investigated. Th e theory allowed us to identify components of pure geometrical origin respo nsible for the asymmetry in the scanning tunneling spectroscopy (STS) spect rum of the carbon nanotubes with respect to bias voltage polarity. The calc ulations show that for tip negative bias the angular dependence of the tran smission is determined by the tip shape. The particular tip shape introduce s an asymmetry on the negative side of the STS spectrum. For tip positive b ias the angular dependence of the transmission depends strongly on the natu re of the nanosystem in the STM gap. While the transmission of the STM tunn el junction with no nanotube present can be well represented by a one dimen sional 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 cont acts between the nanotube and the substrate cause an asymmetry in the posit ive side of the STS spectrum. Calculated STS spectra are compared to experi mental ones.