Electrodynamics of a Coulomb Glass in n-type Silicon

Optical measurements of the real and imaginary frequency dependent conductivity of uncompensated n-type silicon are reported. The experiments are done in the quantum limit, $ \hbar\omega > k_{B}T$, across a broad doping range on the insulating side of the Metal-Insulator transition (MIT). The observed low energy linear frequency dependence shows characteristics consistent with theories of a Coulomb glass, but discrepancies exist in the relative magnitudes of the real and imaginary components. At higher energies we observe a crossover to a quadratic frequency dependence that is sharper than expected over the entire dopant range. The concentration dependence gives evidence that the Coulomb interaction energy is the relevant energy scale that determines this crossover.