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Chessboard-like substrates are introduced in this paper, in order to study the diffusion-limited aggregation (DLA)and the motion of poly-atoms on heterogeneous surfaces. The effect of morphology of such substrates upon the cluster aggregation is investigated using the Monte Carlo simulation. It is found that the growth process and the cluster morphology are goveed by the energetic topography of the substrates. Our simulation also indicate that the island density and the fractal dimension of the clusters depend strongly on the substrate topography and the activation energy.