Quantum size effect of electron density in ultra-thin metal films and its influence on the interlayer relaxation

Further minimization of electronic devices and microelectromechanical systems (MEMS) requires the feature sizes of relevant materials to be shrunk significantly. In such a case, boundary effects, such as interfaces and surfaces, become remarkable, especially in nanometer scale, which must affect their microstructures and properties. In this work, we have analyzed the distribution of electron charge density in Cu and Al ultra-thin films using free electron model. The results show that an electrostatic field may come into being due to quantum size effect, and the interlayer separations must relax to decrease the Coulomb energy, the thinner the films, the larger the relaxation. More interestingly, two opposite deviating directions of the center of negative charges result in two absolutely distinct interlayer relaxations: inwards for Cu and outwards for Al.