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The ordering of quantum dots in three-dimensional quantum dot lattices is investigated by grazing-incidence small-angle X-ray scattering (GISAXS). Theoretical models describing GISAXS intensity distributions for three general classes of lattices of quantum dots are proposed. The classes differ in the type of disorder of the positions of the quantum dots. The models enable full structure determination, including lattice type, lattice parameters, the type and degree of disorder in the quantum dot positions and the distributions of the quantum dot sizes. Applications of the developed models are demonstrated using experimentally measured data from several types of quantum dot lattices formed by a self-assembly process.

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