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

Unlike 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 arrangements have a stronger potential for better performance, while the stochastic structure deteriorates performance by dissipating energy flow through irregularity. People have therefore put much effort into characterizing structural regularity and stochasticity for better establishment of structure-functionality correlations. Conventionally, multiple advanced techniques are used collectively to explore structural details, such as electron microscopy for morphology, X-ray diffraction for crystallinity, and X-ray scattering for domain structures. With fortunate 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 theory, structures are formed by competing long-range and short-range interactions; thus, features across a wide range of scales are correlated. There is a hidden link between structures across different scales, which can be quantified by exploring the overlaps between different renormalization group layers. This type of quantification is embodied in the concept of complexity. Its value corresponds to the extent to which a given structure differs from itself across varying length scales. With it, we successfully quantify the structural complexity of nanocrystals hierarchically, and it 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. Namely, higher complexity corresponds to deteriorated device performance.