Size effects of semiempirical large unit cell method in comparison with nanoclusters properties of diamond-structured covalent semiconductors

Self-consistent Hartree–Fock method within the framework of large unit cell (LUC) formalism using complete neglect of differential overlap (CNDO) is used to simulate size effects on nanoclusters of covalent crystalline diamond-structured semiconductor C, Si, Ge, and Sn using k=0 approximation. Three sizes are investigated namely 8, 64, and 216 atom LUCs. Cohesive energy, energy gap, valence band width, and hybridization orbitals are obtained from electronic structure calculations. Charge distribution, density of states, and orbital wave functions are also reported. Sensitivity analysis of the dependence of some of the calculated properties on model parameters is performed. Results revealed that electronic properties converge to some limit as the size of the LUC increases and that the 216 atoms LUC is very near to the bulk of these materials. Increasing LUC size or atomic number of covalent semiconductor removed some electronic cloud from bonding region to the spherical region around the atom. The same is true in going to higher energy levels. Increasing the size of LUC also resulted in a decrease of energy gap, increasing valance band width, and generally slightly increasing the cohesive energy. The model predicts energy gap reduction in going from ultra-small nanoclusters to the bulk of the four elements to be around 2 eV. The approximations imposed on the present model calculations leading to resemblance with nanoclusters properties in addition to the evidences of such resemblance such as orbital shapes and trends of data are discussed. Small nanoclusters are expected to have stronger directional bonds than in their bulk structure. The smallest cells (8 atoms) are found to be of a slightly longer lattice constant of the order 0.01, 0.1, 0.04, and 0.02 a.u. for diamond, silicon, germanium, and tin, respectively. X-ray form factors show a slight decrease of low-angle lines when we go to larger cells that was also found experimentally. To the best of my knowledge, this is the first systematic determination of covalent nanoclusters lattice constant and X-ray form factors variation with ultra-small nanocluster size.