Exciton Fine Structure in Axially Symmetric Quantum Dots and Rods of III-V and II-VI Semiconductors

Both absorption and emission of light in semiconductor quantum dots occur through excitation or recombination of confined electron-hole pairs, or excitons, with tunable size-dependent resonant frequencies that are ideal for applications in various fields. Some of these applications require control over quantum dot shape uniformity, while for others, control over energy splittings among exciton states emitting light in different polarizations and/or between bright and dark exciton states is of key importance. These splittings, known as exciton fine structure, are very sensitive to the nanocrystal shape. Theoretically, nanocrystals of spheroidal shape are often considered, and their nonsphericity is treated perturbatively as stemming from a linear uniaxial deformation of a sphere. Here, we compare this treatment with a nonperturbative model of a cylindrical box, free of any restrictions on the cylinder's aspect ratio. This comparison allows one to understand the limits of validity of the traditional perturbative model and offers insights into the relative importance of various mechanisms controlling the exciton fine structure. These insights are relevant to both colloidal nanocrystals and epitaxial quantum dots of III-V and II-VI semiconductors.