Influence of electronic correlations on the frequency-dependent hopping transport in Si:P

TL;DR

This study measures the microwave conductivity of Si:P near the metal-insulator transition, revealing the influence of electronic correlations and the Coulomb gap on hopping transport at low temperatures.

Contribution

It introduces a new broadband microwave measurement technique to analyze frequency-dependent hopping transport in Si:P across various doping levels.

Findings

Super-linear frequency dependence of conductivity indicating Coulomb gap effects.

Abrupt change in the power-law behavior of conductivity near the critical doping.

Dielectric constant increases following a power law as doping approaches the transition.

Abstract

At low energy scales charge transport in the insulating Si:P is dominated by activated hopping between the localized donor electron states. Thus, theoretical models for a disordered system with electron-electron interaction are appropriate to interpret the electric conductivity spectra. With a newly developed technique we have measured the complex broadband microwave conductivity of Si:P from 100 MHz to 5 GHz in a broad range of phosphorus concentration $n/n_c$ from 0.56 to 0.95 relative to the critical value $n_c=3.5\times 10^{18}$ cm$^{-3}$ corresponding to the metal-insulator transition driven by doping. At our base temperature of $T =1.1$ K the samples are in the zero-phonon regime where they show a super-linear frequency dependence of the conductivity indicating the influence of the Coulomb gap in the density of the impurity states. At higher doping $n\to n_c$, an abrupt drop in the conductivity power law $\sig(\omega)\sim\omega^\alpha$ is observed. The dielectric function $\eps$ increases upon doping following a power law in ($1-n/n_c$). Dynamic response at elevated temperatures has also been investigated.