Orientational Disorder in Epitaxially Connected Quantum Dot Solids

Periodic arrays of strongly coupled colloidal quantum dots (QDs) may enable unprecedented control of electronic band structure through manipulation of QD size, shape, composition, spacing, and assembly geometry. This includes the possibilities of precisely engineered bandgaps and charge carrier mobilities, as well as remarkable behaviors such as metal-insulator transitions, massless carriers, and topological states. However, experimental realization of these theoretically predicted electronic structures is presently limited by structural disorder. Here, we use aberration-corrected scanning transmission electron microscopy to precisely quantify the orientational disorder of epitaxially connected QD films. In spite of coherent atomic connectivity between nearest neighbor QDs, we find misalignment persists with a standard deviation of 1.9 degrees, resulting in significant bending strain localized to the adjoining necks. We observe and quantify a range of out-of-plane particle orientations over thousands of QDs and correlate the in-plane and out-of-plane misalignments, finding QDs misoriented out-of-plane display a statistically greater misalignment with respect to their in-plane neighbors as well. Using the bond orientational order metric psi(4), we characterize the 4-fold symmetry and introduce a quantification of the local superlattice (SL) orientation. This enables direct comparison between local orientational order in the SL and atomic lattice (AL). We find significantly larger variations in the SL orientation and a statistically robust but locally highly variable correlation between the orientations of the two differently scaled lattices. Distinct AL and SL behaviors are observed about a grain boundary, with a sharp boundary in the AL orientations, but a more smooth transition in the SL, facilitated by lattice deformation between the neighboring grains. Coupling between the AL and SL is a fundamental driver of film growth, and these results suggest nontrivial underlying mechanics, implying that simplified models of epitaxial attachment may be insufficient to understand QD growth and disorder when oriented attachment and superlattice growth occur in concert.