Signature of Electronic Correlations in the Optical Conductivity of the Doped Semiconductor Si:P

TL;DR

This study investigates the optical conductivity of highly doped silicon at THz frequencies, revealing the influence of electronic correlations and the Coulomb gap near the metal-insulator transition, with deviations from existing models.

Contribution

It provides experimental evidence of complex electronic correlation effects and the Coulomb gap in doped silicon's optical conductivity, extending understanding beyond simple theoretical models.

Findings

Qualitative observation of the Efros-Shklovskii crossover in optical conductivity.

Identification of super-linear frequency dependence indicating Coulomb gap effects.

Critical behavior of dielectric constant and localization length near the transition.

Abstract

Electronic transport in highly doped but still insulating silicon at low temperatures is dominated by hopping between localized states; it serves as a model system of a disordered solid for which the electronic interaction can be investigated. We have studied the frequency-dependent conductivity of phosphorus-doped silicon in the THz frequency range (30 GHz to 3 THz) at low temperatures $T\geq 1.8$ K. The crossover in the optical conductivity from a linear to a quadratic frequency dependence as predicted by Efros and Shklovskii is observed qualitatively; however, the simple model does not lead to a quantitative agreement. Covering a large range of donor concentration, our temperature- and frequency-dependent investigations reveal that electronic correlation effects between the localized states play an important and complex role at low temperatures. In particular we find a super-linear frequency dependence of the conductivity that highlights the influence of the density of states, i.e. the Coulomb gap, on the optical conductivity. When approaching the metal-to-insulator transition by increasing doping concentration, the dielectric constant and the localization length exhibit critical behavior.