Excess electron densities, as defined in Sec. I, for closed and open CNTs in the absence of any applied field. (a) Projection onto a plane transverse to the axis, showing the positions of carbon atoms in the top layer (green ), second layer (blue ) and third layer (red ), for closed CNT. (b) Projection onto a plane transverse to the axis, showing the positions of the hydrogen atoms (blue ) and the first ring of carbon atoms (red ), for open CNT. [(c) and (d)] Excess electron densities on planes containing the CNT axis and passing through one of the first layer atoms [the edges of the planes are shown in (a) and (b) as straight lines]. Distances parallel to the CNT axis are measured from the substrate surface. Positive density indicates excess of electrons, so red regions have conventional negative charge while blue regions have conventional positive charge. Note the existence of charge re-arrangements having the general nature of dipoles.
Total EEPEs in the absence of applied field: (a) above the nucleus of a pentagonal-ring atom in the closed CNT; (b) above a hydrogen-atom nucleus in the H-terminated open CNT. The starred points and the solid curve show the calculated values and a fitted curve, respectively.
To illustrate the excess electron densities associated with two of the atoms at the top pentagonal ring of the closed CNT. Field-induced surface dipoles are prominently visible. The plane of the view passes through two of the carbon-atom nuclei and is parallel to (but does not include) the tip axis. The horizontal axis represents distance parallel to the CNT axis.
The EEPE (in eV) in an intersection plane, parallel to the tube axis, through one of the terminated hydrogen atoms of the open CNT, in an applied macroscopic field of .
Variation of electrostatic electron PE for closed (red, solid curve) and open (blue, dotted curve) CNTs, along the lines specified in the text, in an applied macroscopic field of . The dashed green line represents the Fermi level, which is at relative to the zero-field vacuum level.
To show how the FEF varies with applied macroscopic field for (a) the closed CNT and (b) the H-terminated open CNT. The solid lines are fitted curves. The inset in (b) shows the linear relationship between and .
Emission current as a function of applied macroscopic field. The triangular points show the current from the closed CNT while the square points show the current from the open CNT. The inset shows the relationship in the form of FN plots.
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