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Constructing vertical heterostructures by placing graphene (Gr) on two-dimensional materials has recently emerged as an effective way to enhance the performance of nanoelectronic and optoelectronic devices. In this work, first principles calculations are employed to explore the structural and electronic properties of Gr/GeC and Gr/functionalized-GeC by H/F/Cl surface functionalization. Our results imply that the electronic properties of the Gr, GeC and all functionalized-GeC monolayers are well preserved in Gr/GeC and Gr/functionalized-GeC heterostructures, and the Gr/GeC heterostructure forms a p-type Schottky contact. Interestingly, we find that the p-type Schottky contact in Gr/GeC can be converted into the n-type one and into an n-type ohmic contact by H/F/Cl surface functionalization to form Gr/functionalized-GeC heterostructures. Furthermore, we find that electric fields and strain engineering can change …