Size effect of band gap in semiconductor nanocrystals and nanostructures from density functional theory within HSE06

A new approach has been studied to determine the band gap energy based on the density functional theory using the hybrid functional (HSE06) with the modeled lattice expansion of semiconductors for both nanoparticles and nanostructures. At the nanoscale, the lattice parameters play a crucial role in determining the band gap energy. The lattice parameters are first determined using theoretical equations for both nanoparticles and nanostructures. The influence of size on band gap was explored, and the results suggest that for semiconductors with narrow and moderate band gaps, the band gap increases as the size decreases. When the size of the particle decreases, the spaces between the bands get wider due to the lattice parameters rise as the diameter gets smaller. Nanoparticles and nanostructures show the same trend in band gap energy variation, however band gap energy in nanostructures is lower than nanoparticles of the same size due to increased lattice strain and higher surface to volume ratio in nanoparticles compared to nanostructures of the same size. The coincident between the method calculations with the available experimental data of band gap change indicated that the lattice parameters are dependent with the size, and can be used as a successful way to understand the band gap properties.