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High contact resistance keeps black phosphorus (BP) from fully wielding its excellent material property. Using first-principles calculations, we analyze the interfacial binding behavior and the impact of binding on the other layers of a trilayer BP. We found that the interfacial charge density and charge transfer of Scandium (Sc)-contacted trilayer BP are 2.67 and 3.29 times greater than Au-contacted trilayer BP, respectively. Moreover, the interfacial tunneling barrier height and width of Sc-contacted trilayer BP are 0 eV and 1.851 Å, which are significantly smaller than that of 5.1 eV and 2.447 Å observed in Au-contacted trilayer BP. All these facts suggest a strong bonding and efficient carrier transmission between Sc contact and trilayer BP substrate. Therefore, we conclude that the Sc electrode can lead to a superior performance that is consistent with the experiment.