Single-parameter expression for ions reflection from surfaces

Abstract

Based on a detailed analysis of the Boltzmann equation for ion transport in solids, it has been shown that for low-energy ions incident on a heavy element target the distribution function of the ions can be determined by one single parameter, called the scaled transport cross-section, which was defined earlier [1]. This means that the transport quantities of different ion-target-energy combinations should be similar only when their scaled transport cross-section is the same. To test this significant conclusion, we undertook a set of systematic and extensive calculations of reflection coefficients using the improved bipartition model of ion transport. The systematic calculations include 3410 ion-target-energy combinations, namely H, D, T, He, Li, B, C, N, O, Ne ions with energy ranges from 10 eV to 1 MeV normally incident to C, Al, Cu, Mo, Ag, W, Au, Pb, U targets. The only restrictions isM ₁/M ₂<1/6. The calculations verify that particle and energy reflection coefficients present an excellent one-to-one correspondence to the scaled transport cross-section. Furthermore, based on the calculations, universal expressions for both particle reflection coefficients and energy reflection coefficients for normal ion incidence have been obtained by fitting the numerical data. By comparing the results calculated by the universal expressions with experimental and Monte Carlo data, it is shown that the expression can describe reflection coefficients well.