Appearance of a knee on the Fowler–Nordheim plot of carbon nanotubes on a substrate

Existing theories for electron-field emission of carbon nanotubes (CNTs) cannot interpret why there appears in certain cases a knee on some Fowler–Nordheim (F–N) plots while not on others. We consider the interaction between substrate and CNTs and introduce a double-barrier model to explain the knee on the F–N plot. The knee on the F–N plot is a consequence of the transition from direct tunneling to F–N tunneling. The absence of the knee for the CNT films on titanium is attributed to the removal of the interface barrier by the formation of a conductive titanium carbide interlayer. The double-barrier model is helpful in understanding the field emission mechanism of CNTs and can explain the experimental results regardless whether or not there is a knee on F–N plot.