“…We consider the diffusion of a metal atom, which is originally located at the interface, into SiO 2 along the (001) direction and calculate adiabatic potentials for metal-atom diffusion as a function of the distance z of the metal atom from the interface, together with relaxing x-and ycoordinates of the diffusing atom and the positions of the other atoms. 15,17,18) To show the spatial distributions such as electron density, we also adopt this z-coordinate; namely, the interface is located at z = 0, the SiO 2 layers at z > 0, and the metal layers at z < 0. Electronic structures and diffusion potentials are calculated by the standard first-principles method in the density functional theory, using the Vienna ab initio simulation package (VASP) code, [19][20][21][22] where the Perdew-Burke-Ernzerhof exchange-correlation functional is employed in a generalized gradient approximation.…”