Stability of asymmetric grain boundaries in graphene

ECCOMAS Congress 2016 VII European Congress on Computational Methods in Applied Sciences and Engineering M. Papadrakakis, V. Papadopoulos, G. Stefanou, V. Plevris (eds.) Crete Island, Greece, 5–10 June 2016 STABILITY OF ASYMMETRIC GRAIN BOUNDARIES IN GRAPHENE J. P. Mendez1, F. Arca2and M. P. Ariza2 1Division of Engineering and Applied Science, California Institute of Technology, Pasadena, CA 91125, USA e-mail: [email protected] 2Escuela T´ ecnica Superior de Ingenier´ ıa, Universidad de Sevilla, Camino de los descubrimientos, s.n., 41092 Sevilla, Spain e-mail: {farca,mpariza}@us.es Keywords: Graphene, Asymmetric grain boundaries, Thermal stability. Abstract. In the field of electronics, due to its excellent mechanical and electrical properties, graphene has become the most promising material for the production of next generation thin and flexible graphene-based electronic components. In this work, we present an assessment of the thermal stability and dynamics of asymmetric grain boundaries in graphene for different misorientation angles at finite temperature and up to extremely high temperatures. In particular, we have focused on configurations with misorientation angle of 16.1◦, 30◦and 38.2◦. In contrast to pristine defect-free graphene, which has no band-gap and therefore is of limited use for semiconductor-based electronics, it has been shown theoretically that line defects in graphene might insert transport gaps, opening up the possibility of device applications based on the structural engineering of graphene boundaries. 188 J. P. Mendez1, F. Arca2and M. P. Ariza2 1 INTRODUCTION Graphene, owing to its extraordinary properties [1, 2], can be used to a wide range of applications: aerospace, where carbon fibers that are used to reinforce composite materials can be replaced by graphene and, as a result, the weight of aircraft might be reduced considerably as well as the electrical conductivity will be enhanced for lightning strikes during flights; military industry, where graphene can be used as substitution of Kevlar in bulletproof vest [3]; bioengineering, where graphene can be used to fabricate bioelectric sensors [4, 5]; or in the field of electronics, where graphene has become the most promising material for the production of thin and flexible electronic components of next generation [6, 7]. However, the use of graphene in semiconductor-based devices is limited due to the fact that free-defect graphene lacks band gap, which is crucial for the correct operation of these devices. In order to achieve an electrical function and due to the presence of band gap, semiconductors exhibit the ability to switch currents on and off as desired. Many attempts have been carried out in order to introduce this desired band gap, e.g., by doping graphene with boron and nitrogen [8] or by engineering defects such as vacancies, Stone-Wales and dislocations [9], and grain boundaries (GBs) [10]. It has been proved, either experimentally or theoretically, that the presence of point defects modify locally the electronic properties [11, 12], but do not endow the layer with a band gap wide enough for such applications. Nevertheless, it has been seen that the presence of grain boundaries alters the electronic properties, and more specifically, some configurations might introduce a transport gap across them that would block the charge carriers in a range of energy. As a consequence, due to the current technology advances, the design of suited GB configurations opens a new potential via to tailor a tunable transport gap in graphene and, therefore, to use graphene as the base material for the manufacturing of semiconductor-based devices, e.g., nanotransistors [13]. With the main target of tuning the carrier transport in graphene, we will carry out an appraisal of the stability and dynamics of asymmetric GBs that could appear in graphene lattice. Additionally, owing to the fact that temperature is always present during the performance of electronic devices, the thermal stability of these GBs will play an important role when designing electronic nanocomponents. Therefore, in this work we will also conduct an analysis of the thermal stability of the predicted GB configurations during a long period of time and up to extremely high temperatures. To this end, we will proceed by applying the same methodology followed by the authors for the thermal characterization of dislocations [14] and symmetric grain boundaries [10] in graphene. 2 ASYMMETRIC GRAIN BOUNDARIES IN GRAPHENE The simulation model used for studying the stability of GBs is depicted in Fig. 1. This model consists of two grains (A and B) with different crystallographic orientations (θ1and θ2) and periodic boundary conditions applied in both directions (X and Y axis). The boundary effects are an obstacle that one has to tackle in this kind of simulations and usually emerge when the cell size is small. Owing to avoid these effects, the simulation cell has to be as large as possible, therefore, the cell size is of the order of thousands of atoms (∼103) in this study. The misorientation angle, θ, is defined as θ=θ1+θ2, where θ1and θ2are the orientation angles of grain A and B with respect to the horizontal axis X, respectively. Another interesting parameter to be considered here is the inclination angle of the boundary line, ϕ, that is defined as ϕ=|θ1−θ2|. On the other hand, inasmuch as graphene crystallographic structure possesses two high symmetry directions, i.e., the zig-zag and armchair directions (see Fig. 2), we fix the 189 J. P. Mendez1, F. Arca2and M. P. Ariza2 H GRAIN A GRAIN A GRAIN BGB GB ZIGZAG/ARMCHAIR DIRECTION ZIGZAG/ARMCHAIR DIRECTION ZIGZAG/ARMCHAIR DIRECTION θ1θ1 θ2 L L 2L a 2 1 a a 2 1 a a 2 1 a Figure 1: Grain boundary model. zig-zag direction when the orientation angle of grain θi(i= 1,2) is equal to 0◦and therefore the armchair direction is reached when the orientation angle θi(i= 1,2) is equal to 30◦. (a) (b) Figure 2: High symmetry directions of graphene: (a) zig-zag direction and (b) armchair direction. Regarding grain boundary configurations, we can distinguish two types: symmetric and asymmetric. When θ1=θ2, GBs are symmetric and the inclination angle is ϕ= 0, whereas GBs are asymmetric when θ1=θ2and, therefore, ϕ=θ1−θ2= 0. For the purpose of evaluating all possible GB configurations, it is only necessary to cover the range of θ1and θ2 that varies between 0◦and 30◦. Therefore, symmetric configurations posses one degree of freedom θ(θ1or θ2) and have to be defined by the misorientation angle, and asymmetric GBs have two degrees of freedom (θ1and θ2) and can be denoted by (θ1|θ2). Additionally, as GBs are traditionally modelled as a periodic arrangement of dislocations [15], they can be described by (nA, mA)|(nB, mB), where (ni, mi)i=A, B represents the periodic translations vector of grains A and B along GB and referred to their respective basis set (a1,a2). In particular, nA=nBand mA=mBfor symmetric configurations. Finally, the misorientation angle can be calculated in a straightforward manner through θ= arctan((nA−mA)/√3/(mA+nA)) + arctan((mB−nB)/√3/(mB+nB)) (1) 2.1 Structures and energies With the main purpose of finding misorientation angles corresponding to stable configurations at 0K, we have simulated an endless number of configurations with different angles by means of molecular dynamics, covering a wide range of possibilities. Owing to the fact that θ1=θ2for asymmetric GBs, the characterization of these GBs is more challenging than for symmetric configurations [10]. To accomplish this, we have resorted the widely used molecular 190 J. P. Mendez1, F. Arca2and M. P. Ariza2 Misorientation angle(θ) GB configuration Energy θ(θA|θB) (nA,mA)|(nB,mB) (eV/ ˚ A) 16.1◦(16.1◦|0◦) (3,1)|(2,2) 0.932 16.1◦(0◦|16.1◦) (2,2)|(1,3) 0.323 30◦(30◦|0◦) (5,0)|(3,3) 0.361 30◦(0◦|30◦) (3,3)|(0,5) 1.241 38.2◦(8.21◦|30◦) (5,3)|(0,7) 0.394 Table 1: Energies for different asymmetric grain boundaries in graphene. dynamics code LAMMPS (Large-scale Atomic/Molecular Massively Parallel Simulator) and the AIREBO [16] and ReaxFF potentials [17] that are implemented in LAMMPS code. The strategy proceeded to find these configurations is as follows: first, employing the ReaxFF potential and NVE ensemble, we grow two grains with different misorientation angles and force them to interact and form an interface between both grains. It should be noted that sometimes it is necessary to remove atoms along the interface in order to achieve the desired grain boundary structure; and second, we stabilize the GB structure using the AIREBO potential and the Nose-Hoover thermostat (NVT ensemble) at very low constant temperature (∼0K). In our simulations, we have adopted that GBs are constituted by periodic arrays of dislocations. This periodicity can be defined by two periodic translation vectors, (nA,mA) and (nB,mB), belonging to grains A and B, respectively, and parallel to the GB (see Fig. 1). Unlike symmetric configurations, these translation vectors might differ slightly in magnitude for some asymmetric configurations, dA=dB(dA= 2.46(nAcos(30 −θ1) + mAcos(30 + θ1)) and dB= 2.46(nBcos(30 + θ2) + mBcos(30 −θ2))). However, in order to form stable asymmetric GB, the mismatch between both domains at the GB must be quite small and its stored energy must be reasonably low. In order to evaluate the energies and structures of these asymmetric configurations, the height of the computational cell could be considered proportional to dAor to dB. In our model, we take the height of the computational cell Hproportional to dA. In Fig. 3, we present the obtained asymmetric configurations in our calculations, and the corresponding energies for all possible cases and the misorientation angles of 16.1◦,30◦and 38.2◦are tabulated in Table 2.1. First, we have found that asymmetric configurations do not follow the same pattern as symmetric configurations, and a large number of dislocation types and distribution along the grain boundary can be found. For instance, the GB structures with misorientation angles of θ= 30◦and θ= 38.2◦are constructed by (1,0)+(0,1) and (1,0) dislocations, whereas (1,0) dislocations are arranged along an interface of two grains with a misorientation angle of 16.1◦(see Figs. 3 and 4). These results have also been corroborated by previous studies [18, 19]. Second, we have found that our low energy configurations correspond to those with dA< dB. Third, for these low energy configurations, our simulations show the existence of out-of-plane displacement, about 0.5 ˚ A. Finally, these results have been also corroborated experimentally, [20] observed GBs with misorientation angles of ∼16◦and ∼29◦which can be related to the angles of 16.1◦and 30◦ in our calculations, respectively. 3 Thermal stability Afterwards, we have analysed the mechanical behaviour and thermal stability at finite temperature of these GB structures up to extremely high temperatures. For this purpose, we have relaxed each configuration during a long period of time, up to 10.000ps, and at fixed constant 191 J. P. Mendez1, F. Arca2and M. P. Ariza2 (a) (b) (c) Figure 3: Observed structures of GB in graphene lattice (a) 30◦|0◦(θ=30◦) or (5,0)|(3,3) (b) 8.21◦|30◦(θ=38.21◦) or (5,3)|(0,7) and (c) 16.1◦|0◦(θ=16.1◦) or (3,1)|(2,2). b a1 a2 (a) b a1 a2 (b) Figure 4: Dislocation type (a) (1,0) and (b) (1,0)+(0,1). temperature, covering a wide range of temperatures from 0K to temperatures close to the melting point of graphene [21, 22, 23]. Similarly, to carry out the thermal stability analysis, we have employed the LAMMPS code, the full AIREBO potential and the NVT ensemble (∆t= 0.1 fs). As main outcomes of our simulations, we state the following conclusions: 1. Asymmetric configurations remain stable up to very high temperature, around 3000K. As we can observe from Fig. 5a for a misorientation angle of 38.2◦, dislocations type (1,0) and (1,0)+(0,1) which form the grain boundary are unaffected by the temperature. 2. At temperature exceeding 3000K, it is observed transformations, motions and slip-up of dislocations. For instance, as we can see in the rectangles marked in Figs. 5b and c, a (1,0)+(0,1) dislocation segregate into two dislocations, and the resulting dislocations move and one of them joins to a (1,0) dislocation to form new dislocation. Additionally, we show in Fig. 6 as an example the glide motion of a (1,0) dislocation. 192 J. P. Mendez1, F. Arca2and M. P. Ariza2 (a) (b) (c) Figure 5: Observed asymmetric grain boundary structures for a misorientation angle of 38.2◦at different temperatures (a) T≤3000K, (b) T=3500K, and (c) T=4000K. 193 J. P. Mendez1, F. Arca2and M. P. Ariza2 (a) (b) (c) Figure 6: Details of the glide motion of (1,0) dislocations showing at temperatures above 2000K. 3. Above 4000K, asymmetric GBs collapse. Similar to symmetric configurations, the presence of GBs accelerates the melting process and decreases the melting temperature. 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