A spatial distribution study of a beam vapour emitted by electron-beam-heated evaporation sources

This work reports a study of the spatial distribution of atoms evaporated under vacuum and its influence on the thickness distribution of metallic films achieved by this technique. Its goal is to justify the (cos theta)(n) law which has been introduced in an empirical way to explain the thickness distribution obtained when the evaporation rates are high. Taking into account a collision region just above the vapour source, it is possible to determine a new distribution of vapour atom velocities which is no longer a Maxwell form. The spatial distribution of the vapour beam was deduced and then it was fitted experimentally. The comparison between this new distribution function and that deduced from the (cos theta)(n) law leads to a relation able to determine the constant n. This relation shows that the constant n tends to a limiting value when the evaporation rate increases, whatever the metal evaporated. These results were verified when the thickness distribution models were compared with these obtained experimentally for three different metals (Ti, Cu and Al).