In our previous studies, thin Ti-rich diffusion barrier layers were found to be formed at the interface between Cu(Ti) films and SiC2/Si substrates after annealing at elevated temperatures. This technique was called "self-formation of the diffusion barrier," which is attractive for fabrication of ultra-large scale integrated (ULSI) interconnects. In the present study, we investigated the applicability of this technique to Cu(Ti) alloy films which were deposited on the four low dielectric constant (low-k) dielectric layers which are potential dielectric layers of future ULSI-Si devices. The microstructures were analyzed by transmission electron microscopy (TEM) and secondary ion mass spectrometry (SIMS), and correlated with the electrical properties of the Cu(Ti) films. It was concluded that the Ti-rich interface layers were formed in all the Cu(Ti)/dielectric-layer samples. The primary factor to control composition of the self-formed Ti-rich interface layers was the C concentration in the dielectric layers rather than the formation enthalpy of the Ti compounds (TiC and TiSi). Crystalline TiC was formed on the dielectric layers with a C concentration higher than 17 at.%.