Abstract: The surface Green’s function (SGF) method provides an advanced solution for overcoming the intrinsic limitations of conventional slab models in first-principles quantum transport simulations. Traditional slab models suffer from finite-size effects, spurious coupling between two surfaces, and Fermi-level shifts, leading to slow convergence and distorted results in calculations of work functions, surface states, and electrochemical interfaces. The SGF approach partitions a semi-infinite system into a finite surface region and a semiinfinite bulk region, where the latter acts as an infinite electron reservoir coupled to the surface through a self-energy term, enabling self-consistent calculations under open boundary conditions. Implemented within density functional theory and linear combination of atomic orbitals (LCAO) basis sets, the method evaluates the Green’s function via complex contour integration and efficient recursive algorithms, achieving a computational cost that scales linearly with the number of atomic layers and a band convergence behavior far superior to that of slab models. This review systematically surveys the application of the SGF method in representative scenarios including metal work function calculations, band alignment of semiconductor
heterojunctions, accurate description of surface states, and modulation of surface chemistry under external electrostatic fields. The results demonstrate the combined advantages of SGF in accuracy, efficiency, and physical soundness, establishing it as a powerful tool for advanced quantum simulations of surfaces and interfaces.

Key words: surface Green’s function method, first-principles quantum transport simulation, surface electronic structure, semi-infinite systems