Sublattice asymmetry of impurity doping in graphene: A review

Abstract

In this review we highlight recent theoretical and experimental work on sublattice asymmetric doping of impurities in graphene, with a focus on substitutional nitrogen dopants. It is well known that one current limitation of graphene in regards to its use in electronics is that in its ordinary state it exhibits no band gap. By doping one of its two sublattices preferentially it is possible to not only open such a gap, which can furthermore be tuned through control of the dopant concentration, but in theory produce quasi-ballistic transport of electrons in the undoped sublattice, both important qualities for any graphene device to be used competetively in future technology. We outline current experimental techniques for synthesis of such graphene monolayers and detail theoretical efforts to explain the mechanisms responsible for the effect, before suggesting future research directions in this nascent field.

Keywords: band gap; electronic transport; graphene; nitrogen doping; sublattice asymmetry.

Figure 1

Schematic of a graphene lattice with the most common experimentally observed species of substitutional nitrogen dopants: (A) a single graphitic, (B) three pyridinics, (C) one N₂^AA pair, (D) one N₂^AB pair and (E) one N₂^AB′ pair.

Figure 2

STM images of nitrogen doped graphene on (a) 7 nm², (b) 20 nm² and (c) 100 nm² scales, adapted with permission from Zabet-Khosousi et al. [41]. Copyright 2014 American Chemical Society. The dopants locations are identified by finding bright spots on the STM image, corresponding to slight perturbations in the positions of the neighbouring carbon atoms. The dopant sublattice can be found through the orientation of the bright triangle features, where opposite sublattices appear as mirror images of each other as demonstrated in (a). The red and blue triangles in each subfigure correspond to impurities on the different sublattices. Part (c) best demonstrates that although the distribution of dopants appears random, when their sublattice is identified we see two very large domains appear with opposite sublattice segregation. Shown at the bottom, off-center left of (c) is a white 10 nm scalebar.

Figure 3

Predicted band gap against nitrogen dopant concentration. Black circles are calculated values from [36] and the red dashed line shows the expected band gap scaling with concentration, according to the power 3/4 as discussed in the text.

Figure 4

Quantum conductance through a 15 nm wide graphene nanoribbon with a 7.5 nm long scattering region containing a dispersion of substitutional nitrogen impurities, in a similar vein to the method of Botello-Mendez et al. [37], calculated using a recursive Green’s Function method [–56], the Kubo formula for conductance [57] and a configurational average of 50 systems. Energy is in units of the tight binding nearest neighbour hopping energy between carbon atoms, t = 2.7 eV. Shown is the predicted conductance for pristine (black), randomly doped (green solid) and single sublattice doped (red dashed) systems, where a dopant concentration of 1% nitrogen was used.