ab initio Large Unit Cell Calculations of Electronic Structure of Cubic Boron Nitride Nanocrystals

Abstract

Density functional theory at the generalized gradient approximation level of Perdew-Burke-Ernzerhof coupled with the large unit cell method is used to simulate the core and surface parts of cubic boron nitride zinc blende nanocrystals. The cubic boron nitride nanocrystals in our model are represented by a heterojunction between the surface and the core in which the surface represents the outer four layers and the core by the rest of the internal region of a nanocrystal. The present model results show that boron nitride nanocrystals core has generally fluctuating energy gap as the nanocrystals grow up in size for the selected size range. The present work shows decreasing lattice constant and ionicity of the core part with increasing nanocrystal size. The lattice contraction is 2 % of the size of core equilibrium lattice constant. The method also shows increasing cohesive energy (absolute value) and valence band width with increasing nanocrystal size. All the properties reach converged values nearly at 1.4-1.9 nanometer of nanocrystal size. The hydrogenated B-terminated (001)-(1 × 1) nanocrystal surface is also investigated to determine the rule of the surface in nanocrystals electronic structure. Surface results show that energy gap is controlled by the surface part since it has lower energy gap value. The highly degenerated core states are split at the surface causing the reduction of energy gap and widening of both valence and conduction bands. A comparison between the largest investigated core cells with bulk properties reflects the fast convergence of these properties to bulk values and the quality of the present method. Use of symmetry in large unit cell method leads to a huge reduction of computational time with respect to traditional full geometrical optimization.