Utilization of Complexity to Quantify the Regularity and Stochasticity of Nanocrystal Structure

Different than conventional materials which express functionalities by chemical compositions, nanocrystals generate and manipulate their functionalities by hierarchical structures. Considering optoelectronics, it is believed that materials with more regular structural arrangement have stronger potential for better performance, while stochastic structure deteriorates performance by dissipating energy flow through irregularity. People thereafter put strong endeavors into characterizing structural regularity and stochasticity for better establishment of structure-functionality correlations. Conventionally, multiple advanced techniques are used collectively to explore structural details - electron microscopy for morphology, X-ray diffraction for crystallinity and X-ray scattering for domain structures. With cheerful achievement of rich structural information, we, as physicists, ask whether a single and simple parameter can be provided to quantify the structural regularity and stochasticity? Based on renormalization group (RG) theory, structures are formed by competing long-range and short-range interactions and features in wide range of scales are correlated. There exists a hidden link between structures across different scales, which can be quantified by exploring the overlaps between different RG layers. This type of quantification is embodied into the concept of complexity, of which the value corresponds to the extent of how a given structure differs from itself across varying length scales. Using it, we successfully quantify structural complexity of nanocrystals hierarchically and corresponds positively to the regularity and stochasticity characterized by other methods. And the trend of complexity obtained by the novel method correlates well with device performance positively. Namely, stronger stochasticity and lesser regularity identified by higher complexity corresponds to deteriorated device performance.