Measuring the practical particle-in-a-box: Orthorhombic perovskite nanocrystals

A connection between condensed matter physics and basic quantum mechanics is demonstrated as we use the fundamental 3D particle-in-a-box model to explain the optical properties of semiconductor nanocrystals, which are substantially modified due to quantum confinement. We also discuss recent advances in the imaging and measurement capabilities of transmission electron microscopy, which have made it possible to directly image single nanocrystals while simultaneously measuring their characteristic absorption energies. We introduce the basic theory of nanocrystals and derive a simplified expression to approximate the optical bandgap energy of an orthorhombic nanocrystal. CsPbBr₃ perovskite nanocrystals are used to demonstrate this model due to their cubic crystal structure, large absorption cross-section, and favourable dielectric properties, which make them ideal for exploring the applications of this simple classroom problem. Various orthorhombic shapes are explored, and the predicted values of the optical bandgap energies using the proposed model are shown to be in good agreement with the experimentally determined values.