GISAXS – theory, experimental realization and some results

V. Holý

Department of Condensed Matter Physics, Faculty of Mathematics and Physics, Charles University in Prague, Ke Karlovu 5, 121 16 Praha, Czech Republic

holy@mag.mff.cuni.cz

In the last decades, various types of nanostructures have been intensively studied by physical, chemical and biological methods. Since the properties of nanostructures are substantially influenced by their structure, structural research of nanostructures is extremely important for the understanding of their performance. Under the structure of the nanoobjects we understand not only the atomic arrangement (the crystal structure in the case of crystalline objects), but more importantly the shapes, sizes and arrangement of individual nano-objects. Methods based on scattering (x-ray-, electron- or neutron scattering) consist in mapping of a part of reciprocal space, the size of which depends on the size of the nanoobjects. Small-angle x-ray scattering (SAXS) usually probes the reciprocal space up to distances of few reciprocal nm, i.e. the method can study particles of sizes from several nm up to approx. one micrometer. For nanoobjects dispersed on a surface or in a thin layer or multilayer, small-angle scattering method is usually performed in grazing incidence geometry (grazing-incidence small-angle x-ray scattering – GISAXS), in which specular scattering from the surface or from the interfaces in the host layer system plays important role.

The theoretical part of the talk will summarize the basic theoretical approaches describing the scattering process (kinematical approximation, distorted-wave Born approximation – DWBA), as well as several theoretical approaches describing self-organized systems on nanoparticles. Several software packages of GISAXS simulations available mostly free of charge will be introduced as well. The theory of GISAXS can be found in Refs. [1,2].

In the second part of the talk the attention will be paid to several experimental realizations of a GISAXS measurement, including laboratory and synchrotron set-ups. The third part of the talk will focus to several experimental examples including mainly semiconductor quantum dots in epitaxial layered systems (Ge/Si, InAs/GaAs, PbSe/PbEuTe) and semiconductor and metallic nanocrystals in amorphous matrix (Ge/SiO₂, Ge/Al₂O₃, Co/SiO₂, among others).

[1] U., Pietsch, V. Holý and T. Baumbach T., High-Resolution X-Ray Scattering From Thin Films to Lateral Nanostructures, Advanced Texts in Physics, Springer-Verlag Berlin, Heidelberg, New York 2004.

[2] G. Renaud, R. Lazzari and F. Leroy, Surface Science Reports 64, 255-380 (2009).