Large Bandgap Shrinkage from Doping and Dielectric Interface in Semiconducting Carbon Nanotubes

The bandgap of a semiconductor is one of its most important electronic properties. It is often considered to be a fixed property of the semiconductor. As the dimensions of semiconductors reduce, however, many-body effects become dominant. Here, we show that doping and dielectric, two critical features of semiconductor device manufacturing, can dramatically shrink (renormalize) the bandgap. We demonstrate this in quasi-one-dimensional semiconducting carbon nanotubes. Specifically, we use a four-gated device, configured as a p-n diode, to investigate the fundamental electronic structure of individual, partially supported nanotubes of varying diameter. The four-gated construction allows us to combine both electrical and optical spectroscopic techniques to measure the bandgap over a wide doping range.