Fig. 2: Scattering intensity distribution simulated based on conventional distorted-wave Born approximation (DWBA).

a Schematic of conventional DWBA scattering wave vector transfers in the reflection geometry (not to scale) with a layered approach developed for evaluating grazing-incidence small-angle scattering (GISAXS) using incoherent X-rays. In the DWBA scheme, the electron density in a layer is averaged in the x-y plane over the X-ray footprint, as highlighted in the shaded areas of the schematic. b Schematic of the four momentum-transfer terms in the DWBA theory, which constitute the components described in Eqs. (S14–S17) in an arbitrary single layer, e.g., the top layer in the schematic. The shading colors represent the lateral electron density profile in the layer. The red arrows highlight the exit wave vector in each scattering path. c Surface scattering intensity, when all four terms are included in the simulation surface scattering intensity, fails to reproduce the experimental data when αf is between 0° and 0.3°.