Amorphous Ti-Si-N films of approximately 200 and 650 thickness were reactively sputtered on Si wafers using a dc magnetron sputtering system at various $N_2$/Ar flow ratios. Their barrier properties between Cu (750 ) and Si were investigated by using sheet resistance measurements, XRD, SEM, RBS, and AES depth profiling focused on the effect of the nitrogen content in Ti-Si-N thin film on the Ti-Si-N barrier properties. As the nitrogen content increases, first the failure temperature tends to increase up to 46 % and then decrease. Barrier failure seems to occur by the diffusion of Cu into the Si substrate to form Cu$_3$Si, since no other X- ray diffraction intensity peak (for example, that for titanium silicide) than Cu and Cu$_3$Si Peaks appears up to 80$0^{circ}C$. The optimal composition of Ti-Si-N in this study is $Ti_{29}$Si$_{25}$N$_{46}$. The failure temperatures of the $Ti_{29}$Si$_{25}$N$_{465}$ barrier layers 200 and 650 thick are 650 and $700^{circ}C$, respectively.ely.