A highly nonlinear single-mode anomalous dispersion silicon core fiber (SCF) is suitably designed and optimized to generate a high repetition rate pulse train in the temporal domain from a single input pulse at a sufficiently shorter optimum length in comparison to silica-based standard fibers used for the same purpose. The large amount of Kerr-induced nonlinearity of a SCF is effectively utilized here such that input Gaussian pulses or pulse trains transform into a highly repetitive temporal multiplet. The effects of free-carrier generation-induced change in absorption and dispersion are included while studying the nonlinear pulse propagation through the SCF. To declare the generated pulse as a superior-graded triplet, a Q parameter, as a function of relative pulse parameters of the individual pulses of a triplet, is defined for the first time, to the best of our knowledge. Different pulse parameters are thoroughly optimized as well as the effect of external gain is examined from the perspective of requirement of shorter fiber length and development of quality triplets. Finally, the work is further extended for the formation of quadruplet pulses by the same type of SCF. It is to be mentioned here that such a methodical study for the generation of a temporal multiplet using a semiconductor core fiber has not been reported earlier.