Fermi-Level Pinning at Metal/High-$k$ Interface Influenced by Electron State Density of Metal Gate

The Fermi-level pinning (FLP) at the metal/high-k interface and its dependence on the electron state density of the metal gate are investigated. It is found that the FLP is largely determined by the distortion of the vacuum level of the metal which is quantitatively ruled by the electron state density of the metal. The physical origin of the vacuum level distortion of the metal is attributed to an image charge of the interface charge in the metal. Such results indicate that the effective work function of the metal/high-k stack is also governed by the electron state density of the metal.