Metal gate electrodes: Theoretical studies of Zr/ZrO2 and Hf/HfO2 interfaces

Ab initio quantum mechanical calculations have been performed on cluster models of Zr/ZrO2 and Hf/HfO2 interfaces. The theoretical method is a first principles method in which an exact electrostatic Hamiltonian is employed, except for core electron effective potentials, and wavefunctions are constructed by a self-consistent-field (SCF) method in which ionic correlation is included by local configuration interaction (CI). The outcome of the calculations is a detailed prediction of the electronic structure of the interface from which electrical properties can be inferred; e.g., work function, surface dipoles, barriers to electron transport, etc.. The results are compared with and also serve to calibrate electronegativity arguments that lead to predictions of surface dipole changes when Zr or Hf metals are deposited on the respective elemental oxides. In the present work the cluster describing the Zr/ZrO2 interface was embedded in an electrostatic field that simulates more distant Madelung contributions, and removes unphysical solutions as well.