Quantitative correlation between carbon nanotube tip morphology and field emission properties at cryogenic temperature

We present a thorough analysis of the field emission properties of three varieties of vertically aligned carbon nanotubes (VA-CNTs), characterized by different morphologies as a consequence of different post-growth plasma etching treatments. Following the Fowler-Nordheim theory on field emission, we have determined the field enhancement factor β of the samples thanks to a precise measurement of their work function through ultraviolet photoemission spectroscopy, and through the study of the emitted electron current at a temperature of T = 2.8 K. We find that plasma etching has the effect of significantly increasing the β of the samples, reaching a high value of β = (15.2 ± 2.5) × 103 for the sample treated with the strongest etching. We have furthermore studied the morphology of the samples with an atomic force microscope (AFM), and measured the mean radius of curvature of the emitting tips, rc. We have found a relationship of the form β(rc) = k/rc, with k = (175 ± 13) μm, which allows prediction of the field-emission properties of a VA-CNT sample through a simple AFM scan.