Energy gaps of Si nanoparticles using size-dependent Debye-Waller factors

Abstract

A model of size-dependent Debye-Waller screening of effective potential is proposed. The calculated effective potential of silicon nanoparticles (SiNPs) is used to predict the dependence of energy bands on diameter. The empirical pseudopotential method is implemented to calculate the band structure. SiNPs having diameters of 3.753–15.744 nm are studied. The results show that the fundamental (indirect) energy gap increases and shifts toward the center of the Brillouin zone as the diameter decreases. The direct energy gap at point Γ increases slowly as the diameter is reduced to ~5.75 nm and decreases rapidly for diameters below this value. Variations of indirect and direct energy gaps at point Γ are fitted to model equations. The results indicate a conversion to a direct energy gap when the diameter becomes ~1.6 nm. The calculated behavior of the energy gaps and the predicted transition to a direct energy gap are in good agreement with other experimental and theoretical results.