Cu interconnects are essential in advanced integrated circuits to minimize the RC delay. In manufacturing these devices, Cu is deposited electrochemically using a plating bath containing organic additives. The as-deposited nanocrystalline Cu films undergo self-annealing at room temperature to form a micronsized grain structure by abnormal grain growth. Systematic experimental studies of self-annealing kinetics on model Cu films deposited on a Au substrate suggest that the rate of grain size evolution depends primarily on the initial grain size of the as-deposited film. A model for the observed abnormal grain growth process is proposed. Assuming that desorption of the organic additives leads to mobile grain boundaries, the onset of abnormal grain growth is attributed to a sufficiently low additive concentration such that a full coverage of all grain boundaries cannot be maintained. The incubation time of abnormal growth is then a logarithmic function of the initial grain size. The probability to find a growing grain is proportional to the number of grains per unit volume. This assumption is seen to be in good agreement with the experimental observations for subsequent abnormal grain growth rates. The limitations of the proposed model and the challenges to obtain further insight into the complex microstructure mechanisms during self-annealing are delineated.