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

The spectral response from shallow negative donor ions in silicon has been studied over a range of donor concentrations between 1×{}10¹⁴ and 1×{}10¹⁷ cm^-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×{}10¹⁵ cm^-3---about three orders of magnitude lower than the concentration at which the metal-insulator transition occurs in this material.