Based on fractal theory , through the fractal dimension of electro-diffusion, the dimensions of noise time series and grain boundary are corelated. The change of noise dimension is shown to be useful for studying the damage mechanism and determining the parameters for electromigration. The picture of grain boundary becomes complicated in the early period of electromigration, but after the voids are informed, it becomes more regular. So the fractal dimension of time series increases during the early stage of electromigration and goes down after the voids are informed. The theoretical analysis is confirmed by experiment, the dimension of noise time series may be a new characteristic parameter for metallic interconnection electromigration.