A new fabrication technique to prepare ultra-thin barrier layers for nano-scale Cu wires was proposed in our previous studies. Ti-rich layers formed at the Cu(Ti)/dielectric-layer interfaces consisted of crystalline TiC or TiSi and amorphous Ti oxides. The primary control factor for Ti-rich interface layer composition was the C concentration in the dielectric layers rather than the formation enthalpy of the Ti compounds. To investigate Ti-rich interface layer growth in Cu(Ti)/dielectric-layer samples annealed in ultra high vacuum, Rutherford Backscattering Spectrometry (RBS) was employed in the present study. Ti peaks were obtained only at the interface for all the samples. Molar amounts of Ti atoms segregated to the interface (n) were estimated from Ti peak areas. The n value was defined by n = Z·exp(-E/RT) · tm, where Z is a preexponential factor and E the activation energy for the reaction. The Z, E, and m values were estimated from plots of log n vs log t and log n vs 1/T. The m values are similar in all the samples. The E values for Ti atoms reacting with the dielectric layers containing carbon (except SiO2) tended to decrease with decreasing C concentration (decreasing k), while reaction rate coefficients (Z·exp(-E/RT)) were insensitive to C concentration in the dielectric layers. These factors lead to conclusion that growth of the Ti-rich interface layers is controlled by chemical reactions of the Ti atoms with the dielectric layers represented by the Z and E values, rather than diffusion in the Ti-rich interface layers.