First-principles study of field-emission properties of nanoscale graphite ribbon arrays

We applied a simple yet accurate self-consistent method using the density-functional formalism to study the field-emission properties of nanographite ribbons. We found some properties that are unique to nanostructure arrays, including the field-emission current being dominated by the contribution from off-zone-center $\pi$ states in some of the cases because of specific wave function symmetries, and an anomalous current density dependence on the inter-ribbons separation due to edge dipole effects. The applicability of Fowler-Nordheim analysis and some related problems are also discussed.

Figure 1

(a) Structural schematics and (b) orientation of the unit cell for the nanographite ribbons with edges saturated by H atoms (open circles). The boundaries of primitive cells in the $y$ direction are shown using the dashed lines in (a), and the $E$ field $F$ is represented by an arrow in (b).

Figure 2

TED curves of the emission current from four types of ribbons ($D_x=5\mathrm{\AA }$, $F=0.2\mathrm{V}∕\mathrm{\AA }$) with $\vec{k}$ points being sampled in the full BZ for our calculations: (a) pristine zigzag; (b) H-terminated zigzag; (c) pristine armchair; (d) H-terminated armchair.

Figure 3

Band structures of four types of ribbons with $D_x=5\mathrm{\AA }$ under an $E$ field of $F=0.2\mathrm{V}∕\mathrm{\AA }$: pristine zigzag; (b) H-terminated zigzag; (c) pristine armchair; (d) H-terminated armchair.

Figure 4

(Color online) Contours of constant ${\vec{k}}_{\Vert }$-resolved emission current density in the 2D BZ for four types of ribbons with $D_x=5\mathrm{\AA }$ under an $E$ field of $F=0.2\mathrm{V}∕\mathrm{\AA }$: (a) pristine zigzag; (b) H-terminated zigzag; (c) pristine armchair; (d) H-terminated armchair.

Figure 5

TED curves of the emission current from four types of ribbons ($D_x=5\mathrm{\AA }$, $F=0.2\mathrm{V}∕\mathrm{\AA }$) with $\vec{k}$ points being sampled only along $\overline{\Gamma Y}$ line in the BZ for our calculations: (a) pristine zigzag; (b) H-terminated zigzag; (c) pristine armchair; (d) H-terminated armchair.

Figure 6

(a) Contour of real part of the wave function for the state “A” [see Fig. 3c] in the plane $z=2.0\mathrm{\AA }$ away from the ribbon edge; (b) contour of real part of the wave function for the state “B” [see Fig. 3c] in the plane of the ribbon strip. The open circles indicate the positions of the carbon atoms in-cluding four atoms at the pristine armchair ribbon edge: “C1,” “C2,” “C3,” and “C4.”

Figure 7

Contour of real part of the wave function for the dangling bond state at $E_F$ and $\overline{\Gamma }$ point of the pristine zigzag ribbon in the plane of the ribbon strip. The positions of the carbon atoms was indicated by using the open circles.

Figure 8

The total field-emission current density for four types of ribbons with different inter-ribbons distances $D_x$ under an $E$ field of $F=0.2\mathrm{V}∕\mathrm{\AA }$.

Figure 9

(a) Calculated work function ${\varphi }_{\mathrm{GGA}}$ for four types of ribbons with different inter-ribbons distances $D_x$ and (b) plots for ${\varphi }_{\mathrm{GGA}}$ versus $1∕D_x$.

Figure 10

The $y$-averaged local Coulomb potentials with $x$ coordinates fixed in the middle plane between the ribbon strips (solid line) and in the plane of the ribbon strip (dashed line) along the $z$ direction for four types of ribbons ($D_x=5\mathrm{\AA }$, $F=0$): (a) pristine zigzag; (b) pristine armchair; (c) H-terminated zigzag; (d) H-terminated armchair. The $z$-coordinates of all atoms are indicated by using the dot lines.

Figure 11

The FN plots of the total emission current density per the primitive cell along the ribbon edge (unit: $\mu \mathrm{A}∕\mathrm{nm}$) for four types of ribbons with $D_x=5\mathrm{\AA }$.