Breakdown of Richardson's Law in Electron Emission from Individual Self-Joule-Heated Carbon Nanotubes

Probing the validity of classical macroscopic physical laws at the nanoscale is important for nanoscience research. Herein, we report on experimental evidence that electron emission from individual hot carbon nanotubes (CNTs) heated by self-Joule-heating does not obey Richardson's law of thermionic emission. By using an in-situ multi-probe measurement technique, electron emission density (J) and temperature (T) of individual self-Joule-heated CNTs are simultaneously determined. Experimental ln(J/T-2)-1/T plots are found to exhibit an upward bending feature deviating from the straight lines in Richardson plots, and the measured electron emission density is more than one order of magnitude higher than that predicted by Richardson's law. The breakdown of Richardson's law implies a much better electron emission performance of individual CNTs as compared to their macroscopic allotropes and clusters, and the need of new theoretical descriptions of electron emission from individual low-dimensional nanostructures.