Simple model for the dielectric constant of nanoscale silicon particle

As the physical size approaches several nanometers, reduction in the static dielectric constant ε becomes significant. A modified Penn model, taking into account the quantum confinement induced discrete energy states, was applied to a sphere and to a wire. The calculated size dependent ε is consistent with the wave-vector-dependent ε(q). However, this form of ε is more amenable for calculations of donor and exciton binding energies in a finite quantum confined nanoparticle when a full electrostatic boundary value problem must be tackled. The results of our model compare favorably with other, far more sophisticated, calculations.