Recombination in an expanding laser-produced tin plasma for EUV lithography

Modern-day lithography machines make use of an extreme ultraviolette (EUV)-emitting laserproduced plasma (LPP) generated from tin microdroplets. As this plasma expands, mitigation of
the ionic debris becomes key in preserving the lifetime of the EUV optics. Extensive characterization of the plasma expansion can aid in the design of effective mitigation schemes. Here, we
present results of a theoretical study on the role of recombination in expanding tin LPPs relevant
to EUV lithography. Knowledge on the rate of various recombination mechanisms is essential
in determining the ionization balance some distance away from the target. A time-dependent
collisional-radiative model is employed to study how three distinct recombination mechanisms
(three-body, dielectronic and radiative) affect charge state populations. By using comprehensive
atomic calculations of Badnell et. al. on the dielectronic rate coefficients, we demonstrate the
importance of the dielectronic mechanism in expansion for the first time. Moreover, we compute
estimates for the time (and distance) it takes for the charge states to freeze out for a range of initial
electron temperatures and densities. This can be coupled to radiation-hydrodynamic codes such
as RALEF-2D to quantify where the assumption of local thermal equilibrium (LTE) ionization
breaks down. The code serves as a flexible numerical tool to study the effects of recombination.