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.