Evaluation of ordering in single-component and binary nanocrystal superlattices by analysis of their autocorrelation functions.

Self-assembly of colloidal nanocrystals and other nanosized building blocks has led to numerous large-scale and well-ordered superstructures. To quantify the superlattice quality we present a simple and efficient method, based on analysis of the autocorrelation function to determine characteristic order parameters for short-range and long-range ordering. This provides a feedback for further improvements of deposition techniques and self-assembly processes. To show the power of this method, it is applied to various two-dimensional ordered single component and binary nanocrystal assemblies. A quantitative comparison of the normalized long-range order parameter for various colloidal or epitaxially grown superlattice structures evidences that the long-range ordering in monodisperse colloidal superlattices by far supersedes that obtained at best by epitaxially grown quantum dots. Astonishingly, for selected binary nanocrystal superlattices the long-range ordering parameter reaches almost the same values as for single component superlattices. Besides the high sensitivity of the introduced quantification method to lattice imperfections our analysis also reveals any anisotropy in the ordering of the superlattices, which again can be quantified, for example, to identify the areas of highest quality within one specific sample.