On the effect of Knudsen-layer formation on studies of vaporization, sputtering, and desorption

Abstract

We are here concerned with experiments in which time-of-flight (TOF) measurements are made with particles which are vaporized, sputtered, or desorbed due to a pulsed heat source. If the emitted particle number density is low enough, the particles will disperse collisionlessly. Provided the emission is truly thermal, the velocities will then be described by a “half-range” Maxwellian, i.e. a Maxwellian with only positive velocities normal to the target, for which it is well known that the surface temperature, T s, and the energy, Ê, defined by the peak position of the TOF spectrum are related by kT s = E ̂ /2 . More commonly the emitted particle density is high enough that near-surface collisions occur. For as few as 3 collisions per particle a Knudsen layer forms, i.e. there is a layer within a few mean free paths of the target surface in which the distribution function evolves to a “full-range” Maxwellian in a center-of-mass coordinate system. We show that for on-axis measurements the relation kT s = E ̂ /2 is replaced by kT s = E ̂ /η K , with η K ranging from 2.52 for a monatomic species to 3.28 for a species with many accessible internal degrees of freedom. Failure to recognize the formation of a Knudsen layer thus leads to a severely overestimated value for T s, at least for an-axis measurements.