Formation of the Upper Hubbard Band from Negative-Donor-Ion States in Silicon

Abstract

The spectral response from shallow negative donor ions in silicon has been studied over a range of donor concentrations between 1\ifmmode\times\else\texttimes\fi{}${10}^{14}$ and 1\ifmmode\times\else\texttimes\fi{}${10}^{17}$ ${\mathrm{cm}}^{\ensuremath{-}3}$. At low donor concentrations the binding energy of the negative-ion state is well described by the effectivemass theory. The formation of the upper Hubbard band out of these states is observed at a donor concentration of 3\ifmmode\times\else\texttimes\fi{}${10}^{15}$ ${\mathrm{cm}}^{\ensuremath{-}3}$---about three orders of magnitude lower than the concentration at which the metal-insulator transition occurs in this material.