Solid state dielectric screening versus band gap trends and implications

Abstract

High-frequency (optical) and low-frequency (static) dielectric constant versus band gap trends, as well as index of refraction versus band gap trends are plotted for 107 inorganic semiconductors and insulators. These plots are describable via power-law fitting. Dielectric screening trends that emerge from this analysis have important optical and electronic implications. For example, barrier lowering during Schottky emission, phonon-assisted or Fowler-Nordheim tunneling, or Frenkel-Poole emission from a trap is found to be significantly more pronounced with increasing band gap due to a reduction in the optical dielectric constant with increasing band gap. The decrease in the interface state density with increasing band gap is another optical dielectric constant trend. The tendency for a material with a wider band gap to be more difficult to dope is attributed to an increase in the ionization energy of the donor or acceptor dopant, which in turn, depends on the optical dielectric constant and the effective mass. Since the effective mass for holes is almost always larger than that for electrons, p-type doping is more challenging than n-type doping in a wide band gap material. Finally, the polar optical phonon-limited mobility depends critically upon the reciprocal difference of the optical and the static dielectric constant. Consequently, electron and hole mobility tend to decrease with increasing band gap in a polar material.