The influence of diffusion temperature on the formation of one type of Cu center denoted as CuDLB center, the relationship between the concentrations of the CuDLB center after the diffusion of Cu and those of contaminated Cu on sample surfaces, and the transformation of the CuDLB center to another type of Cu center denoted as the CuDLA center by annealing were investigated by photoluminescence and deep-level transient spectroscopy (DLTS) measurements. It was found that the CuDLB center is composed of one core Cu atom and weakly bonded three interstitial Cu atoms around the core and that the CuDLA center is the core of the CuDLB center. For Ni, the depth profiles of the substitutional Ni (Ni center) in silicon diffused with various concentrations of the element were measured by DLTS, and were found to be controlled by the temperature-dependent outdiffusion of Ni.