Many-Body Effects And The Metal–Insulator Transition At Semiconductor Surfaces And Interfaces

The aim of this paper is to present a general perspective of the different correlation effects appearing at semiconductor surfaces and interfaces. The unifying theoretical picture is the generalized Hubbard Hamiltonian. In a first step, we show how such Hamiltonians can be analyzed using both a local density approach and many-body techniques. This discussion shows how to determine the different electron–electron interaction parameters appearing in the generalized Hubbard Hamiltonian, from a set of restricted LDA calculations for the full surface. Then, different surfaces and interfaces are analyzed; in particular, we consider the Si(111)-(7 × 7), -(5 × 5)and -(3 × 3)reconstructions as well as the Si-rich SiC(111)-$(\sqrt{3}\times\sqrt{3})$and -(3 × 3)surfaces. These Si-rich SiC(111) surfaces are shown to behave like a Mott–Hubbard insulator, while the Si(111) reconstructions are charge transfer systems presenting a variety of different behaviors; thus, the Si(111)-(7 × 7)is metallic, while the -(5 × 5)and the -(3 × 3)are found to be insulating. We have also analyzed the Sn/Ge(111)-(3 × 3)reconstruction, the alkali metal/GaAs(110) junction and the K/Si(111)-$(\sqrt{3}\times\sqrt{3})$-B interface. Our discussion shows that the alkali metal/GaAs and K/Si(111) interfaces present also a Mott–Hubbard metal–insulator transition, and that the Sn/Ge(111)-(3 × 3)interface is still metallic in spite of nonnegligible many-body effects appearing in the surface band density of states. We conclude that two-dimensional systems at semiconductor surfaces and interfaces present a rich variety of many-body effects that modify substantially the one-electron picture one gets from LDA calculations.