Modeling the influence of lattice structure and size effects on bond strength and Young’s modulus in semiconductor nanocrystals

Abstract This study explores the mechanical properties of nanocrystalline semiconductors, focusing on the size-dependent behaviour of bond strengths and Young’s modulus. A new theoretical model is developed to calculate the Young’s modulus of nanocrystals (NCs), such as nanofilms (NFs), nanowires (NWs), and nanoparticles (NPs), using lattice parameters to account for nanoscale effects. The model demonstrates how reductions in NCs size lead to a significant decrease in Young’s modulus due to lattice distortions, surface-to-volume ratio effects, and bond relaxation. Building on this foundation, the study establishes a novel relationship between bond strength and mean bond length for group IV, III–V, and II–VI semiconductors. A clear correlation between the mean bond length ( d mean ) and bond strength ( E s ) was found, and this connection is represented as follows: E s = 15.81 GPa . Å 4 × d mean − 4 . Additionally, by adding size-dependent factors through mean bond length at the nanoscale, these obtained relationships were extended to nanoscale semiconductors. When applied to Si NCs, the modified bond strength equation, E s r = 15.81 ( GPa . Å 4 ) × d − 4 r , takes size effects into account without allowing for parameter adjustment. Bond strength and Young’s modulus decrease with decreasing NCs size and dimensionality, especially in NPs smaller than 5 nm. Surface effects dominate, impacting size-dependent bond strength of semiconductors. NPs exhibit the largest fall, followed by NWs and NFs. The theoretical predictions for Young’s modulus align well with existing experimental and simulated data, validating the model’s reliability. These findings provide new insights into the elastic and bonding behaviour of nanoscale semiconductors, with a particular focus on Si. The work offers a valuable framework for understanding size-dependent mechanical properties, with implications for the design and optimisation of nanostructured materials and devices.