On the dual role of the Knudsen layer and unsteady, adiabatic expansion in pulse sputtering phenomena

Abstract

When a surface is bombarded with pulses as from a laser and the number of monolayers sputtered per pulse is sufficiently small, the emitted particles fly freely from the target surface. For yields comparable to 0.5 monolayer in 10 ns, a limited number of gas-phase interactions is known to occur, leading to a Knudsen layer. As a result the particles develop moderate forward peaking (∼cos4 θ) and begin to flow (Mach number, M≊1). It is common, however, for yields to exceed 0.5 monolayer in 10 ns. We show that the resulting gas-phase interactions cause the Knudsen layer to evolve into an unsteady, adiabatic expansion which is formally like a gun which fires a finite charge into an infinite, one-dimensional barrel. An explicit solution can be obtained which has the form a=f1(x/t) and u=f2(x/t), where a is the speed of sound and u is the flow velocity. The solution is assumed to be valid up to a distance where the gas density ρ falls to the critical value ρc where free flight sets in. The particles are then characterized by extents of forward peaking much stronger than ∼cos4 θ (e.g., ∼cos25 θ in work by Namiki et al.) and correspondingly high M (cos25 θ is equivalent to an M near 4). In describing these effects, M and γ (the heat-capacity ratio) take the role of the basic parameters, the knowledge of which is essential for understanding what is happening.