Analytical Model for the Effect of Pressure on the Electronic Structure of Germanium Nanocrystals

Abstract

The electronic structure modification of germanium nanocrystals under the condition of external pressure has been investigated, in order to gain a better understanding of their relevant properties. In this paper, an atomistic insight into the effect of size-pressure variation on the electronic structure of germanium nanocrystals (of 8, 16, 54 atoms) is performed. The effect of pressure on the structural and electronic properties of germanium nanocrystals has been investigated using the large unit cell within the framework of ab initio restricted Hartree-Fock theory and the linear combination of atomic orbital approximation included in Gaussian03 software by considering the effects of size and pressure. Cohesive energy, indirect band gap, valence bandwidth and bulk modulus are all obtained, which is consistent with understanding the interdependence of these quantities and their common atomistic origin originates with size- and pressure-induced change, leading to a variation of the crystal potential. Theoretical results are compared with the experimental measurements. The calculations show an agreement of the calculated lattice constant at equilibrium point, cohesive energy, valence bandwidth, and bulk modulus with the experimental data. Computed band gap is greater than the experimental value. That is what expected from Hartree-Fock method. Band gap shows a good trend compared to theoretical values. The calculations of the effect of pressure on the aforementioned properties are investigated. It is found that the valence bandwidth decrease with the increase of pressure, and cohesive energy decrease with the increase of tensile pressure in 8 atoms while it increase in both 16 and 54 atoms. Lattice constant increase with pressure in three crystals, and energy gap decrease with pressure in both 8, and 16 atoms crystals and increase with pressure in 54 atoms nanocrystal. The maximum value of pressure is taken to be 7.6 GPa, because beyond this value, the phase of Ge transforms from nanocrystals to another phase.