**Figure 1: GISAXS geometry**

The geometry of a GISAXS experiment is illustrated in Figure 1. A monochromatic x-ray beam with the wavevector k

In general, a 2-D detector records the scattered intensity at angles of a few degrees for the observation of lateral sizes ranging from a few up to hundreds of nanometers. The sample detector distance is normally in a range of 1 to 4 meters for GISAXS, and up to 13 meters for grazing incidence ultra small angle scattering (GIUSAXS) experiments whereas the detectable lateral size increases to several micrometers. Gas-filled wire frame detectors, CCD-detectors as well as imaging plates are in use. The direct and the reflected specular beam are often suppressed by two small beamstops to prevent damage or saturation of the detector.

The scattering intensity I(q) for a lateral electron density fluctuation on the surface can be described as

where F is the form factor and S(q) is the total interference function. The interference function describes the spatial arrangement of the objects on the surface and thus their lateral correlations. It is the Fourier transform of the island position autocorrelation function. In the simple Born approximation (BA), F is the Fourier transform of the shape function of the objects and is defined as

If reflection-refraction effects at the surface of the substrate have to be accounted for, F has to be calculated within the distorted wave Born approximation (DWBA) and has a more complex expression. Figure 2 illustrates the physical picture of the full calculation for the scattering cross section in the DWBA, which is given by

**Figure 2: The four scattering events in the DWBA**

The four terms involved are associated to different scattering events, which involve or not a reflection of either the incident beam or the final beam collected on the detector. These waves interfere coherently, giving rise to the effective form factor (F

In Figure 3 the scattering situation of a GISAXS experiment is shown. This situation is only valid for very small angles α

**Figure 3: Top and side-view of a GISAXS experiment**

Contents provided by Dr. A. Meyer - Institute of Physical Chemistry - University of Hamburg