Structural origins of electronic conduction in amorphous copper-doped alumina

We perform an {\it ab initio} modeling of amorphous copper-doped alumina (a-Al$_2$O$_3$:Cu), a prospective memory material based on resistance switching, and study the structural origin of electronic conduction in this material. We generate molecular dynamics based models of a-Al$_2$O$_3$:Cu at various Cu-concentrations and study the structural, electronic and vibrational properties as a function of Cu-concentration. Cu atoms show a strong tendency to cluster in the alumina host, and metallize the system by filling the band gap uniformly for higher Cu-concentrations. We also study thermal fluctuations of the HOMO-LUMO energy splitting and observe the time evolution of the size of the band gap, which can be expected to have an important impact on the conductivity. We perform a numerical computation of conduction pathways, and show its explicit dependence on Cu connectivity in the host. We present an analysis of ion dynamics and structural aspects of localization of classical normal modes in our models.