Stability and migration of small copper clusters in amorphous dielectrics

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.