Dielectric Constants of Silicon Quantum Dots

Quantum mechanical pseudopotential calculations of the absorption spectra and static dielectric constant ${\ensuremath{\epsilon}}_{s}$ of Si quantum dots with \ensuremath{\sim}100-1300 atoms are presented. The predicted ${\ensuremath{\epsilon}}_{s}$ is found to be significantly reduced relative to the bulk value, but is considerably larger than the value deduced from currently available model calculations. A convenient parametrization of ${\ensuremath{\epsilon}}_{s}$ vs size $R$ is provided. We find that for quantum dots with $Rl20$ \AA{} the electron-hole pair is confined by the physical dimension of the dot, not by the Coulomb attraction.