In our previous studies, Ti atoms in Cu(Ti) alloy films were found to segregate at the film surface and the interface between Cu(Ti) alloy films and dielectric layers after annealing in Ar atmosphere at elevated temperatures. Such self-formed Ti-rich interface layers can act as a diffusion barrier layer. This technique was called ''self-formation of the diffusion barrier,'' which is attractive for the fabrication of ultra-large scale integrated interconnects. In the present study, we investigated the growth of Ti-rich barrier layers in Cu(Ti)/dielectric-layer samples with a low Ti content (1 at%) after annealing in ultra high vacuum (UHV). Ti atoms were found to segregate only to the Cu(Ti)/dielectric-layer interface under annealing in UHV. The microstructures were analyzed by transmission electron microscopy and Rutherford backscattering spectrometry, and correlated with the electrical properties of the Cu(Ti) films. It was concluded that Ti-rich interface layers were formed in all the Cu(Ti)/dielectric-layer samples. The Ti-rich interface layers were identified to consist of TiC or TiSi in addition to Ti oxides. The growth of the Ti-rich interface layers consisting of TiC was faster than those consisting of TiSi. Similarly, the resistivities of Cu(Ti)/dielectric-layer samples in which the TiC formation was observed were quickly reduced and those in which the TiSi formation was observed were gradually reduced. Compositions of the self-formed Ti-rich interface layers were concluded to be determined by the C concentration in the dielectric layers rather than by the enthalpy of formation. The growth of the self-formed Ti-rich interface layers consisting of TiC may be controlled by C diffusion in the Ti-rich interface layer. The composition of the dielectric layers was concluded to play an important role on the growth of the Ti-rich interface layers.