Theoretical model for size, dimension and shape effect on electrical behavior of semiconductor nanomaterials

Abstract

The present study is an effort to develop a simple analytical model without any adjustable parameter for observing the collective effect of size, dimension and shape on electrical susceptibility and dielectric constant of nanomaterials. The size dependence of electrical susceptibility and dielectric constant has been observed for some pure as well as binary semiconductor nanomaterials, in three different dimensions (i.e., nanoparticles, nanowires and nanofilms). It has been observed that the electrical susceptibility and dielectric constant both show reduction with the decrement in size, due to the increased surface-to-volume ratio and lower coordination number. The present study reveals that the difference between the values of electrical susceptibility of nanoparticles and nanowires (5–50%) is less in comparison with nanofilms (10–90%). This difference diminishes on moving toward the higher size range. The decrement in the value of dielectric constant with size is found, maximum for nanoparticles (10–80%) followed by nanowires (10–70%) and minimum in nanofilms (5–60%). The outcomes for the size-dependent dielectric constant have been compared with the available experimental and other theoretical data and found consistency in calculated results with experimental data. The model has been extended to investigate the cross-sectional shape effect along with size on the electrical susceptibility and dielectric constant of nanowires due to large applications by incorporating shape factor. Four different cross-sectional shapes: spherical, square, rectangular and hexagonal nanowires, have been taken for the present study. The calculated results of dielectric constant have been compared with the available experimental data, and close agreement was found. It has been observed that the electrical susceptibility and dielectric constant have the highest value for spherical cross-sectional-shaped nanowires and the lowest for rectangular cross-sectional-shaped nanowires. Deviation graphs show that the values of electrical susceptibility and dielectric constant for rectangular, square and hexagonal cross-sectional-shaped nanowires deviate from spherical nanowires as 2–14%, 2–4% and 1–2%, respectively. The present study confirms the importance of shape effect along with size and dimension for electrical properties of semiconductor nanomaterials.