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The grazing incidence small-angle X-ray scattering (GISAXS) from structures within a thin film on a substrate is generally a superposition of the two scatterings generated by the two X-ray beams (reflected and transmitted beams) converging on the film with a difference of twice the incidence angle (α i) of the X-ray beam in their angular directions; these two scatterings may overlap or may be distinct, depending on α i. The two scatterings are further distorted by the effects of refraction. These reflection and refraction effects mean that GISAXS is complicated to analyze. To quantitatively analyze GISAXS patterns, in this study we derived a GISAXS formula under the distorted wave Born approximation. We applied this formula to the quantitative analysis of the GISAXS patterns obtained for various compositions of polystyrene-b-polyisoprene (PS-b-PI) diblock copolymer thin films on silicon substrates with native oxide layers. This analysis showed that the diblock copolymer thin films consist of hexagonally packed cylinder (HEX) structures, hexagonally perforated layer (HPL) structures, and gyroid structures, all with characteristic preferential orientations, depending on the composition of the copolymer. This is the first report of GISAXS studies of HEX, HPL, and gyroid microdomain structures in block copolymer thin films. Moreover, our study also provides a simple method for understanding GISAXS patterns and for determining the structure factor or interference function from them. Thus, the use of the GISAXS technique with our derived GISAXS formula as a data analysis engine is a very powerful tool for determining the morphologies of polymer thin films on substrates.

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