Theory of Electronic Properties of Thin Films ofd-Band Metals

Abstract

We have examined the changes in the nature of the $d$-band states in crystals of fcc transition and noble metals as the crystals become very thin. The calculated effects can be categorized as size effects and as surface effects. The size effects are the changes from states having a semicontinuous variation of energy with varying wave vector parallel to the small dimension to states having discrete energy values. These effects result from the loss of translational and cubic symmetry, and exist even when the overlap integrals are the same within the surface planes as within the interior planes of the crystal. The effects found are qualitatively different for single-crystal fcc films with $〈100〉$ and $〈111〉$ normals, respectively. Surface effects are changes in the electronic structure associated with changes of overlap integrals within the surface planes. We show how such changes lead to the existence of $d$-band surface states for a $〈100〉$ film. For $〈111〉$ films, there is an even more striking qualitative effect involving surface states. This is the appearance of surface states for one area of the two-dimensional Brillouin zone even when the overlap integrals within the boundary planes are the same as those within the interior planes of the film. We illustrate all these effects by calculations for the ${\Gamma }_{12}$ bands (i.e., the bands corresponding to $E$-symmetry $d$ atomic states), using realistic parameters for Ni with crystals 5 and 11 atomic layers thick. Finally, we discuss the prospects for experimental work - in particular, investigations of the density of states and of various anisotropic effects associated with the departure from cubic symmetry on going to a very thin film.