Dielectric Constants of Silicon Quantum Dots

Quantum mechanical pseudopotential calculations of the absorption spectra and static dielectric constant ${\epsilon }_s$ of Si quantum dots with ∼100-1300 atoms are presented. The predicted ${\epsilon }_s$ 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 ${\epsilon }_s$ vs size $R$ is provided. We find that for quantum dots with $R<\mathrm{}20\mathrm{}$ Å the electron-hole pair is confined by the physical dimension of the dot, not by the Coulomb attraction.