Detailed analysis of gyroid structures in diblock copolymer thin films with synchrotron grazing-incidence X-ray scattering

A grazing-incidence X-ray scattering (GIXS) formula is derived for gyroid structures in substrate-supported thin films. Two-dimensional GIXS measurements were carried out for gyroid structures developed in polystyrene-b-polyisoprene diblock copolymer thin films supported on silicon substrates, and a quantitative analysis of the two-dimensional GIXS data was demonstrated successfully by using the scattering formula.