Born–Mayer scattering model for KeV argon ions and fast neutrals in a charge-exchange atomic source for high-aspect-ratio etching

Neutral-beam and neutral-beam-assisted reactive etching circumvent the plasma-process-induced damage, which originates from surface charging and ultraviolet radiation. For high-aspect-ratio etching, a tightly collimated beam is needed to avoid sidewall distortion and subsurface modifications of the atomic structure; e.g., for an aspect ratio of 100, scattering must be kept small beyond a divergence angle of θtol ≈ 0.01 rad and set to 0.25° (lab frame) in this study. The directionality of the beam will depend on several design factors. In this work, we examine a gas-phase neutral beam source based on charge-exchange conversion of energetic ions, focusing on the fundamental constraints imposed by ion–atom and atom–atom scattering in the neutralization region. For argon ions and fast neutrals in the keV range, scattering at angles θ > θtol is dominated by the repulsive wall of the interaction potential, which is well described by a Born–Mayer form Ae−br. This yields a simple yet accurate model suitable for Monte Carlo simulations. In particular, a known method is used to compute the scattering angle, θ(p), where p is the impact parameter. The angle is given in terms of a modified Bessel function, whose argument is obtained by solving a nonlinear equation. The model can be trusted to predict the angular distribution for θ > θtol and thus determine the flux scattered into these angles. We provide model-based predictions for the angular distributions, compare these with a representative experimental dataset, and propose a lumped one-dimensional formulation to describe both small- and large-angle scattered ion and fast-atom fluxes. The flux of fast atoms scattered at small angles θ < θtol, normalized to the incident ion flux, attains its maximum when L/λcx ∼ 1, where L is the beam propagation length and λcx is the mean free path for charge exchange.