Mathematical modeling of vapor-plume focusing in electron-beam evaporation

A Monte Carlo model of titanium evaporating from a disk surface shows that collisions between evaporant atoms give rise to plume focusing from the ideal cosine distribution to a cos' distribution, as has been widely reported in experiments. Further, it is shown that under conditions in which hard-sphere models are accurate, the cosine power of the distribution (which indicates the extent of focusing) and the fraction of evaporant atoms which recondense at the source are both universal functions of an effective local Knudsen number for the source, which can be empirically fitted to a simple functional form. This function leads to the property that, for a given total evaporation rate, a smaller and more intense vapor source gives rise to more focusing than a broader source. Ring sources are also modeled, and, for a given ratio of ring thickness to outer radius, these also show a dependence of the cosine power and recondensation fraction on the local Knudsen number.