Knock-on damage in bilayer graphene: Indications for a catalytic pathway

We study by high-resolution transmission electron microscopy the structural response of bilayer graphene to electron irradiation with energies below the knock-on damage threshold of graphene. We observe that one type of divacancy, which we refer to as the butterfly defect, is formed for radiation energies and doses for which no vacancies are formed in clean monolayer graphene. By using first principles calculations based on density-functional theory, we analyze two possible causes related with the presence of a second layer that could explain the observed phenomenon: an increase of the defect stability or a catalytic effect during its creation. For the former, the obtained formation energies of the defect in monolayer and bilayer systems show that the change in stability is negligible. For the latter, ab initio molecular dynamics simulations indicate that the threshold energy for direct expulsion does not decrease in bilayer graphene as compared with monolayer graphene, and we demonstrate the possibility of creating divacancies through catalyzed intermediate states below this threshold energy. The estimated cross section agrees with what is observed experimentally. Therefore, we show the possibility of a catalytic pathway for creating vacancies under electron radiation below the expulsion threshold energy.

Figure 1

Two different displacement cross sections as a function of the incoming electronic energy. The function obtained by McKinley and Feshbach (dark) predicts a displacement threshold energy of $E_{\mathrm{thr}}^{MF}\approx 110$ keV. If the zero-point motion of the carbon atoms in graphene is taken into account (light), the displacement threshold energy is not well defined and the experimental results are much better reproduced.

Figure 2

Experimental images obtained by HRTEM on bilayer graphene. (a) Overview image showing Moiré pattern. In the regions marked by the circles the distortions of the pattern are visible. (b) The same area, but the honeycomb lattices of both layers are removed by Fourier filtering. Characteristic patterns in the shape of double dumbbells appear inside the circles indicating the same type of lattice distortion in all three places. (c) Enlarged image of one of the distorted Moiré pattern areas. (d)–( f) Fourier filtered images of enlarged area with the second (d), first (e) and both graphene layers filtered out (f). The image of the first layer only (d) can be directly interpreted in terms of atom positions and reveals a V${}_2$(5555-6-7777) butterfly defect formation in this layer. The image of the second layer (e) cannot be interpreted directly and needs simulations in order to find its origin.

Figure 3

(a) Experimental image averaged over all observed butterfly defects clearly showing its structure and a corresponding drawing of the defect. Four heptagonal (red), four pentagonal (green), and one rotated central hexagonal (blue) rings are formed instead of the original hexagonal lattice. (b) Atomic model of the graphene layers used for image simulations. One of the layers is rotated an angle $\alpha =11.2^{\circ }$. Different local stackings are formed in different small areas within the large hexagons.

Figure 4

Central part of the simulated image shown at the same scale and with the same processing as experimental images in Figs. 2c, 2d, 2e, 2f. The butterfly defect is located in the first layer and the second one is kept pristine. The feature similar to Fig. 2e is observed on the simulated second layer (c) comprising pristine graphene. It can be thus concluded that this feature in the second layer is an artifact of Fourier filtering.

Figure 5

Enlarged experimental HRTEM images obtained during experiment. The second honeycomb latticeis filtered out. (a) Two V${}_2$(5-8-5) divacancies are distinguished in the first layer. (b) After 7.5 $e$/nm${}^2$ of electronic dose, one of the divacancies (left) is in the process of transformation while the other (right) is converted into a butterfly defect.

Figure 6

Calculated atomic displacements multiplied by a factor of 200 in the perpendicular direction of the graphene sheets made by the presence of the butterfly defect in monolayer and bilayer graphene. The formation energy difference of the defect between both systems is negligible in this context.

Figure 7

(a) Initial state of the AIMD simulation with a Stone-Wales defect. It is made by two heptagonal (red) and two pentagonal (green) carbon rings. The blue arrow points in the direction ($\theta ={12}^{\circ }$, $\phi =1^{\circ }$) of the initial velocity ($T=17$ eV) which is given to the scattered atom (atom 1). (b) Final state of the same simulation in which the intimate Frenkel pair is stabilized. In the upper layer a vacancy is formed (black) and the scattered atom remains trapped between both layers (blue, atom 1) bridging the upper layer (dark) with the lower layer (light). Atom 2 is “kicked” in the next simulation to obtain the intimate bi-Frenkel pair.

Figure 8

Final relaxed configuration of an intimate bi-Frenkel pair. The initial state contains a unique intimate Frenkel pair (Fig. 6) and a certain velocity ($T=15$ eV, $\theta ={20}^{\circ }$, $\phi ={153}^{\circ }$) is given to the scattered atom. The V${}_2$(5-8-5) divacancy (black) is formed in the upper layer while the two scattered atoms (blue) are bridging the upper layer (dark) with the lower layer (light). (a) and (b) correspond to different perspectives.