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We present a comprehensive study on the rear contact formation of rear surface-passivated silicon solar cells by full-area screen printing and alloying of aluminum pastes on the locally opened passivation layer. We show that the point contact distance has a significant influence on the local alloying process for the contact formation resulting in different structural and electrical contact properties when applying conventional Al pastes. Increasing the distance leads to 1) high contact depths resulting in an enlargement of the contact area and 2) severely reduced thicknesses of the Al-doped p+ regions in the contact points, leading to a strong increase in recombination within the contact points. This inadequate contact formation can be directly linked to the deficiently low percentage of silicon that dissolves into the Al-Si melt during alloying. We demonstrate that by intentionally adding Si to the Al paste, the contact point geometry can be significantly improved and particularly becomes independent of the contact distance. Further investigations on the internal reflectance and the specific resistivity of the rear contact suggest an upper limit for the Si content added to the Al paste. In summary, we present a simple way to significantly improve the rear contact formation of rear surface-passivated silicon solar cells.