Structural and Electronic Properties of Graphene and Silicene: An FP-(L)APW+lo Study

Abstract

We report here the structural and electronic properties of graphene and silicene (the silicon analogue of graphene) investigated using first-principles calculations of their ground state energies employing full-potential (linearized) augmented plane wave plus local orbital (FP-(L)APW+lo) method. On structure optimization, we found that the graphene-like honeycombstructure of Si is buckled (buckling parameter Δ ≃ 0.44 Å) in contrast with graphene whose structure is planar (Δ = 0.0 Å). In spite of the buckled-structure, silicene has an electronic structure similar to that of graphene. The results are in agreement with previous reports based on other methods. We have also calculated the lower bounds of the lattice constant "a" of these 2D systems, within the present method of study which are our new results.

Characterization of Thin Film Materials using SCAN meta-GGA, an Accurate Nonempirical Density Functional

“…In this way, we determine V 0 (from which the equilibrium lattice constant a was extracted), B 0 and . It should be noted that we are extending the Murnaghan fit to 2D materials, and quantities such as the bulk modulus should be regarded as fitting parameters rather than physical quantities as discussed by Behera and Mokhopadhyay [BM]39. BM simulated the 2D-hexagonal structure of graphene and silicene using 3D-hexagonal supercells with large values of the lattice parameter c to keep the interlayer interaction negligibly small.…”

“…One originates from the Murnaghan fit, taken as , where a M is the Murnaghan fit lattice constant, and a B is the Birch lattice constant obtained by applying the constraint . The second source of error is the interpolation of the vacuum layer c to ∞, as calculated by Behera and Mokhopadhyay39.…”

Graphene and some of its structural analogues: full-potential density functional theory calculations

“…Considering the facts that LDA usually underestimates and GGA [39] usually overestimates the lattice constant, the calculated value of a 0 slightly depends on the cparameter used for super cells in DFT based calculations as we have seen before [31] for graphene (0.12% lower value of a for c → ∞) and silicene (0.075% lower value of a for c → ∞), and the different methods of study used by different authors, our results in Table 1 are acceptable.…”

“…In Figures 2-4, we present our calculated results selecting one example from each group of materials considered here: graphene (ML-C) for Group-IV material, ML-BN for Group-III-V material and MLZnS for Group-II-VI material. As seen in the Figures 2-4, these structures have minimum energy at ∆ = 0.00Å , which means that these materials adopt 2D planar structures in the ground state (T = 0 • K) unlike the case with silicene (graphene analogue of Si) [22,31] that adopts a buckled structure in its ground state. It is to be noted that these results do not conflict with the theory of stability of 2D crystals [10][11][12].…”

“…We use the DFT based full-potential (linearized) augmented plane wave plus local orbital (FP-(L)APW+lo) method [27][28][29] as implemented in the elk-code (http:// elk.sourceforge.net/) and the Perdew-Zunger [30] variant of local density approximation (LDA) for our calculations. The accuracy of this method and code has been successfully tested in our previous studies [31][32][33][34][35][36][37]. For plane wave expansion in the interstitial region, we have used 8 ≤ |G + k| max × R mt ≤ 9, where R mt is the smallest muffin-tin radius, for deciding the plane wave cut-off.…”