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It is well known that sodium at grain boundaries (GBs) increases the photovoltaic efficiencies of CuInSe2 and Cu2ZnSnS4 significantly. However, the mechanism of how sodium influences the GBs is still unknown. Based on the recently proposed self-passivation rule, it is found that the dangling bonds in the GBs can completely be saturated through doping the Na, thus GB states are successfully passivated. It is shown that the Na can easily incorporate into the GB with very low formation energy. Although Cu can also passivate the GB states, it requires a copper rich condition which, however, suppresses the formation of copper vacancies in the bulk and thus decreases the concentration of hole carriers, so copper passivation is practically not as beneficial as sodium. The present work reveals the mechanism about how the Na enhances the photovoltaic performance through passivating the dangling bonds in the GBs of chalcogenide semiconductors, and sheds light on how to passivate dangling bonds in GBs with alterative processes. [ABSTRACT FROM AUTHOR]