Density functional theory was applied to simulate copper diffusion in silicon oxide, nitride, and carbide (SiOx, SiNx, SiCx). Because copper drift into oxide is significantly enhanced by negative bias, copper ions are the active diffusing species. Clusters and, in some cases supercells, modeling various ring configurations of the amorphous networks of silicon oxide, nitride, and carbide were employed. Interactions of both neutral copper and its cation, Cu+, with the network were explored. Calculations revealed a strong binding of Cu+ to SiOx, SiCx, and SiNx in contrast with neutral Cu. The Cu+ attraction to carbide clusters is significantly lower than to SiOx and SiNx, explaining the effective barrier properties of SiCx. The estimated lower bounds for activation energies for Cu+ hops between stable ring clusters of SiOx and SiNx are similar. This implies that the difference in Cu diffusion properties between oxides and nitrides is likely due to a higher percentage of large rings in amorphous oxides compared with nitrides. An approach to increasing the resistance of oxides to Cu+ diffusion is suggested.