A novel model for bulk modulus and bond energy calculation of Si and its binary compounds, tetrahedral ternary semiconductors in bulk and nanocrystals

This study investigates the correlations between bulk modulus, mean bond length, mean bond ionicity, and bond energy for a variety of tetrahedral group semiconductors, such as IV, III-V, II-VI, I-III-VI₂, II-IV-V₂, I₂-IV-VI₃, I₃-V-VI₄, and III₂-VI₃ elements and compounds. A clear correlation between the mean bond length (<i>d</i>_mean), and bond energy (<i>E</i>_b) was found in the form: <i>E</i>_b = 74.115 (eV A²) × <i>d</i>_mean^-2 × (1 + <i>f</i>_i), where <i>f</i>_i is the group compound ionicity. For every group, ionicity values between 0 and 0.75 were calculated. Additionally, a consistent link between bulk modulus (<i>B</i>) and bond energy was found and used to compute bulk modulus (in GPa) and bond energy (in eV) for a variety of groups, including II-IV-V₂, I-III-VI₂, III₂-VI₃, I₂-IV-VI₃, and I₃-V-VI₄, which were previously unavailable. Additionally, by adding size-dependent factors through mean bond length <i>d</i>_mean at the nanoscale, extended the obtained relationships to a nanoscale semiconductor. When applied to Si nanocrystals, the modified bulk modulus equation, <i>B</i>(<i>r</i>) = 0.7775 (GPa eV^-1.85) × (<i>E</i>_b(<i>r</i>))^1.85 × (1 - <i>f</i>_i) takes size effects into account without allowing for parameter adjustment. Because of variations in the surface-to-volume ratio, lattice characteristics, bond ionicity, and mean bond length, the bulk modulus drops from 98 GPa in bulk Si to 90 GPa in 5 nm Si nanoparticles (NPs). The bulk modulus of semiconductor materials noticeably decreases with decreasing size; NPs exhibit the largest fall, followed by nanowires (NWs) and nanofilms (NFs). These discrepancies result from changes in the nanoscale's mean bond length and bond energy. The findings emphasize the significance of these effects for adjusting the mechanical characteristics of nanostructured materials, and simulations and experimental evidence corroborate them.