Modeling Dielectric Constant of Semiconductor Nanocrystals

A simple and unified model has been established for size- and composition-dependent dielectric constant $\varepsilon (x,\,D)$ based on a size-dependent melting-temperature model, where $x$ is the fraction of composition, $D$ denotes the diameter of nanoparticles and nanowires, and the thickness of thin films. It demonstrates that depending on the dimension of nanocrystals, $\varepsilon (x,\,D)$ decreases with different trend as $D$ drops, while $\varepsilon (x,\,D)$ is a nonlinear function of $x$ . The theoretical prediction agrees approximately with experimental and computer simulation results of semiconductor nanocrystals in single phase or multiphases.