Three-dimensional Schwoebel-Ehrlich barrier

It is well known that the Schwoebel-Ehrlich barrier affects, and even dictates, surface microstructure evolution - such as the transition of growth modes from layer-by-layer to island growth. The conventional Schwoebel-Ehrlich barrier refers to the case when an adatom diffuses down an island of one monolayer. During thin film deposition. an adatom often needs to diffuse down an island of multiple layers. For the latter, we demonstrate and calculate the cot-responding Schwoebel-Ehrlich barrier - which we call three-dimensional Schwoebel-Ehrlich barrier. Our calculations show that the three-dimensional Schwoebel-Ehrlich barrier can be large even if its conventional Counterpart is small - as in aluminum. We further propose and demonstrate a possible process of engineering surface faceting and film texture, by modifying the three-dimensional Schwoebel-Ehrlich barrier.