Gate-dependent vacancy diffusion in graphene

Abstract

Kinetics of vacancy defect in graphene drives structural modifications leading to disorder, multivacancy complex and edge reconstruction. Within the first-principles calculations, we study the dynamic Jahn-Teller distortion and diffusion of a vacancy defect. Further, the intricate dependence of carrier doping is systematically investigated. The experimental observation of dynamic Jahn-Teller distortion is argued to be blocked by defect functionalization and charge doping. We demonstrate that lattice relaxation perpendicular to the graphene sheet along with the in-plane strain relaxation play predominant roles in predicting the correct microscopic mechanism for vacancy diffusion. The importance of quantum correction to the classical barrier is discussed. The calculated activation barrier increases upon both electron and hole doping and the observed trends are explained by the differential charge density distribution and hardening of the responsible low-energy phonon modes. Electron doping essentially freezes the vacancy motion, and thus any degradation mediated by it. While tracking and analyzing the vacancy diffusion experimentally in graphene is a difficult task, the present results will motivate new experimental efforts and assist interpretation of the results. arXiv:1803.04384v2 [cond-mat.mes-hall]

Mechanistic insights in phosphorene degradation

“…In comparison, the vacancy relaxation in graphene results in multiple Jahn-Teller distorted configurations, where the planar (5|9) vacancy is the ground state. [33] The second configuration SV(55|66) in phosphorene undergoes minor displacement of atoms to form pentagon and hexagon pairs [ Figure 1(b)]. The P-P bond along the armchair direction (2.57 Å) is weaker than both pristine (2.27 Å) and SV(5|9) defect with 2.41 Å bonds.…”

“…[59] The SV(5|9) vacancy is thermodynamically more stable than the SV(55|66) configuration [ Figure 1(c) and Table I]. Further, owing to a much lower E f , the vacancy formation is much easier in phosphorene than in graphene (∼ 7.5 eV) [33] and in mono-elemental bulk semiconductors such as Si and…”

“…In contrast, a relatively high barrier of 0.72 eV was calculated for the vacancy migration in graphene. [33] The aggregation of vacancy defects in an anisotropic environment will lead to the formation of line defects and grain boundaries, which in turn will act as a sink for diffusing vacancies. [37] Now we investigate the effect of layer thickness on the in-plane vacancy diffusion, and also discuss how the migration is affected while the vacancy is embedded in fewlayer phosphorene ( Figure 3).…”

“…[31] Thermally activated diffusion of point-defects holds the key to structural changes. Vacancy transformation, diffusion, and aggregation leading to the formation of complex defects and grain boundaries have been extensively studied in graphene, [32,33] where the weak bonding at the edges and vacancies initiate structural degradations. The few-layer phosphorene is observed to undergo anisotropic degradation, amorphization, and sublimation when heated above 650 K. [28,34,35] However, the current description of structural degradation stands at the diffusion of isolated vacancy within a single layer, [26,36,37] which severely limits our microscopic understanding.…”

“…Note that the vacancy formation is much easier in the few-layer phosphorene owing to the much lower E f compared to graphene and other mono-elemental bulk semiconductors. [33,38,39] However, the nature of oxygen-defect interaction in phosphorene is a subject of debate at present without any experimental understanding. While the oxidation is proposed to be an activated process, it is more favourable at a lattice vacancy than the pristine surface.…”