  We use density functional theory (DFT) to study the thermodynamic stability
and migration of copper ions and small clusters embedded in amorphous silicon
dioxide. We perform the calculations over an ensemble of statistically
independent structures to quantify the role of the intrinsic atomic-level
variability in the amorphous matrix affect the properties. The predicted
formation energy of a Cu ion in the silica matrix is 2.7+/-2.4 eV,
significantly lower the value for crystalline SiO2. Interestingly, we find that
Cu clusters of any size are energetically favorable as compared to isolated
ions; showing that the formation of metallic clusters does not require
overcoming a nucleation barrier as is often assumed. We also find a broad
distribution of activation energies for Cu migration, from 0.4 to 1.1 eV. This
study provides insights into the stability of nanoscale metallic clusters in
silica of interest in electrochemical metallization cell memories and
optoelectronics.
