• The energy and the HM gaps were calculated as 0.57 and 0.12 eV. • The HM is preserved at the Sc1 and Ge-terminated (111) surfaces. • The adhesion energy shows that the Sc1-Sb shape is more stable than the others. Our study showed that full-Heusler Sc 2 CrGe displays half metallic ferromagnetism with an energy gap of 0.57 eV and a spin-flip gap of 0.12 eV in the majority spin channel at an optimization equilibrium lattice constant of 6.5 Å. In this study, we investigate extensively the electronic and magnetic features of the (111), (001), and (110) surfaces and the interface with the semiconductor InSb (111) via applying the first-principles computations of the density functional theory. The atomic density of states confirms that the half-metallicity discovered in the bulk Sc 2 CrGe is kept at the Sc(2)Ge-terminated (001), Sc(1)-, and Ge-terminated (111) surfaces, but it is lost at the Sc(2)- and Cr-terminated (111), Sc(1)Cr- terminated (001), and Sc 2 CrGe (110) surfaces. For the Sc 2 CrGe/InSb (111) interface, the bulk half-metallicity is destroyed at the Sc(1)-In, Sc(1)-Sb, and Ge-In configurations while the Ge-Sb configuration exhibits a full spin polarization. Moreover, the computed interfacial adhesion energy shows that the Sc(1)-Sb shape is more stable than the others. The calculated magnetic moments of interface atoms (Sc and Ge) decrease compared to the corresponding bulk values. [ABSTRACT FROM AUTHOR]