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First-principles calculation is employed to investigate atomic and electronic properties of Ge/SiC heterojunction with different Ge orientations. Based on the density functional theory, the work of adhesion, relaxation energy, density of states, and total charge density are calculated. It is shown that Ge(110)/4H-SiC(0001) heterointerface possesses higher adhesion energy than that of Ge(111)/4H-SiC(0001) interface, and hence Ge/4H-SiC(0001) heterojunction with Ge[110] crystalline orientation exhibits more stable characteristics. The relaxation energy of Ge(110)/4H-SiC(0001) heterojunction interface is lower than that of Ge(111)/4H-SiC(0001) interface, indicating that Ge(110)/4H-SiC(0001) interface is easier to form at relative low temperature. The interfacial bonding is analysed using partial density of states and total charge density distribution, and the results show that the bonding is contributed by the Ge-Si bonding.