Propagation of Structural Disorder in Epitaxially Connected Quantum Dot Solids from Atomic to Micron Scale

Epitaxially connected superlattices of self-assembled colloidal quantum dots present a promising route toward exquisite control of electronic structure through precise hierarchical structuring across multiple length scales. Here, we uncover propagation of disorder as an essential feature in these systems, which intimately connects order at the atomic, superlattice, and grain scales. Accessing theoretically predicted exotic electronic states and highly tunable minibands will therefore require detailed understanding of the subtle interplay between local and long-range structure. To that end, we developed analytical methods to quantitatively characterize the propagating disorder in terms of a real paracrystal model and directly observe the dramatic impact of angstrom scale translational disorder on structural correlations at hundreds of nanometers. Using this framework, we discover improved order accompanies increasing sample thickness and identify the substantial effect of small fractions of missing epitaxial bonds on statistical disorder. These results have significant experimental and theoretical implications for the elusive goals of long-range carrier delocalization and true miniband formation.